Domain walls and instantons in N=1, d=4 supergravity

TL;DR

This paper investigates supersymmetric domain walls and instantons in N=1, d=4 supergravity, revealing how sources affect solutions and proposing a reformulation where coupling constants are scalar fields.

Contribution

It introduces a new perspective on sources in supergravity, linking them to local coupling constants and proposing a scalar field reformulation of the theory.

Findings

Domain walls couple to two 3-forms with charges and tension related to the superpotential.

Sources modify solutions, suggesting a need for reformulating supergravity with scalar coupling constants.

Explicit supersymmetric instanton solutions are constructed and analyzed.

Abstract

We study the supersymmetric sources of (multi-) domain-wall and (multi-) instanton solutions of generic N=1, d=4 supergravities, that is: the worldvolume effective actions for said supersymmetric topological defects. The domain-wall solutions naturally couple to the two 3-forms recently found as part of the N=1, d=4 tensor hierarchy (i.e. they have two charges in general) and their tension is the absolute value of the superpotential section L. The introduction of sources (we study sources with finite and vanishing thickness) is equivalent to the introduction of local coupling constants and results in dramatic changes of the solutions. Our results call for a democratic reformulation of N=1,d=4 supergravity in which coupling constants are, off-shell, scalar fields. The effective actions for the instantons are always proportional to the coordinate orthogonal to the twist-free embedding of the null-geodesic (in the Wick-rotated scalar manifold) describing the instanton. We show their supersymmetry and find the associated supersymmetric (multi-) instanton solutions.