# Heterotic Kerr-Schild Double Field Theory and Classical Double Copy

## TL;DR

This paper extends the Kerr-Schild formalism to heterotic double field theory, enabling linearization of equations and establishing a double copy correspondence for heterotic supergravity and string theory.

## Contribution

It introduces a heterotic Kerr-Schild ansatz with a novel null vector structure, allowing linearized equations and a double copy framework in heterotic DFT.

## Key findings

- Heterotic Kerr-Schild ansatz reduces equations to linear form.
- Established single and zeroth copy for heterotic supergravity.
- Derived Maxwell and scalar equations consistent with heterotic string theory.

## Abstract

We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O(d,d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.