arXiv subjects

Fedor K. Popov

Publications and source records attributed to Fedor K. Popov.

At least 19 recordsLinked to original sources

arXiv2026

Towers of Operators in CFTs and Convexity Bounds at Large Charge

In arXiv:2406.19441, it was shown that for 3d CFTs with a moduli space along which a $U(1)$ symmetry is spontaneously broken, the minimum scaling dimension at large charge $Q$ scales as $Δ_{\min}(Q)=α_1 Q+α_0+O(1/Q)$. Motivated by the holographic swampland program, we study possible bounds on the coefficients $α_i$. For $α_0$, the weak gravity conjecture motivates the CFT charge convexity conjecture, which requires the bound $α_0\leq 0$. Using the moduli space EFT we prove this bound for the $\textit{projected}$ $Δ_{\min}(Q)$, obtained by fixing a single charge $Q$ and minimizing the dimension while allowing all other charges to vary. This provides a WGC-motivated bound that is explicitly provable using CFT methods. On the other hand, we show that $α_1$ admits no universal bound apart from the trivial bound $α_1\geq 0$. We also compute $α_1$ and $α_0$ in several new 3d $\mathcal{N}=1$ theories via the $ε$-expansion and large-$N$ methods.

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

$\mathcal{PT}$-symmetric Field Theories at Finite Temperature

We investigate the thermal properties of $\mathcal{PT}$-symmetric scalar field theories with purely imaginary couplings. The free energy governs the asymptotic density of states, providing an effective measure of the number of degrees of freedom, while thermal masses and one-point functions provide predictions for operator dimensions and three-point functions in the corresponding $d=2$ Conformal Field Theories. Naive finite-temperature perturbation theory near upper critical dimensions is spoiled by infrared divergences. To remove these divergences, we introduce a ''thermal normal-ordering'' scheme that resums these contributions and yields a systematic $ε$-expansion. This framework allows us to compute the free energy, thermal masses, and one-point functions in the cubic and quintic $O(N)$ models. We compare the thermal free energy density, thermal masses, and one-point function in two dimensions with exact results derived from the proposed Ginzburg-Landau descriptions of the non-unitary minimal models $M(2,5)$ and $M(3,8)_D$. Eventually, we employ two-sided Padé extrapolations to obtain estimates for the thermal free energy in $d=3,4,5$.

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 Fusion and Casimir Energy in Higher Dimensions

We study the operator algebra of extended conformal defects in more than two spacetime dimensions. Such algebra structure encodes the combined effect of multiple impurities on physical observables at long distances as well as the interactions among the impurities. These features are formalized by a fusion product which we define for a pair of defects, after isolating divergences that capture the effective potential between the defects, which generalizes the usual Casimir energy. We discuss general properties of the corresponding fusion algebra and contrast with the more familiar cases that involve topological defects. We also describe the relation to a different defect setup in the shape of a wedge. We provide explicit examples to illustrate these properties using line defects and interfaces in the Wilson-Fisher CFT and the Gross-Neveu(-Yukawa) CFT and determine the defect fusion data thereof.

hep-th↗

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

Do null defects dream of conformal symmetry?

We initiate the study of null line defects in Lorentzian conformal field theories in various dimensions. We show that null lines geometrically preserve a larger set of conformal isometries than their timelike and spacelike counterparts, explain a connection to non-relativistic systems, and constrain correlation functions using conformal Ward identities. We argue that having conformal symmetry, and especially maximal conformal symmetry, is extremely constraining -- nearly trivializing systems. We consider the (3+1)d scalar pinning field and null Wilson line examples in depth, compare their results to ultraboosted limits of timelike and spacelike systems, and argue that shockwave-type solutions are generic. A number of physical consistency conditions compel us to consider defect correlators as distributions on a restricted subspace of Schwartz test functions. Consequently, we provide a resolution to the longstanding problem of ultraboosted limits of gauge potentials in classical electromagnetism. We briefly analyze semi-infinite sources for the scalar in ($4-ε$)-dimensions, consider solutions on the Lorentzian cylinder, and introduce the ''perfect null polygon'' which emerges for compatibility between Gauss' law and ultraboosted limits.

hep-th↗

arXiv2025

Holography on the Quantum Disk

Motivated by recent study of DSSYK and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime known as the quantum disk proposed by L. Vaksman. The quantum disk is defined as the space whose isometries are generated by the quantum algebra $U_q(\mathfrak{su}_{1,1})$. We review how this algebra is defined and its associated group $SU_q(1,1)$ that it generates, highlighting its non-trivial coproduct that sources bulk non-commutativity. We analyze the structure of holography on the quantum disk and study the imprint of non-commutativity on the putative boundary dual.

hep-th↗

arXiv2025

Factorizing Defects from Generalized Pinning Fields

We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain unbounded operators on the Hilbert space and prove that when inserted on codimension-one surfaces they factorize the spacetime into two halves. The factorization channels are further constrained by symmetries in the bulk. As a corollary, we solve such critical impurities in the 2d minimal models and establish the factorization phenomena previously observed for localized mass deformations in the 3d ${\rm O}(N)$ model.

hep-th↗

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↗

arXiv2025

Hidden Wave Function of Twisted Bilayer Graphene: Flat Band as a Landau Level

We study the chirally symmetric continuum model (CS-CM) of the twisted bilayer graphene. The equation on a flat band could be interpreted as a Dirac equation on a torus in the external non-abelian magnetic field. We prove that the existence of the flat band implies that the wave-function has a zero and vice verse. We found a hidden solution in the CS-CM model that has a pole instead of a zero. Our main result is that in the basis of the flat band and hidden wave functions the flat band could be interpreted as Landau level in the external magnetic field. From that interpretation we show the existence of extra flat bands in the magnetic field.

cond-mat.str-el↗

arXiv2024

On Real Time Dynamics of Large $N$ Models

We analyze the real-time dynamics of the large $N$ vector model, focusing on heavy states with energies of the order $N$. In this regime, we demonstrate that interactions become sufficiently strong to produce non-zero condensate of the Hubbard-Stratonovich field $σ$, which, in turn, induces particle production. This process leads to a significant transformation of the initial state and potential thermalization. For homogeneous perturbations, our results show that the equations become integrable, yet can still lead to thermalization in the continuum limit. Furthermore, we calculate the energies of these heavy states and their contributions to the thermal free energy, thereby determining the free energy of the critical $O(N)$ model by operator counting.

hep-th↗

arXiv2024

Effective Field Theory of Conformal Boundaries

We introduce an effective field theory (EFT) for conformal impurity by considering a pair of transversely displaced impurities and integrating out modes with mass inversely proportional to the separation distance. This EFT captures the universal signature of the impurity seen by a heavy local operator. We focus on the case of conformal boundaries and derive universal formulas from this EFT for the boundary structure constants at high energy. We point out that the more familiar thermal EFT for conformal field theory is a special case of this EFT with distinguished conformal boundaries. We also derive, for general conformal impurities, non-positivity and convexity-like constraints on the Casimir energy which determines the leading EFT coefficient.

hep-th↗

arXiv2024

Beyond $N=\infty$ in Large $N$ Conformal Vector Models at Finite Temperature

We investigate finite-temperature observables in three-dimensional large $N$ critical vector models taking into account the effects suppressed by $1\over N$. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalar $O(N)$ model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in $1\over N$, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infinite $N$, while in special cases the discrepancies only start to appear at the next-to-subleading order.

hep-th↗

arXiv2023

Deterministic Chaos vs Integrable Models

In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved charges change under a small deformation of the initial conditions, we conclude that the inverse scattering map is responsible for the presence of these features, in spite of the system being integrable. We investigate this phenomenon in the explicit examples of the KdV equation and the sine-Gordon model and further provide general arguments supporting this statement.

hep-th↗

arXiv2023

Magic Angle Butterfly in Twisted Trilayer Graphene

We consider a configuration of three stacked graphene monolayers with commensurate twist angles $θ_{12}/θ_{23}=p/q$, where $p$ and $q$ are coprime integers with $0<p<|q|$ and $q$ can be positive or negative. We study this system using the continuum model in the chiral limit when interlayer coupling terms between $\textrm{AA}_{12}$ and $\textrm{AA}_{23}$ sites of the moiré patterns $12$ and $23$ are neglected. There are only three inequivalent displacements between the moiré patterns $12$ and $23$, at which the three monolayers' Dirac zero modes are protected. Remarkably, for these displacements and an arbitrary $p/q$ we discover exactly flat bands at an infinite set of twist angles (magic angles). We provide theoretical explanation and classification of all possible configurations and topologies of the flat bands.

cond-mat.str-el↗