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.
Highlights
Double field theory (DFT) [28,29,30,31,32,33] is a low energy effective field theory of strings with manifest O(d, d) T-duality [34,35,36,37]
We show that the KS equations are the same as the ones for pure double field theory (DFT), because all the terms containing the structure constant do not contribute in the flat background
We extended the KS formalism for pure DFT to the heterotic DFT case
Summary
We introduce a generalized Kerr-Schild ansatz for heterotic DFT. First we give a brief review of heterotic DFT. We consider properties of the null vectors in the generalized tangent space. We introduce the KS ansatz for the heterotic generalized metric and show that it is of the same form as the KS ansatz in pure DFT. We represent the ansatz in terms of heterotic supergravity fields which are expressed by a pair of d-dimensional vectors: null and non-null vectors. We discuss the Buscher rule for the generalized KS ansatz and show that T-duality maps a generalized KS ansatz to another one
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