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  1. A<sc>bstract</sc>

    We study a surface defect in the free and criticalO(N) vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of thed-dimensional CFT. We compute the beta function for the corresponding defect renormalization group (RG) flow, and provide evidence that at long distances the system flows to a nontrivial defect conformal field theory (DCFT). We use epsilon and largeNexpansions to compute several physical quantities in the DCFT, finding agreement across different expansion methods. We also compute the defect free energy, and check consistency with the so-calledb-theorem for RG flows on surface defects.

     
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  2. A<sc>bstract</sc>

    We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS2geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS2black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS2string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to SL(2,) invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in$$ \mathcal{N} $$N= 4 SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.

     
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  3. A<sc>bstract</sc>

    We study line defects in the fermionic CFTs in the Gross-Neveu-Yukawa universality class in dimensions 2< d <4. These CFTs may be described as the IR fixed points of the Gross-Neveu-Yukawa (GNY) model ind= 4 −ϵ, or as the UV fixed points of the Gross-Neveu (GN) model, which can be studied using the largeNexpansion in 2< d <4. These models admit natural line defects obtained by integrating over a line either the scalar field in the GNY description, or the fermion bilinear operator in the GN description. We compute the beta function for the defect RG flow using both the epsilon expansion and the largeNapproach, and find IR stable fixed points for the defect coupling, thus providing evidence for a non-trivial IR DCFT. We also compute some of the DCFT observables at the fixed point, and check that theg-function associated with the circular defect is consistent with theg-theorem for the defect RG flow.

     
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  4. 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 two-point 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 $$ {\Delta }_j\sim \frac{\left(d-s\right)}{2}j $$ ∆ 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 4-point 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. 
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  5. A bstract We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu 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 Gross-Neveu 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 Wilson-Fisher fixed point of the Gross-Neveu-Yukawa 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 F-theorem. We also compute some of the BCFT observables in these theories, including bulk two-point functions of scalar and fermions, and four-point functions of boundary fermions. 
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  6. A bstract We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar N = 4 supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling 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 two-point function of large charge insertions by evaluating the on-shell 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 rank-1 $$ \mathcal{N} $$ N = 2 superconformal field theories, but our results hold also for non-extremal cases. 
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  7. 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 one-parameter 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 low-lying Kaluza-Klein 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 one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect. 
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  8. A bstract We study operators in the rank- j totally symmetric representation of O ( N ) in the critical O ( N ) model in arbitrary dimension d , in the limit of large N and large charge j with j/N ≡ $$ \hat{j} $$ j ̂ fixed. The scaling dimensions of the operators in this limit may be obtained by a semiclassical saddle point calculation. Using the standard Hubbard-Stratonovich description of the critical O ( N ) model at large N , we solve the relevant saddle point equation and determine the scaling dimensions as a function of d and $$ \hat{j} $$ j ̂ , finding agreement with all existing results in various limits. In 4 < d < 6, we observe that the scaling dimension of the large charge operators becomes complex above a critical value of the ratio j/N , signaling an instability of the theory in that range of d . Finally, we also derive results for the correlation functions involving two “heavy” and one or two “light” operators. In particular, we determine the form of the “heavy-heavy-light” OPE coefficients as a function of the charges and d . 
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