From effective actions to the background geometry

TL;DR

This paper explores how background geometries like AdS3, S3, and T*S3 can be derived from one-loop effective actions in non-supersymmetric theories with external abelian fields, linking them to topological strings and matrix models.

Contribution

It reveals the geometric structures underlying effective actions and connects low-energy amplitudes to topological string theories and matrix models.

Findings

Effective actions involve integration over specific geometries depending on external fields.

Topological string interpretations are found for the effective actions in selfdual fields.

Low energy MHV amplitudes relate to type B topological string amplitudes in mirror geometries.

Abstract

We discuss how the background geometry can be traced from the one-loop effective actions in nonsupersymmetric theories in the external abelian fields. It is shown that upon the proper identification of the Schwinger parameter the Heisenberg-Euler abelian effective action involves the integration over the $AdS_3$, $S_3$ and $T^{*}S^3$ geometries, depending on the type of the external field. The interpretation of the effective action in the sefdual field in terms of the topological strings is found and the corresponding matrix model description is suggested. It is shown that the low energy abelian MHV one-loop amplitudes are expressed in terms of the type B topological string amplitudes in mirror to $T^{*}S^3$ manifold. We also make some comments on the relation between the imaginary part of the effective action and the branes in SU(2) as well as on the geometry of the contours relevant for the path integral.