Matrix Dilaton-Axion for Heterotic String in Three Dimensions

TL;DR

This paper introduces a new, simple matrix-based representation of the heterotic string effective action in three dimensions, revealing symmetries and automorphisms that facilitate solution generation, including a double-Kerr solution.

Contribution

It presents a novel complex potential formulation of the heterotic string action as a Kähler sigma-model with matrix dilaton-axion, enabling new solution-generating techniques.

Findings

Derived a simple matrix dilaton-axion representation

Identified automorphisms relating U-duality transformations

Constructed a double-Kerr solution using new techniques

Abstract

New and surprisingly simple representation is found for the heterotic string bosonic effective action in three dimensions in terms of complex potentials. The system is presented as a K\"ahler $\sigma$--model using complex symmetric $2\times 2$ matrix (matrix dilaton--axion) which depends linearly on three Ernst--type potentials and transforms under $U$--duality via matrix valued $SL(2,R)$. Two discrete automorphisms relating ten isometries of the target space (U--duality transformations) are found and used to generate the non--trivial Ehlers--Harrison sector by a map from the trivial gauge sector. Finite transformations are obtained in a simple form in terms of complex potentials. New solution generating technique is used to construct EMDA double--Kerr solution.