# Understanding Higher-Spin Gravity through Bilocal Holography for Free Fermions

## TL;DR

This paper constructs an explicit holographic mapping between free fermion theories and higher-spin gravity, providing a quantum Vasiliev gravity model with loop corrections, thus advancing the understanding of AdS/CFT duality.

## Contribution

It introduces a bilocal field approach to explicitly relate free fermion theories to higher-spin gravity, including quantum loop effects, and demonstrates a non-supersymmetric AdS/CFT duality.

## Key findings

- Established a holographic map for free fermions and higher-spin gravity.
- Constructed a quantum Vasiliev gravity with loop corrections.
- Provided a non-supersymmetric example of AdS/CFT duality.

## Abstract

We consider a simple theory of N free fermions in d dimensions with O\left(N\right) or U\left(N\right) symmetry. The singlet sector of this theory is expected from holography to be dual to the notoriously complicated Vasiliev gravity. By defining bilocal fields we find an explicit holographic mapping between the two theories, similar to what was done previously for scalars, which allows us to construct a quantum version of Vasiliev gravity, including loop (=1/N) corrections. Further more, such a mapping establishes a non-supersymmetric instance of the AdS/CFT duality.