arXiv subjects

Gabriel Cuomo

Publications and source records attributed to Gabriel Cuomo.

At least 19 recordsLinked to original sources

arXiv2026

Impurities Near the Light Cone

The lightlike Wilson line cusp underlies the Sudakov double logarithm and is a central ingredient in gauge-theory factorization. We ask what replaces this behavior for general conformal line defects in Lorentzian signature. We argue that, when the defects admit local endpoint operators, the cusp anomalous dimension has a finite large-boost limit fixed by the scaling dimensions of the corresponding defect-creation operators. We further analyze the distinct analytic continuations of the cusp, elucidate their physical interpretations, and derive a positivity condition on the Lorentzian cusp anomalous dimension. We test these predictions in several perturbative examples, including pinning-field defects and spin impurities, and discuss their possible implications for gauge theories.

hep-th↗

arXiv2026

The two-flavor Schwinger model at 50: Solving Coleman's puzzles

In his 1976 paper "More about the massive Schwinger model", Coleman introduced $1+1$-dimensional Quantum Electrodynamics coupled to two charged massive fermions. By applying Abelian bosonization, he elucidated much of the physics of this two-flavor Schwinger model, but he listed three puzzles at the end of his paper. We present new analytical and numerical calculations to solve Coleman's three puzzles and thereby deepen our understanding of this model. These puzzles pertain to the theory with equal fermion masses at $\theta = 0$ and at $\theta = \pi$, as well as the size of isospin-breaking effects when the fermion masses are unequal. For the puzzle at $\theta = \pi$, the solution is related to the structure of the zero-temperature phase diagram arXiv:2305.04437: for equal fermion masses $m$, the model exhibits spontaneous breaking of charge conjugation symmetry and absence of confinement for any value of the gauge coupling $g$, so that there is a smooth interpolation from weak to strong coupling. Using two-loop Renormalization Group and integrability methods, we show that the mass gap behaves as $\sim m e^{-0.111 g^2/m^2}$ in the strong coupling regime $m\ll g$. Our numerical results using the lattice Hamiltonian are in good agreement with this behavior. For the puzzle at $\theta = 0$, the solution is related to a level crossing between two isosinglet particles with different discrete quantum numbers; we demonstrate the necessity of such a crossing by comparing integrability and weak coupling calculations, and we also exhibit the crossing numerically. Finally, we provide a new estimate for the size of isospin-breaking effects caused by different fermion masses at strong coupling.

hep-th↗

arXiv2025

Conformal Collider Physics at Large Charge

We study energy correlators and other event shapes in states created by operators with large global $U(1)$ charge $Q$ in Conformal Field Theories. Focusing on theories whose large charge sector is described by the superfluid Effective Field Theory (EFT), we develop a systematic framework to compute event shapes within the EFT. As formerly observed, event shapes at leading order in $1/Q$ factorize into a product of classical expectation values determined by symmetry. In contrast, the subleading contribution to energy-energy and charge-charge correlators is a nontrivial prediction of the EFT, which we compute explicitly. Our results reveal a sharp collinear enhancement of the correlation between detectors, induced by the propagation of sound. We also generalize our findings to a broad class of event shapes.

hep-th↗

arXiv2024

Quantum vorticity: a not so effective field theory

We provide a comprehensive picture for the formulation of the perfect fluid in the modern effective field theory formalism at both the classical and quantum level. Due to the necessity of decomposing the hydrodynamical variables $(\rho, p, u^\mu)$ into other internal degrees of freedom, the procedure is inherently not unique. We discuss and compare the different inequivalent formulations. These theories possess a peculiarity: the presence of an infinite dimensional symmetry implying a vanishing dispersion relation $\omega = 0$ for the transverse modes. This sets the stage for UV-IR mixing in the quantum theory, which we study in the different formulations focussing on the incompressible limit. We observe that the dispersion relation gets modified by quantum effects to become $\omega \propto \mathbf{k}^2$, where the fundamental excitations can be viewed as vortex-anti-vortex pairs. The spectrum exhibits infinitely many types of degenerate quanta. The unusual sensitivity to UV quantum fluctuations renders the implementation of the defining infinite symmetry somewhat subtle. However we present a lattice regularization that preserves a deformed version of such symmetry.

hep-th↗

arXiv2024

The EFT of Large Spin Mesons

We use effective string theory to study mesons with large spin $J$ in large $N_c$ QCD as rotating open strings. In the first part of this work, we formulate a consistent effective field theory (EFT) for open spinning strings with light quarks. Our EFT provides a consistent treatment of the endpoints' singularities that arise in the massless limit. We obtain results, in a systematic $1/J$ expansion, for the spectrum of the leading and daughter Regge trajectories. Interestingly, we find that the redshift factor associated with the quarks' acceleration implies that the applicability regime of the EFT is narrower compared to that of static flux tubes. In the second part of this work, we discuss several extensions of phenomenological interests, including mesons with heavy quarks, the quarks' spin and the daughter Regge trajectories associated with the worldsheet axion, a massive string mode identified in lattice simulations of $4d$ flux tubes. We compare our predictions with $4d$ QCD spectroscopy data, and suggest potential $stringy$ interpretations of the observed mesons. We finally comment on the relation between the EFT spectrum and the Axionic String Ansatz, a recently proposed characterization of the spectrum of Yang-Mills glueballs.

hep-th↗

arXiv2024

Moduli Spaces in CFT: Large Charge Operators

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is ${\it also}$ broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional ${\cal N}=1$ CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space.

hep-th↗

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

Moduli Spaces in CFT: Bootstrap Equation in a Perturbative Example

Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data such as the spectrum of asymptotic states in the broken vacuum and form factors. The simplest bootstrap equation arises by expanding a two-point function of local operators in two channels, at short distance using the OPE and at large distance using the EFT in the broken vacuum. We illustrate this equation in what is arguably the simplest perturbative model that exhibits conformal symmetry breaking, namely the real $ABC$ model in $d = 4 -\epsilon$ dimensions. We investigate the convergence properties of the bootstrap equation and check explicitly many of the non-trivial relations that it imposes on theory data.

hep-th↗

arXiv2023

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↗

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

Spontaneous symmetry breaking on surface defects

Coleman's theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). In this work we consider surface (i.e. two-dimensional) defects in $d$-dimensional conformal field theories (CFTs) invariant under a continuous internal symmetry group $G$. We study under which conditions it is possible for a surface defect to break spontaneously a continuous internal symmetry. We find that spontaneous symmetry breaking (SSB) is impossible under reasonable assumptions on the defect Renormalization Group (RG) flow. Counterexamples are possible only for exotic RG flows, that do not terminate at a fixed-point. We discuss an example of this kind. We also illustrate our no-go result with an effective field theory analysis of generic defect RG flows. We find a generic weakly coupled defect universality class (with no SSB), where correlation functions decay logarithmically. Our analysis generalizes the recent discovery by Metlitski of the extraordinary-log boundary universality class in the $O(N)$ model.

hep-th↗

arXiv2023

Numerical tests of the large charge expansion

We perform Monte-Carlo measurements of two and three point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

hep-lat↗

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.

hep-th↗

arXiv2022

Spin Impurities, Wilson Lines and Semiclassics

We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher $O(3)$ model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in $2+1$ dimensional magnets. Finally, we also study $1/2$-BPS Wilson lines in large representations of the gauge group in rank-1 $\mathcal{N}=2$ superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.

hep-th↗

arXiv2022

Localized magnetic field in the $O(N)$ model

We consider the critical $O(N)$ model in the presence of an external magnetic field localized in space. This setup can potentially be realized in quantum simulators and in some liquid mixtures. The external field can be understood as a relevant perturbation of the trivial line defect, and thus triggers a defect Renormalization Group (RG) flow. In agreement with the $g$-theorem, the external localized field leads at long distances to a stable nontrivial defect CFT (DCFT) with $g<1$. We obtain several predictions for the corresponding DCFT data in the epsilon expansion and in the large $N$ limit. The analysis of the large $N$ limit involves a new saddle point and, remarkably, the study of fluctuations around it is enabled by recent progress in AdS loop diagrams. Our results are compatible with results from Monte Carlo simulations and we make several predictions that can be tested in the future.

hep-th↗

arXiv2022

Renormalization Group Flows on Line Defects

We consider line defects in d-dimensional Conformal Field Theories (CFTs). The ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in 4 dimensions.

hep-th↗

arXiv2021

Boundary Conformal Field Theory at Large Charge

We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a $|ϕ|^6$ interaction in three dimensions and the $O(2)$ Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether's theorem in perturbative theories.

hep-th↗