# Linearized Field Equations of Gauge Fields from the Entanglement First Law

## TL;DR

This paper derives linearized gauge field equations in AdS from the entanglement first law in CFTs, revealing how gauge fields influence holographic entanglement entropy beyond the Ryu-Takayanagi formula.

## Contribution

It introduces a method to obtain gauge field equations from entanglement principles, extending the holographic entanglement entropy framework to include gauge fields.

## Key findings

- Derived linearized equations for vector and tensor gauge fields from entanglement law.
- Identified additional gauge-dependent term in holographic entanglement entropy.
- Extended the Ryu-Takayanagi formula to incorporate gauge field contributions.

## Abstract

In the context of the AdS/CFT correspondence linearized field equations of vector and antisymmetric tensor gauge fields around an AdS background are obtained from the entanglement first law of CFTs. The holographic charged entanglement entropy contains a term depending on the gauge field in addition to the Ryu-Takayanagi formula.