We use effective string theory to study mesons with large spin $\textit{J}$ in large $\textit{N}$ 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/$\textit{J}$ 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 4$\textit{d}$ flux tubes. We compare our predictions with 4$\textit{d}$ QCD spectroscopy data, and suggest potential $\textit{stringy}$ 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.

United States

Gabriel Cuomo

Sergei Dubovsky

Uruguay

Guzmán Hernández-Chifflet

Alexander Monin

Shahrzad Zare

The EFT of large spin mesons

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 − ϵ 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.

Leonardo Rastelli

Adar Sharon

Moduli spaces in CFT: bootstrap equation in a perturbative example

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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 ε-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.

Canada

Yin-Chen He

Zohar Komargodski

Impurities with a cusp: general theory and 3d Ising

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 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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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.

Moduli spaces in CFT: large charge operators

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.

Portugal

J.M.Viana Lopes

Switzerland

José Matos

Júlio Oliveira

João Penedones

Numerical tests of the large charge expansion

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.

Shuyu Zhang

Spontaneous symmetry breaking on surface defects

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 QED4, and also in the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetric Yang-Mills theory. We also consider Wilson lines in 2+1 dimensional conformal gauge theories such as QED3 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.

Israel

Ofer Aharony

United Kingdom

Márk Mezei

Avia Raviv-Moshe

Phases of Wilson lines: conformality and screening

We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> and <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> 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 <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions and determine the screening cloud due to bosons or fermions. We also study QED in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions in the large <math><msub><mi>N</mi><mi>f</mi></msub></math> limit and identify the nontrivial conformal Wilson lines. We briefly discuss ‘t Hooft lines in <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>-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 <math><mrow><mi>S</mi></mrow></math> 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.

Phases of Wilson Lines in Conformal Field Theories

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.

Giant Vortices and the Regge Limit

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.