We consider gluons scattering in Type IIB string theory on AdS5 x S^5/Z2 in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d N=2 USp(2N) gauge theory with SO(8) flavor symmetry. We compute this holographic correlator in the large N and finite string coupling tau expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in 1/N and finite tau using localization. In particular, we fix the F^4 correction to gluon scattering on AdS in terms of Jacobi theta functions, and the D^2F^4 correction in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a remarkably similar form as the flat space Veneziano amplitude. Finally, we combine the numerical conformal bootstrap with the localization constraints to study the correlator at finite N and tau.

We consider graviton scattering in maximal supergravity on Anti-de Sitter space (AdS) in d+1 dimensions for d=3,4,and 6 with no extra compact spacetime factor. Holography suggests that this theory is dual to an exotic maximally supersymmetric conformal field theory (CFT) in d dimensions whose only light single trace operator is the stress tensor. This contrasts with more standard cases like Type IIB string theory on AdS_5x S^5 dual to N=4 Super-Yang-Mills, where the CFT has light single trace operators for each Kaluza-Klein mode on S^5. We compute the 1-loop correction to the pure AdS_{d+1} theory in a small Planck length expansion, which is dual to the large central charge expansion in the CFT. We find that this correction saturates the most general non-perturbative conformal bootstrap bounds on this correlator in the large central charge regime for d=3,4,6. After imposing theory-specific constraints from localization in d=3,4, the bootstrap constraints strengthen and are then saturated by the string/M-theory dual CFT data.

We study the N = 4 SYM stress tensor multiplet 4-point function for any value of the complexified coupling tau, and in principle any gauge group (we focus on SU(2) and SU(3) for simplicity). By combining non-perturbative constraints from the numerical bootstrap with two exact constraints from supersymmetric localization, we are able to compute upper bounds on low-lying CFT data (e.g. the Konishi) for any value of tau. These upper bounds are very close to the 4-loop weak coupling predictions in the appropriate regime. We also give preliminary evidence that these upper bounds become small islands under reasonable assumptions, in which case our method would provide a numerical solution to N = 4 SYM for any gauge group and tau. -------- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant.

We study the N = 4 SU(N) super-Yang-Mills stress tensor multiplet four-point function at large N and finite complexified Yang-Mills coupling tau, which is dual to the Type IIB graviton correlator on AdS_5 × S^5 at large string length and finite string coupling. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of m, b, and tau of the sphere free energy deformed by mass m and squashing parameter b, which can be computed using supersymmetric localization. We show that at each order in 1/N, these quantities can be written in terms of modular invariants, such as the well studied non-Holomorphic Eisenstein series as well as some new generalizations thereof. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space, which is the first check of AdS/CFT at finite string coupling, and have interesting implications for the structure of the analogous expansion in AdS_5 × S^5. Zoom Join Zoom Meeting https://zoom.us/j/93725965823?pwd=Q2lmeEhjQnJmZUsxMkp2THdVZ1cxUT09 Meeting ID: 937 2596 5823 Passcode: 640955

We derive an explicit map between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two and to all orders in 1/N, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

We apply two non-perturbative methods, the numerical conformal bootstrap and supersymmetric localization, to four point functions of half-BPS operators in 3d maximally supersymmetric ABJM theory. This correlator is dual to scattering of gravitons and KK-modes in M-theory on AdS_4 x S^7, and determines the M-theory S-matrix in the flat space limit. Using localization, we compute OPE coefficients of certain protected operators exactly at small N and to all orders in 1/N at large N. We apply these analytic results to the numerical bootstrap in two ways. First, we find that numerical bootstrap bounds for these OPE coefficients are saturated by the analytic results, which allows us to read off all low-lying CFT data in the correlator, including for unprotected operators. Second, by imposing the analytical results we find precision islands in the space of certain quarter and eighth BPS OPE coefficients. This numerical data can be used to determine the M-theory S-matrix, which we confirm at leading order in large N.