Quantum Corrections to Supergravity on AdS$_2\times S^2$

TL;DR

This paper calculates quantum corrections to supergravity on AdS$_2\times S^2$ by explicitly diagonalizing the spectrum, identifying physical and boundary modes, and summing over these to find leading quantum effects.

Contribution

It provides a detailed off-shell spectrum analysis of supergravity on AdS$_2\times S^2$, including boundary modes, and computes the leading quantum correction.

Findings

Explicit diagonalization of supergravity equations of motion.

Classification of bulk modes into physical, gauge violating, and pure gauge.

Calculation of the leading quantum correction as a sum over physical and boundary modes.

Abstract

We compute the off-shell spectrum of supergravity on AdS$_2\times S^2$ by explicit diagonalization of the equations of motion for an effective AdS$_2$ theory where all fields are dualized to scalars and spin-${1\over 2}$ fermions. Classifying all bulk modes as physical, gauge violating, and pure gauge let us identify boundary modes as physical fields on $S^2$ that are formally pure gauge but with gauge function that is non-normalizable on AdS$_2$. As an application we compute the leading quantum correction to AdS$_2\times S^2$ as a sum over physical fields including boundary states.