Triangle Seminars

Abstract:
Conformal symmetry relates the metric on AdS_2 x S^1 to that of S^3. This implies that under a suitable choice of boundary conditions for fields on AdS_2 the partition function of conformal field theories on these spaces must agree which makes AdS_2 \times S^1 a good testing ground to study supersymmetric localization on non-compact spaces. We evaluate the partition function of N=2 supersymmetric Chern-Simons theory on AdS_2 x S^1 using localization, where the radius of S^1 is q times that of AdS_2. With boundary conditions on AdS_2 x S^1 which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS_2, we find that the result for the partition function precisely agrees with that of the theory on the q-fold covering of S^3.

Abstract:
In this talk, I will discuss transport phenomena in two classes of theories with holographic dual. In the first part, I will discuss systems where U(1) current is non-conserved due to anomaly and illustrate how one can show that the anomalous conductivities are non-renormalised in a large class of holographic RG flow. The holographic RG flow we considered is generated by arbitrary dilaton potentials and arbitrary higher derivative terms that do not break global symmetries, incorporating coupling constant corrections to the boundary theory in an expansions around infinite coupling. In the second part, I will focus on systems where translational symmetry is broken by slowly varying scalar fields and show that the bound shear viscosity/entropy density is violate. I will also discuss how to understand the violation in the language of forced fluid dynamics.

Abstract:
I will present a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a higher-dimensional CFT with a two-dimensional defect. The proof is applicable only to renormalization group flows that preserve locality, reflection positivity, and Euclidean invariance along the boundary or defect, and that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton” field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.

Abstract:
I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies.
I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.