Emergent Worldsheet for the AdS Virasoro-Shapiro Amplitude.

We construct a representation for the first anti-de Sitter curvature correction to the Virasoro-Shapiro amplitude, as an integral over the Riemann sphere. The integrand is that of the Virasoro-Shapiro amplitude in flat space, with the extra insertion of a linear combination of single-valued multiple polylogarithms of weight three. The integral representation implies an elegant, manifestly single-valued representation for the Wilson coefficients of the low-energy expansion.

Pure Anti-de Sitter Supergravity and the Conformal Bootstrap.

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_{5}×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 one-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 nonperturbative conformal bootstrap bounds on this correlator in the large central charge regime for d=3, 4, 6, while the one-loop correction to CFTs with string and M-theory duals all lie inside the allowed region.

Supersymmetric Five-Point Gluon Amplitudes in AdS Space.

We present the tree-level five-point amplitude of the lowest Kaluza-Klein mode of super-Yang-Mills theory on AdS_{5}×S^{3}, dual to the correlator of the flavor current multiplet in the dual 4d N=2 superconformal field theory. Its color and kinematical structure is particularly simple and resembles that of the flat-space gluon amplitude.

All Tree-Level Correlators for M Theory on AdS_{7}×S

We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on AdS_{7}×S^{4}. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional (2,0) theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler maximally R-symmetry violating amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.

Loop Corrections to Supergravity on AdS_{5}×S

We consider the four-point correlator of the stress-energy tensor multiplet in N=4 super Yang-Mills theory. In the planar limit and at large 't Hooft coupling, such a correlator is given by the corresponding holographic correlation function in IIB supergravity on AdS_{5}×S^{5}. We consider subleading corrections in the number of colors, i.e., order 1/N^{4}, at large 't Hooft coupling. This corresponds to loop corrections to the supergravity result. Consistency conditions, most notably, crossing symmetry, constrain the form of such corrections and lead to a complete determination of the spectrum of leading-twist intermediate operators.

Large Spin Perturbation Theory for Conformal Field Theories.

We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalized free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories around generalized free fields.

Gravity dual of supersymmetric gauge theories on a squashed five-sphere.

We present the gravity dual of large N supersymmetric gauge theories on a squashed five-sphere. The one-parameter family of solutions is constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplifts to massive type IIA supergravity. By renormalizing the theory with appropriate counterterms we evaluate the renormalized on-shell action for the solutions. We also evaluate the large N limit of the gauge theory partition function, and find precise agreement.

Central charges of Liouville and Toda theories from M5-branes.

We show that the central charge of the Liouville and Toda theories of type A, D, and E can be reproduced by equivariantly integrating the anomaly eight-form of the corresponding six-dimensional N=(0,2) theories, which describe the low-energy dynamics of M5-branes.