Completing the D7-brane local gaugino action

TL;DR

This paper derives a local 10d Lagrangian for D7-brane gaugino condensation, addressing non-locality issues and improving the understanding of string theory de Sitter vacua constructions.

Contribution

It introduces a local counterterm in the 10d supergravity framework that removes divergences and reproduces the 4d supergravity action for gaugino condensation.

Findings

A local counterterm removes divergence in the 10d action.

The counterterm reproduces the relevant 4d supergravity potential.

Advances understanding of 10d supergravity and dS vacua in string theory.

Abstract

Within the ongoing debate about de Sitter (dS) vacua in string theory, different aspects of explicit dS proposals have come under intense scrutiny. One key ingredient is D7-brane gaugino condensation, which is usually treated using effective 4d supergravity. However, it is clearly more desirable to derive the relevant scalar potential directly from a local 10d Lagrangian. Such a local 10d description captures the interactions among the various localized sources and the background fields which are smeared in the 4d Lagrangian. While progress in this endeavour has recently been made, some form of non-locality related to the 4-gaugino term has remained hidden in the available proposals. We spell out the local counterterm removing the divergence that arises when integrating out the 3-form flux and which, upon dimensional reduction, serves to reproduce the relevant part of the 4d supergravity action. This is both a step towards a more complete understanding of 10d type-IIB supergravity as well as specifically towards better control of dS constructions in string theory involving gaugino condensation.