This series consists of talks in the area of Superstring Theory.
We construct the gravity duals of large N supersymmetric gauge theories on a squashed five-sphere. They are constructed in Euclidean Romans F(4) gauged supergravity in six-dimensions. We find a one- as well as a two-parameter family of solutions and evaluate the renormalised on-shell and fundamental string action for these solutions to find precise agreement with gauge theory.
We provide a framework for describing gravity duals of four-dimensional N=1 superconformal field theories obtained by compactifying a stack of M5-branes on a Riemann surface. The gravity solutions are completely specified by two scalar potentials whose pole structures on the Riemann surface correspond to the spectrum of punctures that labels different theories. We discuss how to identify these puncture in gravity.
We study a class of 4d N=1 SCFTs obtained from partial compactifications of 6d N=(2, 0) theory on a Riemann surface with punctures. We identify theories corresponding to curves with general type of punctures through nilpotent Higgsing and Seiberg dualities. The `quiver tails' of N=1 class S theories turn out to differ significantly from N=2 counterpart and have interesting properties. Various dual descriptions for such a theory can be found by using colored pair-of-pants decompositions. Especially, we find N=1 analog of Argyres-Seiberg duality for the SQCD with various gauge groups.
There is a proposed dS/CFT duality in 3+1 dimensions, with higher-spin gravity in the bulk subject to Bunch-Davies boundary conditions. I consider replacing these with antipodally symmetric conditions, which allow for real values of the bulk fields. I present spanning sets of solutions in global dS_4 for free gauge fields of all spins (including photons and gravitons), and use them to establish relations between antipodal symmetry and asymptotic behavior. Some of these relations can be extended to interacting theories, including ordinary and higher-spin gravity.
We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of this theory on a two-torus, with arbitrary supersymmetry preserving twists, using the topological vertex formalism. Alternatively, we show that this can also be obtained by computing the elliptic genus of an orbifold of recently studied M-strings.
We present explicit computations and conjectures for 2 → 2 scattering matrices in large N U(N) Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the ’t Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering.
There is a close connection between Symmetry Protected Topological Phases and anomalies: a surface of an SPT phase typically has a global symmetry with a nonvanishing 't Hooft anomaly which is canceled by the anomaly inflow from the bulk. This observation together with the known results about the classification of SPT phases suggest that anomalies are much more ubiquitous than thought previously and do not require chiral fermions We elucidate the physical mechanism of anomalies and give examples of bosonic theories with 't Hooft anomalies in various dimensions.
The entanglement entropy of the vacuum of a quantum field theory contains information about physics at all scales and is UV sensitive. A simple refinement of entanglement entropy gets rid of its UV divergence, and allows us to extract entanglement per scale. In two and three spacetime dimensions this quantity can be used as a proxy for the number of degrees of freedom, as it decreases under RG flow. We investigate its behavior around fixed points, and reveal its interesting analytic structure in the space of couplings.
There have been a number of attempts to achieve a localization of gravity on a braneworld hypersurface embedded in an infinite spacetime, but these have all fallen short of what might be desired, for various reasons. There have even been no-go theorems claimed for constructions made using just accepted elements of string or M theory. The talk will present a proposed resolution of this problem based upon a hyperbolic solution of type IIA theory with a superposed NS-5 brane.