Seminars: Spring 2013

Speaker: Rene Meyer
Department: IPMU, Tokyo
Slides: [PDF]
Time: Tuesday 5 February 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: After a general introduction into modular invariance in the fractional quantum Hall effect I will present recent progress on a holographic model which implements SL(2,Z) symmetry and has ground states similar to fractional quantum Hall plateaux states. The main improvement over previous work, which I am going to review, is that the quantum Hall plateaux states do have a gap for the charged excitations.

The quest for the Higgs boson and the LHC (department colloquium)

Speaker: Paraskevas Sphicas
Department: CERN and Athens U.
Time: Thursday 7 February 2013 at 17:15
Venue: The 3rd floor seminar room of the physics department
Abstract: In the past 20 years, the Standard Model of elementary particles and their interactions has provided a remarkably accurate description of all experiments with and without high-energy accelerators, establishing that we understand the “physics of the very small” up to energy scales of 100 GeV. The Large Hadron Collider of CERN was conceived to probe the physics of the next frontier, that of the TeV energy scale, providing a definitive statement on whether the infamous Higgs boson exists, but also looking for “new physics”. In July 2012, the two general-purpose experiments announced the observation of a new massive boson, consistent with the very Higgs boson of the Standard Model, possibly signaling the end of a forty-year hunt. The talk will present a broad-brush picture of the why, the what and the how this search has been carried out, along with the latest results since the first announcement. We will conclude with the implications of the new findings on possible physics “beyond the SM”, along with a short summary of the status of some key searches for new physics.

Taming waves in theory and experiment (department colloquium)

Speaker: Stefan Rotter
Department: University of Crete
Time: Friday 21 February 2013 at 17:00
Venue: The 3rd floor seminar room of the physics department
Abstract: I will speak about recent advances in shaping and controlling waves in cavities and random media [1]. In particular, I will show how the experimentally accessible information stored in a system's scattering matrix can be used to create highly collimated wave beams which traverse this system without being diffracted [2,3]. The key tool to realize such particle-like scattering states is the so-called time-delay operator which can be implemented with electromagnetic as well as with acoustic waves. In the second part of my talk I will explain how a suitably designed disorder can be used to control the coherent transmission through waveguides [4] as well as the emission properties of a so-called random laser [5]. [1] Mosk, Lagendijk, Lerosey, Fink, Nature Phot. 6, 283, (2012). [2] Rotter, Ambichl, Libisch, PRL 106, 120602 (2011) . [3] Appell, Phys. Rev. Focus 27, 13 (2011). [4] Dietz et al., PRB 86, 201106(R) (2012) [5] Hisch et al. (in preparation)

Spontaneous symmetry breaking and the Englert-Brout-Higgs mechanism (department colloquium)

Speaker: Jean Iliopoulos
Department: École Normale Supérieure
Time: Thursday 28 February 2013 at 17:15
Venue: The 3rd floor seminar room of the physics department
Abstract: We review the phenomenon of spontaneous symmetry breaking in Classical and Quantum Physics. It is associated with the appearance of massless excitations in the spectrum of states, known as "Goldstone modes". In Relativistic Quantum Physics in the presence of long- range gauge interactions, the phenomenon takes an unexpected new form, the Englert-BroutHiggs mechanism. We believe that it describes the origin of mass generation in the early Universe. The recent discovery of a new particle at the CERN Large Hadron Collider opens the way for an experimental study of this phenomenon.

Black Holes as Gravity Laboratories

Speaker: Thomas Sotiriou
Department: SISSA
Time: Tuesday 12 March 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: Black holes are natural laboratories for the gravitational interaction and for fundamental physics in general. I will try to provide support for this claim by discussing specific examples of black holes endowed with scalar fields and black holes in Lorentz-violating theories.

Aspects of string phenomenology in the LHC era

Speaker: Ignatios Antoniadis
Department: CERN
Slides: [PDF]
Time: Tuesday 26 March 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department

The Non-Gaussian Sky

Speaker: Alex Kehagias
Department: National Technical University of Athens
Slides: [PDF]
Time: Thursday 28 March 2013 at 15:15
Venue: The 2nd floor seminar room of the physics department
Abstract: I will discuss multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special con- formally invariant. I will describe how standard field-theoretic techniques, like operator product expansion may determine the spectrum and bispectrum and specify the trispectrum in the squeezed and collapsed limit.

New transport properties of holographic superfluids

Speaker: Daniel Fernandez
Department: University of Barcelona
Slides: [PDF]
Time: Monday 1 April 2013 at 14:00
Venue: The 3rd floor seminar room of the physics department
Abstract: In the context of holography applied to condensed matter theory, I will present an analysis of transport properties of p-wave superfluids by means of a gravity dual. Fluctuation modes in the SU(2) Einstein-Yang-Mills theory are considered, and phenomenological implications are derived. Due to the spatial anisotropy of the system, a non-universal shear viscosity is obtained, along with a new coefficient associated to normal stress differences. I will also discuss how the transport phenomena in this model is related to the thermoelectric, flexoelectric and piezoelectric effects (mixing of electric current, heat flux and mechanical stress).


T-duality, closed strings and Wilson loops

Speaker: Arkady Tseytlin
Department: Imperial College
Slides: [PDF]
Time: Tuesday 2 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: We will demonstrate that small closed string in the bulk of AdS space are related by T-duality periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincare patch. This suggests that closed string amplitudes with one of the closed strings falling into the Poincare horizon may be dual to gauge theory correlators involving local operators and a Wilson loop of the "T-dual" theory.

Observables in Strongly Coupled Anisotropic Theories

Speaker: Dimitrios Giataganas
Department: Witwatersrand University
Time: Wednesday 3 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: We review certain anisotropic gauge/gravity dualities, focusing more on a theory with space dependent axion terms. Then we discuss and also present some new results for several observables: the static potential and force, the imaginary part of the static potential, the quark dipole in the plasma wind, the drag force and diffusion time, the jet quenching of heavy and light quarks, the energy loss of rotating quarks, the photon production and finally the violation of the holographic viscosity over entropy bound. The corresponding weakly coupled results are also discussed. Finally we investigate the bounds of the parameters of the current anisotropic theories attempting to match them with the observed quark-gluon plasma and report the problems appear.

New Perspectives on Yang-Mills-Chern-Simons theory

Speaker: Måns Henningson
Department: Chalmers University of Technology, Göteborg
Slides: [KEY]
Time: Thursday 4 April 2013 at 14:00
Venue: The 3rd floor seminar room of the physics department
Abstract: Three-dimensional Yang-Mills theory with a Chern-Simons term is an interesting toy model for quantum field theory. It has a mass-gap that is visible already in perturbation theory. We investigate a supersymmetric version of the theory on a spatial two-torus. A basic quantity to compute is the supersymmetric index, i.e. the number of zero-energy ground states. A generalization is to consider states with an energy that remains finite also in the limit of a small torus. Non-simply connected gauge groups give rise to interesting topological complications.

Supergravity helps Condensed Matter Physics. A first example: Holographic Superconductors.

Speaker: Francesco Aprile
Department: Barcelona University
Slides: [PDF]
Time: Tuesday 9 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: In the context of the AdS/CFT correspondence I will consider models of (s-wave) holographic superconductors. In the simplest cases, these models contain gravity, a gauge field and a complex scalar. Then, the scalar is related to the condensate in the superconducting phase of the dual field theory. There are several reasons to go beyond this phenomenological formulation, first the need of a precise dictionary for the microscopic dual field theory. Strings embeddings have shown that the dynamics of holographic superconductors is quite universal, the only exception being the retrograde condensate. In this framework, I will describe the bosonic sector of N=2 sugra coupled to one hypermultiplet. The phase diagram of the model is surprisingly rich. The potential has a topological flat direction whose modulus label the superconducting solutions. The modulus turns out to be the coupling of a marginal deformation in the dual field theory. The IR of the bulk solutions is sensible to the strength of this deformation and the resulting geometry is nicely understood in terms of the entanglement entropy.

Defects, Super-Poincaré line bundle and Fermionic T-duality

Speaker: Eliezer Rabinovici
Department: Hebrew University
Time: Wednesday 10 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: Topological defects are interfaces joining two conformal field theories, for which the energy momentum tensor is continuous across the interface. A class of the topological defects is provided by the interfaces separating two bulk systems each described by its own Lagrangian, where the two descriptions are related by a discrete symmetry.
In this paper we elaborate on the cases in which the discrete symmetry is a bosonic or a fermionic T- duality. We review how the equations of motion imposed by the defect encode the general bosonic T- duality transformations for toroidal compactifications. We generalize this analysis in some detail to the case of topological defects allowed in coset CFTs, in particular to those cosets where the gauged group is either an axial or vector U(1). This is discussed in both the operator and Lagrangian approaches. We proceed to construct a defect encoding a fermionic T-duality. We show that the fermionic T-duality is implemented by the Super-Poincaré line bundle. The observation that the exponent of the gauge invariant flux on a defect is a kernel of the Fourier-Mukai transform of the Ramond-Ramond fields, is generalized to a fermionic T-duality. This is done via a fiberwise integration on supermanifolds.

Metal-Insulator transition in holography

Speaker: Aristomenis Donos
Department: Imperial College
Slides: [PDF]
Time: Thursday 11 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department

Black hole complementarity without firewalls

Speaker: Larus Thorlacius
Department: Nordita, Stockholm, and the University of Iceland
Time: Tuesday 16 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: Hawking's information paradox arises when one considers the formation and subsequent evaporation of a black hole. In a gravity theory with a gauge theory dual, the paradox must be resolved in favor of unitary evolution and the challenge is then to implement unitarity on the gravity side. A key issue, at the center of the recent debate on firewalls, is whether this requires giving up the equivalence principle or locality in spacetime.

Entanglement Entropy in the presence of defects via holography

Speaker: Efstratios Tsatis
Department: Patras University
Time: Thursday 18 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: I will discuss the issue of generalizing the holographic computation of the Entanglement Entropy (due to Takayanagi et al.) in the case where the dual field theory has defects.

Spectral Lines at the GeV scale; a signal of Dark Matter Annihilation?

Speaker: Ilias Cholis
Department: Fermilab
Slides: [PDF]
Time: Tuesday 23 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: Recently a series of indications have been put forward suggesting the presence of two gamma-ray lines at ~110-130 GeV Signals of these lines have been observed towards the Galactic center, at some galaxy clusters and among some of the unassociated point sources of the 2 years Fermi catalogue. Such a combination of signals could possibly be explained by dark matter annihilations in the main galactic dark matter halo, in its substructures and in near by galaxy clusters. Cosmological simulations that include baryons, have suggested the presence of a disk-like dark matter (dark disk) which if dominant would impact the smaller DM structures. By studying the full gamma-ray sky one can test the DM hypothesis and its sensitivity to galactic and extragalactic -non-DM originated- background assumptions; as well as the consistency between the number of gamma-ray events observed at the lines energies and the predictions of cosmological simulations such as via Lactea II and extrapolations of its mass-function. I will also discuss the possible implications of a dark disk on the distribution of the 110 and 130 GeV photons on the sky. that are neither observed towards the galactic center, the unassociated points sources or the galaxy clusters. Finally I will present new data from searches for gamma-ray lines at energies ~3-10 GeV related to annihilations of light WIMPs in the galactic center.

A more comprehensive AdS/QCD

Speaker: Sophia Domokos
Department: Weizmann Institute
Slides: [PDF]
Time: Thursday 25 April 2013 at 14:15
Venue: The 3rd floor seminar room of the physics department
Abstract: I will discuss an extension of standard AdS/QCD to encompass all QCD dimension 3 operators. When these are included, we successfully reproduce all (relevant) meson resonances up to about 1300 MeV, and produce expected chiral symmetry breaking patterns. I will present results for the full meson spectrum and some coupling constants in this model from a new, more comprehensive fit to the QCD data.

The Effective Theory of Long Strings

Speaker: Zohar Komargodski
Department: Weizmann Institute
Time: Friday 26 April 2013 at 9:00
Venue: The 3rd floor seminar room of the physics department
Abstract: We present the low-energy effective theory on long strings in quantum field theory, including a streamlined review of previous literature on the subject. Such long strings can appear in the form of solitonic strings, as in the 4d Abelian Higgs model, or in the form of confining strings, as in Yang-Mills theories. The bottom line is that upon expanding in powers of 1/L the energy levels of long (closed) strings (where L is the length of the string), all the terms up to (and including) order 1/L^5 are universal. We argue that for excited strings in D>3 space-time dimensions there is a universal deviation at order 1/L^5 from the naive formula that is usually used to fit lattice results. For D=3 this naive formula is valid even at order 1/L^5. At order 1/L^7 non-universal terms generically appear in all cases. We explain the physical origin of these results, and illuminate them in three different formulations of the effective action of long strings (the relationships among which we partly clarify). In addition, we corroborate these results by an explicit computation of the effective action on long strings in confining theories which have a gravitational dual. These predictions can be tested by precise simulations of 4d Yang-Mills theory on the lattice.

Novel applications of Derrick-like theorems

Speaker: Jacob Sonnenschein
Department: University of Tel Aviv
Time: Friday 26 April 2013 at 14:00
Venue: The 3rd floor seminar room of the physics department
Abstract: We derive a set of constraints on soliton solutions using geometric deformations, and transformations by internal symmetries with space-dependent parameters. We show that Derrick's theorem and a more complete set of constraints due to Manton are special cases of these deformation constraints (DC). We demonstrate also that known soliton solutions obey the DC, and extract novel results by applying the constraints to systems of D-branes, taking into account both Dirac-Born-Infeld and Wess-Zumino actions, and examining cases with and without D-brane gauge fields. We also determine a relation with the Hamiltonian constraint for gravitational systems, and discuss configurations of finite extent, like Wilson lines.

Non abelian T-duality in Type II supergravity

Speaker: Daniel Thompson
Department: Vrije Universiteit Brussel
Slides: [PDF]
Time: Tuesday 14 May 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: I shall review some recent progress concerning the use of a non-abelian generalisation of T-duality as a solution generating technique in supergravity, focussing on backgrounds with well understood field theory duals. For $AdS_5\times S^5$ this results in a background related to those introduced by Gaiotto and Maldacena as duals to certain N=2 gauge theories obtained by wrapping M5 branes on Riemann surfaces. For the Klebanov-Witten case, this results in a solution of the type recently proposed as N=1 cousins of these. In non-conformal cases we obtain new smooth duals in massive IIA supergravity. To initiate the field theory interpretation of these geometries I shall show how some quantities, namely central charge and entanglement entropy, are left invariant and how these backgrounds indicate signs of Seiberg duality, domain walls and confinement in the IR.

Time permitting I shall present brand new results that explain how to interpret these solutions using the language of G-structures, give flavour to the above geometries and detail a new class of supersymmetric solutions obtained as the dual of Y^{p,q} spaces.

AdS/Ricci-flat correspondence

Speaker: Blaise Goutéraux
Department: Nordita, Stockholm
Slides: [PDF]
Time: Wednesday 15 May 2013 at 15:15
Venue: The 2nd floor seminar room of the physics department
Abstract: We show that for every asymptotically AdS solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress-energy tensor of AdS to the stress-energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. The stress-energy tensor on the flat side is finite, but fails to be captured by the Brown-York procedure or previously proposed counterterms for reasons we will elaborate upon. Applying it to the known solutions describing the hydrodynamic regime in AdS/CFT, we derive the hydrodynamic stress-tensor of asymptotically flat black branes to second order, which is constrained by the parent conformal symmetry. We compute the dispersion relation of the Gregory-Laflamme unstable modes through cubic order in the wavenumber, finding remarkable agreement with numerical data.

New Skins for an Old Ceremony (The Conformal Bootstrap and the Ising Model)

Speaker: Sheer El-Showk
Department: Saclay
Slides: [PDF]
Time: Thursday 16 May 2013 at 15:15
Venue: The 2nd floor seminar room of the physics department
Abstract: The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and OPE coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the Extremal Functional Method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the 2d Ising model based solely on the dimension of a single scalar quasi-primary – no Virasoro algebra required. Our work serves as a benchmark for applications to more interesting, less known CFTs (such as the 3d Ising model) in the near future.

Quantum computation using topological states of matter (department colloquium)

Speaker: Ady Stern
Department: Weizmann Institute
Time: Thursday 16 May 2013 at 17:15
Venue: The 3rd floor seminar room of the physics department
Abstract: In this talk I will introduce the fascinating world of topological states of matter and the ways by which they may be exploited to carry out topological quantum computation. I will describe the building blocks for such computation, called non-abelian anyons. I will explain what are the physical systems in which they will be formed, how they can be detected and manipulated, and the means by which we may engineer them. Most importantly, my talk will NOT assume any prior knowledge of these scary-looking terms.

QCD matter created at LHC

Speaker: Barbara Erazmus
Department: CERN and SUBATECH, Nantes
Slides: [PPT]
Time: Tuesday 28 May 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: Heavy ion collisions at high energy allow to study extreme states of nuclear matter.

The results obtained with the ALICE experiment in lead-lead and proton-lead collisions at the Large Hadron Collider at CERN will be presented. Properties of the hot and dense medium created in lead-lead collisions can be deduced from measured multiplicity distributions, spectra and yields of the emitted particles. The observed collective phenomena are well described by hydrodynamic approaches. Hard probes available at the LHC open new possibilities for precise measurements of the properties of the QCD matter.

f(T) Gravity and Cosmology

Speaker: Emmanuel Saridakis
Department: National Technical University of Athens and Baylor University
Slides: [PDF]
Time: Thursday 30 May 2013 at 15:15
Venue: The 2nd floor seminar room of the physics department
Abstract: Torsion has been proved to be crucial in gauging gravity, which is in turn a necessary step towards its quantization. On the other hand, almost all the efforts in modifying gravity has been performed in the usual curvature-based framework. We investigate the case where one modifies gravity based on its simplest torsional-teleparallel formulation, namely the f(T) gravity paradigm, and its cosmological applications. In particular, we analyze the perturbations of the theory examining the growth history, we construct a cosmological bounce, and we use solar system observations in order to impose constraints on the f(T) forms. Additionally, we study the case where T is nonminimally coupled to a scalar field, that is the scenario of “teleparallel dark energy”. Finally we analyze the charged black hole solutions of the theory, performing a comparison between f(R) and f(T) modifications.

Cosmic Strings meet Multiferroics: Understanding Topological Defect Formation in Crystals

Speaker: Sinéad Griffin
Department: ETH Zurich
Time: Tuesday 11 June 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: Jumping from the expanse of galactic scales to land in the laboratory might seem a gargantuan task. Common to both, however, is the the concept of symmetry breaking and in particular the formation of topological defects. Here I discuss the formation of topological defects in multiferroic YMnO3 whose ferroelectric behavior enables the direct imaging of these defects. I also show how this material can be used to study the Kibble-Zurek model of topological defect formation in the early universe and give quantitative insights on the number of domains formed during the spontaneous symmetry breaking phase transition. We also uncover a surprising 'beyond Kibble-Zurek' behaviour, and discuss this in the context of the material's properties.

Probe Branes on Flavored ABJM Background

Speaker: Javier Mas
Department: University of Santiago de Compostela
Slides: [PDF]
Time: Thursday 13 June 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: In this talk we will review the construction of a background dual to Chern-Simons theory with fundamental fields added (flavoured ABJM). On top of this background we will place probe D6 branes and study the thermodynamics thereof. We speculate on the possible obtention of a charged background.

Results from Planck (department colloquium)

Speaker: James Bartlett
Department: Université Paris Diderot
Time: Thursday 13 June 2013 at 17:15
Venue: The 3rd floor seminar room of the physics department
Abstract: Since its launch in May 2009, Planck has been surveying the sky in nine frequency bands spanning 30 to 857 GHz. Its combination of sensitivity, angular resolution and frequency coverage produces an extremely rich data set for a wide array of science, from fundamental cosmology with the primary cosmic microwave background (CMB) anisotropies to the largescale distribution of light and dark matter since recombination. Our results support the standard spatially flat cosmological model with a cosmological constant and Gaussian matter perturbations to a precision never before attained. This is a remarkable statement of the simplicity of the universe. The Planck parameters differ slightly, but notably, from the WMAP cosmology, and the high precision has unveiled mild tension with some astrophysical measurements. In particular, Planck prefers a high matter density and low Hubble constant. Planck also provides important new results on the evolution of the universe after recombination through observations of galaxy clusters, gravitational lensing and of the light emitted by early star forming galaxies. Of specific note is an intriguing tension between results from analysis of the primary CMB anisotropies and those from the cluster redshift distribution, a consequence of the high matter density.

Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models

Speaker: Konstantinos Anagnostopoulos
Department: National Technical University of Athens
Slides: [PDF]
Time: Friday 14 June 2013 at 14:30
Venue: The 2nd floor seminar room of the physics department
Abstract: It has long been speculated that the spontaneous symmetry breaking (SSB) of SO(D) occurs in matrix models obtained by dimensionally reducing super Yang-Mills theory in D = 6, 10 dimensions. In particular, the D = 10 case corresponds to the IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory, and the SSB may correspond to the dynamical generation of four-dimensional space-time. Recently, it has been shown by using the Gaussian expansion method that the SSB indeed occurs for D = 6 and D = 10, and interesting nature of the SSB common to both cases has been suggested. Here we study the same issue by a Monte Carlo method in the D = 6 case. The complex-action problem is overcome by using the factorization method, and various quantities obtained by appropriate scaling analyses turn out to be consistent with the previous results obtained by the Gaussian expansion method.

Elementary excitations in gapped quantum spin systems

Speaker: Spiros Michalakis
Department: Caltech
Time: Tuesday 13 August 2013 at 14:15
Venue: The 2nd floor seminar room of the physics department
Abstract: For quantum lattice systems with local interactions, the popular Lieb-Robinson velocity acts as an alternative to the speed of light, allowing us to translate several famous results of relativistic quantum field theory to the setting of local Hamiltonians with a spectral gap. In this talk in particular, we show that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector, can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state. The error decreases exponentially in the size of the support of the local operator, with a rate that is set by the gap below and above the targeted eigenvalue. In other words, our intuition that low-energy excitations look like elementary particles with fixed momentum, is actually pretty accurate.