arXiv subjects

Zohar Komargodski

Publications and source records attributed to Zohar Komargodski.

At least 55 records · Page 3Linked to original sources

arXiv2018

Comments on Abelian Higgs Models and Persistent Order

A natural question about Quantum Field Theory is whether there is a deformation to a trivial gapped phase. If the underlying theory has an anomaly, then symmetric deformations can never lead to a trivial phase. We discuss such discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We emphasize the role of charge conjugation symmetry in these anomalies; for example, we obtain nontrivial constraints on the degrees of freedom that live on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions. In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the Abelian Higgs model is dual to the Ising model. We also study variations of the Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical particle of unit charge. These models have a center symmetry and additional discrete anomalies. In the absence of a dynamical unit charge particle, the Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These models without a unit charge particle exhibit a remarkably persistent order: we prove that the system cannot be disordered by either quantum or thermal fluctuations. Equivalently, when these theories are studied on a circle, no matter how small or large the circle is, the ground state is non-trivial.

hep-th↗

arXiv2018

Curious Aspects of Three-Dimensional ${\cal N}=1$ SCFTs

We study the dynamics of certain 3d ${\cal N}=1$ time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared and there exists (nonetheless) an exact moduli space of vacua. This theory has a dual description with manifest time reversal symmetry. Second, we consider some surprising facts about ${\cal N}=2$ $U(1)$ gauge theory coupled to two chiral superfields of charge 1. This theory is claimed to have emergent $SU(3)$ global symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a theory of scalars and fermions but no gauge fields) with manifest $SU(3)$ symmetry but only ${\cal N}=1$ supersymmetry. We argue that this Wess-Zumino model must have enhanced supersymmetry in the infrared. Finally, we make some brief comments about the dynamics of ${\cal N}=1$ $SU(N)$ gauge theory coupled to $N_f$ quarks in a time reversal invariant fashion. We argue that for $N_f<N$ there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted.

hep-th↗

arXiv2018

Phases Of Adjoint QCD$_3$ And Dualities

We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the theory as a function of the gauge group, the Chern-Simons level $k$, and the fermion mass. We propose an inherently quantum mechanical phase of adjoint QCD with small enough $k$, where the infrared is described by a certain Topological Quantum Field Theory (TQFT). For a special choice of the mass, the theory has ${\cal N}=1$ supersymmetry. There this TQFT is accompanied by a massless Majorana fermion - a Goldstino signaling spontaneous supersymmetry breaking. Our analysis leads us to conjecture a number of new infrared fermion-fermion dualities involving $SU$, $SO$, and $Sp$ gauge theories. It also leads us to suggest a phase diagram of $SO/Sp$ gauge theories with a fermion in the traceless symmetric/antisymmetric tensor representation of the gauge group.

hep-th↗

arXiv2018

Phases of ${\cal N}=1$ Theories in 2+1 Dimensions

We study the dynamics of 2+1 dimensional theories with ${\cal N}=1$ supersymmetry. In these theories the supersymmetric ground states behave discontinuously at co-dimension one walls in the space of couplings, with new vacua coming in from infinity in field space. We show that the dynamics near these walls is calculable: the two-loop effective potential yields exact results about the ground states near the walls. Far away from the walls the ground states can be inferred by decoupling arguments. In this way, we are able to follow the ground states of ${\cal N}=1$ theories in 2+1 dimensions and construct the infrared phases of these theories. We study two examples in detail: Adjoint SQCD and SQCD with one fundamental quark. In Adjoint QCD we show that for sufficiently small Chern-Simons level the theory has a non-perturbative metastable supersymmetry-breaking ground state. We also briefly discuss the critical points of this theory. For SQCD with one quark we establish an infrared duality between a $U(N)$ gauge theory and an $SU(N)$ gauge theory. The duality crucially involves the vacua that appear from infinity near the walls.

hep-th↗

arXiv2018

Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets

We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum anti-ferromagnets. In the presence of $\mathbb{Z}_2$ preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the Valence Bond Solid (VBS) phase of quantum magnets. We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is $SU(2)_1$ WZW). Either way the fundamental scalar particles (i.e. spinons) which are confined in the bulk are deconfined on the domain-wall. This $\mathbb{Z}_2$ phase can be realized either with spin-1/2 on a rectangular lattice, or spin-1 on a square lattice. In both cases the domain wall contains spin-1/2 particles (which are absent in the bulk). We discuss the possible relation to recent lattice simulations of domain walls in VBS. We further generalize the discussion to Abrikosov-Nielsen-Olsen (ANO) vortices in a dual superconductor of the Abelian-Higgs model in 3+1 dimensions, and to the easy-plane limit of anti-ferromagnets. In the latter case the wall can undergo a variant of the BKT transition (consistent with the anomalies) while the bulk is still gapped. The same is true for the easy-axis limit of anti-ferromagnets. We also touch upon some analogies to Yang-Mills theory.

cond-mat.str-el↗

arXiv2017

A Symmetry Breaking Scenario for QCD$_3$

We consider the dynamics of 2+1 dimensional $SU(N)$ gauge theory with Chern-Simons level $k$ and $N_f$ fundamental fermions. By requiring consistency with previously suggested dualities for $N_f\leq 2k$ as well as the dynamics at $k=0$ we propose that the theory with $N_f> 2k$ breaks the $U(N_f)$ global symmetry spontaneously to $U(N_f/2+k)\times U(N_f/2-k)$. In contrast to the 3+1 dimensional case, the symmetry breaking takes place in a range of quark masses and not just at one point. The target space never becomes parametrically large and the Nambu-Goldstone bosons are therefore not visible semi-classically. Such symmetry breaking is argued to take place in some intermediate range of the number of flavors, $2k< N_f< N_*(N,k)$, with the upper limit $N_*$ obeying various constraints. The Lagrangian for the Nambu-Goldstone bosons has to be supplemented by nontrivial Wess-Zumino terms that are necessary for the consistency of the picture, even at $k=0$. Furthermore, we suggest two scalar dual theories in this range of $N_f$. A similar picture is developed for $SO(N)$ and $Sp(N)$ gauge theories. It sheds new light on monopole condensation and confinement in the $SO(N)$ and $Spin(N)$ theories.

hep-th↗

arXiv2017

The Sum Over Topological Sectors and $θ$ in the 2+1-Dimensional $\mathbb{C}\mathbb{P}^1$ $σ$-Model

We discuss the three spacetime dimensional $\mathbb{C}\mathbb{P}^N$ model and specialize to the $\mathbb{C}\mathbb{P}^1$ model. Because of the Hopf map $π_3(\mathbb{C}\mathbb{P}^1)=\mathbb{Z}$ one might try to couple the model to a periodic $θ$ parameter. However, we argue that only the values $θ=0$ and $θ=π$ are consistent. For these values the Skyrmions in the model are bosons and fermions respectively, rather than being anyons. We also extend the model by coupling it to a topological quantum field theory, such that the Skyrmions are anyons. We use techniques from geometry and topology to construct the $θ=π$ theory on arbitrary 3-manifolds, and use recent results about invertible field theories to prove that no other values of $θ$ satisfy the necessary locality.

cond-mat.str-el↗

arXiv2017

Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions

We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $θ$-parameter. For generic $m$ and $θ$ the theory has a single gapped vacuum. However, as $θ$ is varied through $θ=π$ for large $m$ there is a first order transition. For $N_f=1$ the first order transition line ends at a point with a massless $η'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the $4d$ bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different $3d$ phases. These turn out to be the phases of the recently studied $3d$ Chern-Simons matter theories, thus relating the dynamics of QCD$_4$ and QCD$_3$, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless $4d$ theory has an $SU(N_f)$ sigma model, the domain wall theory at low (nonzero) mass supports a $3d$ massless $CP^{N_f-1}$ nonlinear $σ$-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

hep-th↗

arXiv2017

Theta, Time Reversal, and Temperature

$SU(N)$ gauge theory is time reversal invariant at $θ=0$ and $θ=π$. We show that at $θ=π$ there is a discrete 't Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at $θ=π$ the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at $θ=0$ is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at $θ=π$, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for $SU(2)$ gauge theory. The underlying symmetry at $θ=π$ is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two $O(2)$-symmetric fixed points. It may also be that the four-dimensional theory around $θ=π$ is gapless, e.g. a Coulomb phase could match the underlying anomalies.

hep-th↗

arXiv2016

Shortening Anomalies in Supersymmetric Theories

We present new anomalies in two-dimensional ${\mathcal N} =(2, 2)$ superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from ${\mathcal N} =(2, 2)$ spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond ${\mathcal N} =(2, 2)$. These anomalies explain why the conformal manifolds of the K3 and $T^4$ sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no ${\mathcal N} =(2, 2)$ gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.

hep-th↗

arXiv2016

Conformal Field Theories and Deep Inelastic Scattering

We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of minimal-twist operators of even spin s \geq 2. In the case of s=2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s>2 the bounds are new.

hep-th↗

arXiv2016

Correlation Functions of Coulomb Branch Operators

We consider the correlation functions of Coulomb branch operators in four-dimensional N=2 Superconformal Field Theories (SCFTs) involving exactly one anti-chiral operator. These extremal correlators are the "minimal" non-holomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the four-sphere partition function of an appropriate deformation of the SCFT. This relation between the extremal correlators and the deformed four-sphere partition function is non-trivial due to the presence of conformal anomalies, which lead to operator mixing on the sphere. Evaluating the deformed four-sphere partition function using supersymmetric localization, we compute the extremal correlators explicitly in many interesting examples. Additionally, the representation of the extremal correlators mentioned above leads to a system of integrable differential equations. We compare our exact results with previous perturbative computations and with the four-dimensional tt^* equations. We also use our results to study some of the asymptotic properties of the perturbative series expansions we obtain in N=2 SQCD.

hep-th↗

arXiv2016

Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude

We consider weakly-coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime $s,t \gg 1$, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, $j(t)$, is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higher-spin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.

hep-th↗

arXiv2016

Anomalies, Conformal Manifolds, and Spheres

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2 supersymmetric theories in d=4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kahler-Hodge and we further argue that it has vanishing Kahler class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that the relation between the sphere partition function and the Kahler potential of M follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.

hep-th↗

arXiv2016

Is the Relaxion an Axion?

We consider the recently proposed cosmological relaxation mechanism where the hierarchy problem is ameliorated, and the electroweak scale is dynamically selected by a slowly rolling axion field. We argue that, in its simplest form, the construction breaks a gauge symmetry that always exists for pseudo-Nambu-Goldstone bosons (in particular the axion). The small parameter in the relaxion model is therefore not technically natural as it breaks a gauge symmetry rather than global symmetries only. The consistency of the theory generically implies that the cutoff must lie around the electroweak scale, but not qualitatively higher. We discuss several ways to evade the above conclusion. Some of them may be sufficient to increase the cutoff to the few-TeV range (and therefore may be relevant for the little-hierarchy problem). To demonstrate the ideas in a concrete setting we consider a model with a familon, the Nambu-Goldstone boson of a spontaneously broken chiral flavor symmetry. The model has some interesting collider-physics aspects and contains a viable weakly interacting dark matter candidate.

hep-ph↗

arXiv2015

Disorder in Large-N Theories

We consider Euclidean Conformal Field Theories perturbed by quenched disorder, namely by random fluctuations in their couplings. Such theories are relevant for second-order phase transitions in the presence of impurities or other forms of disorder. Theories with quenched disorder often flow to new fixed points of the renormalization group. We begin with disorder in free field theories. Imry and Ma showed that disordered free fields can only exist for d>4. For d>4 we show that disorder leads to new fixed points which are not scale-invariant. We then move on to large-N theories (vector models or gauge theories in the `t Hooft limit). We compute exactly the beta function for the disorder, and the correlation functions of the disordered theory. We generalize the results of Imry and Ma by showing that such disordered theories exist only when disorder couples to operators of dimension Δ> d/4. Sometimes the disordered fixed points are not scale-invariant, and in other cases they have unconventional dependence on the disorder, including non-trivial effects due to irrelevant operators. Holography maps disorder in conformal theories to stochastic differential equations in a higher-dimensional space. We use this dictionary to reproduce our field theory results. We also study the leading 1/N corrections, both by field theory methods and by holography. These corrections are particularly important when disorder scales with the number of degrees of freedom.

hep-th↗

arXiv2015

The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories

We propose an exact formula for the energy radiated by an accelerating quark in N=2 superconformal theories in four dimensions. This formula reproduces the known Bremsstrahlung function for N=4 theories and provides a prediction for all the perturbative and instanton corrections in N=2 theories. We perform a perturbative check of our proposal up to three loops.

hep-th↗

arXiv2015

Quantum Electrodynamics in d=3 from the epsilon-expansion

We study Quantum Electrodynamics in d=3 (QED_3) coupled to N_f flavors of fermions. The theory flows to an IR fixed point for N_f larger than some critical number N_f^c. For N_f<= N_f^c, chiral-symmetry breaking is believed to take place. In analogy with the Wilson-Fisher description of the critical O(N) models in d=3, we make use of the existence of a perturbative fixed point in d=4-2epsilon to study the three-dimensional conformal theory. We compute in perturbation theory the IR dimensions of fermion bilinear and quadrilinear operators. For small N_f, a quadrilinear operator can become relevant in the IR and destabilize the fixed point. Therefore, the epsilon-expansion can be used to estimate N_f^c. An interesting novelty compared to the O(N) models is that the theory in d=3 has an enhanced symmetry due to the structure of 3d spinors. We identify the operators in d=4-2epsilon that correspond to the additional conserved currents at d=3 and compute their infrared dimensions.

hep-th↗