SL(2,Z) Action on AdS/BCFT and Hall Conductivities

TL;DR

This paper investigates how boundary conformal field theories respond to electromagnetic fields within a holographic framework, revealing new insights into Hall conductivities, duality transformations, and string theory embeddings.

Contribution

It introduces a holographic approach to study Hall conductivities in BCFTs, analyzes SL(2,Z) duality effects, and explores a string theory embedding of the model.

Findings

Derived relations among Hall conductivities and transport coefficients.

Demonstrated non-trivial SL(2,Z) duality action on BCFT conductivity.

Embedded the holographic setup into type IIA string theory.

Abstract

We study the response of a conserved current to external electromagnetic fields in a holographic system with boundaries using the recently proposed AdS/BCFT (boundary conformal field theory) framework. This, in particular, allows us to extract the Hall current, the Hall conductivity, plus some potentially novel transport coefficients, and relations among them. We also analyze the action of SL(2,Z) duality in the gravity bulk, which acts non-trivially on the conductivity of the BCFT. Finally we consider a type IIA string theory embedding of our setup.