A well-behaved field theory living on a fixed background has a causality structure defined by the background metric. In holography, however, signals can travel through the bulk, and some bulk metrics would allow a signal to travel faster than the speed of light as seen on the boundary. These are called boundary causality violating metrics. Holographers usually work with a classical bulk metric, in which case they declare that boundary causality violating metrics are forbidden. However, in a full quantum gravity path integral, these metrics do contribute. The question is then: how to avoid causality violation in this context? In this talk I will give a prescription that achieves this.

I will discuss a string theory perspective on the Bethe/Gauge correspondence for the XXX superspin chain. I explain how to realize 4d Chern-Simons theory with gauge supergroup using branes, and how the brane configurations for the superspin chain get mapped to 2d N = (2,2) quiver gauge theories proposed by Nekrasov. This is based on my ongoing work with Nafiz Ishtiaque, Faroogh Moosavian and Surya Raghavendran.

I will discuss a precise connection between renormalization group (RG) and quantum chaos. Every RG flow between two conformal fixed points can be described in terms of the dynamics of Nambu-Goldstone bosons of broken symmetries. The theory of Nambu-Goldstone bosons can be viewed as a theory in anti-de Sitter space with the flat space limit. This enables an equivalent formulation of these 4d RG flows in terms of spectral deformations of a generalized free CFT in 3d. This approach provides a precise relation between C-functions associated with 4d RG flows and certain out-of-time-order correlators that diagnose chaos in 3d. As an application, I will show that the 3d chaos bound imposes constraints on the low energy effective action associated with unitary RG flows in 4d with a broken continuous global symmetry in the UV. These bounds, among other things, imply that the proof of the 4d a-theorem remains valid even when additional global symmetries are broken.