arXiv subjects

Zohar Komargodski

Publications and source records attributed to Zohar Komargodski.

At least 19 recordsLinked to original sources

arXiv2026

Anyon Crystallization by Statistics

We revisit the long-standing problem of the anyon gas. We study the solvable near-bosonic limit of a large number of anyons $N$ at fixed $N/k$, where $1/k$ characterizes the statistical interaction. In this limit, the ground state is a crystal with order $N/k$ lattice sites. The statistical interactions, mediated by a long-range gauge field, are completely screened within the crystalline phase. The resulting state is a conventional crystal without superfluidity. We characterize this anyon crystal by determining its unit-cell size, ground-state energy, acoustic excitations, angular momentum crossings, and other properties. Our results indicate a quantum phase transition between the crystal at $k>k_c$ and a superfluid at $k<k_c$, with a critical value $k_c\simeq2\text{--}5$. These results imply that an anyon gas with only statistical interactions is not necessarily a superfluid, contrary to common lore. We also present a detailed analysis of the renormalization-group evolution of anyon--anyon interactions, identifying many new potential fixed points and elucidating finite-size effects.

hep-th↗

arXiv2026

Symmetry Enhancement, SPT Absorption, and Duality in QED$_3$

Quantum Electrodynamics in 2+1 dimensions (QED$_3$) with two Dirac fermions displays time reversal symmetry, nontrivial SPT phases and anomalies. The fate of this theory in its strongly coupled regime has been debated extensively. Surprisingly, we find that gluing together the phase diagrams of two standard Wilson-Fisher $O(4)$ theories suffices to reproduce all the SPT phases, anomalies, and semi-classical limits. A central mechanism behind it is ``SPT absorption''. The patching of the $O(4)$ transitions makes very concrete predictions for the behavior of the theory in its strongly coupled limits; for instance, the $θ=π$ sigma model with $S^3$ topology appears due to monopole condensation.

hep-th↗

arXiv2026

Temperature-Resistant Order in 2+1 Dimensions

High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking $\mathbb{Z}_2 \to \emptyset$ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.

hep-th↗

arXiv2026

Regge's Inferno

We study large-spin operators in conformal field theories (CFTs) in spacetime dimensions $d>2$ by placing the theory on appropriate pp-wave backgrounds. We show that these geometries admit Heisenberg-group symmetries, and that these symmetries, combined with locality of quantum fields on such spacetimes, impose strong constraints on the asymptotic spectrum in the large-spin limit. The pp-wave backgrounds probe both the small-twist regime, corresponding to the Regge or light-cone bootstrap, and a strongly coupled regime of large twist. Finally, we demonstrate that causality (or the requirement that the energy be bounded from below) leads to a new unitarity bound in $3+1$ dimensions.

hep-th↗

arXiv2026

Minimal Models of Entropic Order

Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order that arise from very simple interactions. Our main examples are the Arithmetic Ising Model (AIM) and its quantum analogue, where usual Ising spins are replaced by non-negative integers. Using a large-flavor expansion together with numerical simulations, we find that the high-temperature phase is ordered in the classical and quantum models. We also introduce classical gas models whose interactions drive the system to a crystal at high temperatures.

cond-mat.stat-mech↗

arXiv2026

Trapping $\tfrac{h}{2e}$ Flux in Metals

We report on a new flux quantization phenomenon in metals. We study the response of normal metals to the presence of localized magnetic flux. We find that, due to backreaction effects, the metal traps 0 flux or $\tfrac{h}{2e}$ flux (half flux). We exhibit this effect both for metals pierced by magnetic solenoids and metals wrapping a magnetic solenoid. In the latter case we demonstrate the trapping of magnetic flux analytically. Furthermore, we find that as the solenoid is adiabatically turned off, a logarithmically enhanced localized equilibrium current persists, reflecting perfect defect-diamagnetism of the Fermi gas.

cond-mat.str-el↗

arXiv2025

Defect Anomalies, a Spin-Flux Duality, and Boson-Kondo Problems

We show that the infrared phases of certain line defects in 2+1d quantum field theories are determined by anomalies, including anomalies in the space of defect coupling constants, together with a symmetry-refined corollary of the $g$-theorem. As an example, we prove that the spin-$1/2$ impurities in the 2+1d critical $O(2)$ and $O(3)$ models (known respectively as the Halon and Boson-Kondo defects) flow to non-trivial conformal line operators in the IR, and we supply evidence that the same extends to all spin $s$. We also argue that, under particle/vortex duality, the Halon impurity is exchanged with the $π$-flux vortex line leading to spin-flux duality, a proposal which we test with a detailed matching of symmetries, anomalies, and phases. Finally, we write down quantum lattice Hamiltonians which can be used to test our predictions, and give an argument on the lattice in favor of spin-flux duality.

hep-th↗

arXiv2025

Disclinations, dislocations, and emanant flux at Dirac criticality

What happens when fermions hop on a lattice with crystalline defects? The answer depends on topological quantum numbers which specify the action of lattice rotations and translations in the low energy theory. One can understand the topological quantum numbers as a twist of continuum gauge fields in terms of crystalline gauge fields. We find that disclinations and dislocations -- defects of crystalline symmetries -- generally lead in the continuum to a certain ``emanant'' quantized magnetic flux. To demonstrate these facts, we study in detail tight-binding models whose low-energy descriptions are (2+1)D Dirac cones. Our map from lattice to continuum defects explains the crystalline topological response to disclinations and dislocations, and motivates the fermion crystalline equivalence principle used in the classification of crystalline topological phases. When the gap closes, the presence of emanant flux leads to pair creation from the vacuum with the particles and anti-particles swirling around the defect. We compute the associated currents and energy density using the tools of defect conformal field theory. There is a rich set of renormalization group fixed points, depending on how particles scatter from the defect. At half flux, there is a defect conformal manifold leading to a continuum of possible low-energy theories. We present extensive numerical evidence supporting the emanant magnetic flux at lattice defects and we test our map between lattice and continuum defects in detail. We also point out a no-go result, which implies that a single (2+1)D Dirac cone in symmetry class AII is incompatible with a commuting $C_M$ rotational symmetry with $(C_M)^M = +1$.

cond-mat.str-el↗

arXiv2025

Entropic Order

Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist to arbitrarily high temperature. This is possible since order in one degree of freedom can enable other degrees of freedom to strongly fluctuate, leading to "entropic order", whereby typical high energy states are ordered. Our construction, which utilizes interacting bosons, avoids existing no-go theorems on long-range order or entanglement at high temperature. We propose a simple model for high-temperature superconductivity using these general principles.

cond-mat.stat-mech↗

arXiv2024

Impurities with a cusp: general theory and 3d Ising

In CFTs, the partition function of a line defect with a cusp depends logarithmically on the size of the line with an angle-dependent coefficient: the cusp anomalous dimension. In the first part of this work, we study the general properties of the cusp anomalous dimension. We relate the small cusp angle limit to the effective field theory of defect fusion, making predictions for the first couple of terms in the expansion. Using a concavity property of the cusp anomalous dimension we argue that the Casimir energy between a line defect and its orientation reversal is always negative ("opposites attract"). We use these results to determine the fusion algebra of Wilson lines in $\mathcal{N}=4$ SYM as well as pinning field defects in the Wilson-Fisher fixed points. In the second part of the paper we obtain nonperturbative numerical results for the cusp anomalous dimension of pinning field defects in the Ising model in $d=3$, using the recently developed fuzzy-sphere regularization. We also compute the pinning field cusp anomalous dimension in the $O(N)$ model at one-loop in the $\varepsilon$-expansion. Our results are in agreement with the general theory developed in the first part of the work, and we make several predictions for impurities in magnets.

hep-th↗

arXiv2024

Chiral Modes of Giant Superfluid Vortices

We discuss rapidly rotating states of a superfluid. We concentrate on the Giant-Vortex (GV) state, which is a coherent rotating solution with a macroscopic hole at the center. We show that, for any trap, the fluctuations obey an approximately chiral dispersion relation, describing arbitrary shape deformations moving with the speed of the ambient superfluid. This dispersion relation is a consequence of a peculiar infinite symmetry group that emerges at large angular velocity and implies an infinite ground-state degeneracy. The degeneracy is lifted by small corrections which we determine both for smooth traps and the hard trap.

cond-mat.quant-gas↗

arXiv2024

Trace Anomalies and the Graviton-Dilaton Amplitude

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to $Δc-Δa$ along any RG flow, where $Δc$ and $Δa$ are the differences of the UV and IR $c$- and $a$-trace anomalies respectively. This allows us to relate $Δc-Δa$ to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

hep-th↗

arXiv2024

The Baryon Junction and String Interactions

We study junctions between confining strings. We show that the effective theory of such junctions is very predictive with only one new parameter, the junction's mass, controlling the first couple of terms in the expansion in the system size. By open-closed duality these considerations about the baryon junction map to interaction vertices of closed strings. Therefore, we calculate the interaction vertices of closed strings in theories such as Yang-Mills theory. We find some surprising selection rules for string interactions in 3+1 dimensions. Requiring perturbative stability and that the string coupling is weak, we suggest constraints on the junction's mass.

hep-th↗

arXiv2023

Phases of Wilson Lines: Conformality and Screening

We study the rich dynamics resulting from introducing static charged particles (Wilson lines) in 2+1 and 3+1 dimensional gauge theories. Depending on the charges of the external particles, there may be multiple defect fixed points with interesting renormalization group flows connecting them, or an exponentially large screening cloud can develop (defining a new emergent length scale), screening the bare charge entirely or partially. We investigate several examples where the dynamics can be solved in various weak coupling or double scaling limits. Sometimes even the elementary Wilson lines, corresponding to the lowest nontrivial charge, are screened. We consider Wilson lines in 3+1 dimensional gauge theories including massless scalar and fermionic QED$_4$, and also in the ${\mathcal N}=4$ supersymmetric Yang-Mills theory. We also consider Wilson lines in 2+1 dimensional conformal gauge theories such as QED$_3$ with bosons or fermions, Chern-Simons-Matter theories, and the effective theory of graphene. Our results in 2+1 dimensions have potential implications for graphene, second-order superconducting phase transitions, etc. Finally, we comment on magnetic line operators in 3+1 dimensions ('t Hooft lines) and argue that our results for the infrared dynamics of electric and magnetic lines are consistent with non-Abelian electric-magnetic duality.

hep-th↗

arXiv2023

Anomalies and Symmetry Fractionalization

We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $Γ$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $Γ$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $Γ$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory.

hep-th↗

arXiv2023

Monopoles, Scattering, and Generalized Symmetries

We reconsider the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle as, in certain circumstances, they necessarily carry fractional quantum numbers. We argue that consistency requires such outgoing particles to be attached to a topological co-dimension 1 surface, which ends on the monopole. This surface cannot participate in a 2-group with the magnetic 1-form symmetry and is often non-invertible. Equivalently, the outgoing radiation lies in a twisted sector and not in the original Fock space. The outgoing radiation therefore not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory. We exemplify these ideas in the 1+1 dimensional, chiral 3450 model which shares many of the same features. We comment on the effects of gauge field fluctuations on the lowest angular momentum fermion scattering states in the presence of a magnetic monopole. While, to leading order, these zero modes can penetrate into the monopole core, in the full theory some of the zero modes are lifted and develop a small centrifugal barrier. The dynamics of the zero modes is that of a multi-flavor Schwinger model with a space-dependent gauge coupling. Symmetries and anomalies constrain the fate of the pseudo-zero modes.

hep-th↗

arXiv2023

Phases of Wilson Lines in Conformal Field Theories

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to interesting renormalization group flows and for sufficiently large representations to complete or partial screening by charged fields. This result is universal: in large enough representations, Wilson lines are screened by the charged matter fields. We observe that the onset of the screening instability is associated with fixed-point mergers. We study this phenomenon in a variety of applications. In some cases, the screening of the Wilson lines takes place by dimensional transmutation and the generation of an exponentially large scale. We identify the space of infrared conformal Wilson lines in weakly coupled gauge theories in 3+1 dimensions and determine the screening cloud due to bosons or fermions. We also study QED in 2+1 dimensions in the large $N_f$ limit and identify the nontrivial conformal Wilson lines. We briefly discuss 't Hooft lines in 3+1-dimensional gauge theories and find that they are screened in weakly coupled gauge theories with simply connected gauge groups. In non-Abelian gauge theories with S-duality, this together with our analysis of the Wilson lines gives a compelling picture for the screening of the line operators as a function of the coupling.

hep-th↗

arXiv2023

Giant Vortices and the Regge Limit

In recent years it has been shown that strongly coupled systems become analytically tractable in the regime of large quantum numbers, such as large spin or large charge. The effective theories that emerge in these two limits are Regge theory and superfluid theory, respectively. Here we make a proposal for a new phase, the ``giant vortex,'' describing an intermediate regime with large spin and charge. The new phase connects superfluid theory with the large-spin expansion. The giant vortex admits a semi-classical effective theory description with peculiar chiral excitations (moving at the speed of light) and a Fock space of states that is reminiscent of the multi-twist operators in Regge theory, including the leading and daughter Regge trajectories. A similar giant vortex phase appears for Bose-Einstein condensates in a rotating trap, and our results should be applicable in that context as well. We show that the transition from the giant vortex to the Regge regime is accompanied by the scaling dimension turning from being larger than to being smaller than the mean field theory value, i.e. gravity switches from being the weakest force at small AdS distance to being the strongest force at large AdS distance.

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