All extremal instantons in Einstein-Maxwell-dilaton-axion theory

TL;DR

This paper explicitly constructs all extremal instanton solutions in a specific supergravity theory, revealing a large and diverse solution space including known, new, and potentially supersymmetric instantons with various charge configurations.

Contribution

The paper provides a complete classification of extremal instantons in Einstein-Maxwell-dilaton-axion theory using algebraic methods, including new solutions and insights into their supersymmetry and charge structures.

Findings

Large space of finite action solutions including new ALF and ALE instantons.

Identification of solutions satisfying no-force conditions, some potentially supersymmetric.

Explicit calculation of the instanton on-shell action using background subtraction.

Abstract

We construct explicitly all extremal instanton solutions to $\mathcal{N}=4,\, D=4$ supergravity truncated to one vector field (Einstein-Maxwell-dilaton-axion (EMDA) theory). These correspond to null geodesics of the target space of the sigma-model $G/H=Sp(4,\mathbb{R})/GL(2,\mathbb{R})$ obtained by compactification of four-dimensional Euclidean EMDA on a circle. They satisfy a no-force condition in terms of the asymptotic charges and part of them (corresponding to nilpotent orbits of the $Sp(4,\mathbb{R})$ U-duality) are presumably supersymmetric. The space of finite action solutions is found to be unexpectedly large and includes, besides the Euclidean versions of known Lorentzian solutions, a number of new asymptotically locally flat (ALF) instantons endowed with electric, magnetic, dilaton and axion charges. We also describe new classes of charged asymptotically locally Euclidean (ALE) instantons as well as some exceptional solutions. Our classification scheme is based on the algebraic classification of matrix generators according to their rank, according to the nature of the charge vectors and according to the number of independent harmonic functions with unequal charges. Besides the nilpotent orbits of $G$, we find solutions which satisfy the asymptotic no-force condition, but are not supersymmetric. The renormalized on-shell action for instantons is calculated using the method of matched background subtraction.