A bstract We compute 1 /λ corrections to the fourpoint functions of halfBPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of KaluzaKlein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to oneloop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »
AdS bulk locality from sharp CFT bounds
A bstract It is a longstanding conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higherspin singletrace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆ gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆ gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and Smatrix dispersion relations in appropriate limits. This dictionary allows us to apply recentlydeveloped flatspace methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flatspace bounds. Our results imply the validity of twicesubtracted dispersion relations for any Smatrix arising from the flatspace limit of AdS/CFT.
 Award ID(s):
 1915093
 Publication Date:
 NSFPAR ID:
 10376824
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2021
 Issue:
 11
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
More Like this


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 RGmore »

A bstract We study the fourpoint function of the lowestlying halfBPS operators in the $$ \mathcal{N} $$ N = 4 SU( N ) superYangMills theory and its relation to the flatspace fourgraviton amplitude in type IIB superstring theory. We work in a large N expansion in which the complexified YangMills coupling τ is fixed. In this expansion, nonperturbative instanton contributions are present, and the SL(2 , ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the massdeformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the fourpoint correlator at separated points. In a normalization where the twopoint functions are proportional to N 2 − 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the fourpoint correlator are proportional to the nonholomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$more »

A bstract Using the fact that flat space with a boundary is related by a Weyl transformation to antide Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O ( N ) model in general dimension d , as well as its perturbative descriptions in the epsilonexpansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion,more »

A bstract In the AdS/CFT correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of averaging over an ensemble of boundary theories. But in examples in dimension D ≥ 3, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of “fixed energy” or “subthreshold” observables that we claim do not show effects of ensemble averaging. These are amplitudes that involve states that are above the ground state by only a fixed amount in the large N limit, and in particular are far from being black hole states. To support our claim, we explore the example of D = 3, and show that connected solutions of Einstein’s equations with disconnected boundary never contribute to these observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic threemanifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a largemore »