The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in
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Abstract SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter $\mathcal{N}=4$ζ has a nontrivial beta function and may be viewed as a running coupling constant in a 1D defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rankk symmetric representation ofSU (N ), we also consider a certain ‘semiclassical’ limit wherek is taken to infinity with the productkζ ^{2}fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms ofN commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the largek limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1D RG flow and comment on the consistency of the results with the 1D defect version of the Ftheorem. 
A bstract We study operators with large charge j in the d dimensional O ( N ) model with long range interactions that decrease with the distance as 1/ r d + s , where s is a continuous parameter. We consider the double scaling limit of large N , large j with $$ j/N=\hat{j} $$ j / N = j ̂ fixed, and identify the semiclassical saddle point that captures the twopoint function of the large charge operators in this limit. The solution is given in terms of certain ladder conformal integrals that have recently appeared in the literature on fishnet models. We find that the scaling dimensions for general s interpolate between $$ {\Delta }_j\sim \frac{\left(ds\right)}{2}j $$ ∆ j ∼ d − s 2 j at small $$ \hat{j} $$ j ̂ and $$ {\Delta }_j\sim \frac{\left(d+s\right)}{2}j $$ ∆ j ∼ d + s 2 j at large $$ \hat{j} $$ j ̂ , which is a qualitatively different behavior from the one found in the short range version of the O ( N ) model. We also derive results for the structure constants and 4point functions with two large charge and one or two finite charge operators. Using a description of the long range models as defects in a higher dimensional local free field theory, we also obtain the scaling dimensions in a complementary way, by mapping the problem to a cylinder in the presence of a chemical potential for the conserved charge.more » « less

A bstract The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed holographic duality between the gravitational $$ \mathcal{S} $$ S matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and soft dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of SYK provides an instructive toy model for the soft limit of the gravitational sector in 4D asymptotically flat spacetime. We find that the symmetries and soft dynamics of the 2D SYK model capture the salient features of the celestial theory: exhibiting chaotic dynamics, conformal invariance, and a w 1+ ∞ symmetry. The holographic map from 2D SYK operators to the 4D bulk employs the Penrose twistor transform.more » « less

A bstract Celestial holography proposes a duality between gravitational scattering in asymptotically flat spacetime and a conformal field theory living on the celestial sphere. Its dictionary relates the infinite dimensional spacetime symmetry group to Ward identities of the CFT. The spontaneous breaking of these asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here we show that this sector encodes nontrivial backreaction effects that exhibit characteristics of maximal quantum chaos. A key element in the derivation is the identification of the Hilbert space of celestial CFT, defined through radial quantization, with that of a constantly accelerating Rindler observer. From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior due to shockwave interactions that shift the observer horizon. From the point of view of the boundary, the superrotation Goldstone modes affect the relevant representations of the celestial Virasoro symmetry in a manner that induces Lyapunov behavior of outoftimeordered celestial correlators.more » « less

A bstract We study the boundary critical behavior of conformal field theories of interacting fermions in the GrossNeveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large N methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the GrossNeveu CFT. At large N and general dimension d , we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the WilsonFisher fixed point of the GrossNeveuYukawa model, two of these phases correspond respectively to the choice of Neumann or Dirichlet boundary condition on the scalar field, while the third one corresponds to the case where the bulk scalar field acquires a classical expectation value. One may flow between these boundary critical points by suitable relevant boundary deformations. We compute the AdS free energy on each of them, and verify that its value is consistent with the boundary version of the Ftheorem. We also compute some of the BCFT observables in these theories, including bulk twopoint functions of scalar and fermions, and fourpoint functions of boundary fermions.more » « less

A bstract We study the large charge sector of the defect CFT defined by the halfBPS Wilson loop in planar N = 4 supersymmetric YangMills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the doublescaling limit where the ’t Hooft coupling λ and the large charge J are sent to infinity, with the ratio J/ $$ \sqrt{\lambda } $$ λ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large J limit. We also compute the twopoint function of large charge insertions by evaluating the onshell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an “emergent” matrix model whose matrix size is proportional to J and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank1 $$ \mathcal{N} $$ N = 2 superconformal field theories, but our results hold also for nonextremal cases.more » « less

A bstract We study monodromy defects in O ( N ) symmetric scalar field theories in d dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on S 1 × H d− 1 , where H d− 1 is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along S 1 . In this description, the codimension two defect lies at the boundary of H d− 1 . We first study the general monodromy defect in the free field theory, and then develop the large N expansion of the defect in the interacting theory, focusing for simplicity on the case of N complex fields with a oneparameter monodromy condition. We also use the ϵ expansion in d = 4 − ϵ , providing a check on the large N approach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory on S 1 × H d− 1 . It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RG flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the lowlying KaluzaKlein modes on H d− 1 . We also show that, adapting standard techniques from the AdS/CFT literature, the S 1 × H d− 1 setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including onepoint functions of bulk operators, scaling dimensions of defect operators, and fourpoint functions of operator insertions on the defect.more » « less

A bstract Extending earlier work, we find the twoloop term in the betafunction for the scalar coupling ζ in a generalized Wilson loop operator of the $$ \mathcal{N} $$ N = 4 SYM theory, working in the planar weakcoupling expansion. The betafunction for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric WilsonMaldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the betafunction, we obtain a prediction for the twoloop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higherloop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ ) coming from the scalar ladder graphs determining the corresponding terms in the fiveloop betafunction. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the Ftheorem. We also compute (to two loops in the planar ladder model approximation) the twopoint correlators of scalars inserted on the Wilson line.more » « less