4D effective action from non-Abelian DBI action with magnetic flux background

TL;DR

This paper derives a 4D $ ext{N}=1$ supersymmetric effective theory from a 10D non-Abelian DBI action with magnetic fluxes, revealing a new matter K"ahler metric and confirming consistency with supergravity.

Contribution

It introduces a novel matter K"ahler metric dependent on fluxes and moduli, derived from the non-Abelian DBI action, extending previous supergravity-based models.

Findings

New matter K"ahler metric depends on fluxes and moduli

Superpotential derived from F-term scalar interactions

Scalar potential consistent with supergravity

Abstract

We study a systematic derivation of four dimensional $\mathcal{N}=1$ supersymmetric effective theory from ten dimensional non-Abelian Dirac-Born-Infeld action compactified on a six dimensional torus with magnetic fluxes on the D-branes. We find a new type of matter K\"{a}hler metric while gauge kinetic function and superpotential are consistent with previous studies. For the ten dimensional action, we use a symmetrized trace prescription and focus on the bosonic part up to $\mathcal{O}(F^4)$. In the presence of the supersymmetry, four dimensional chiral fermions can be obtained via index theorem. The new matter K\"{a}hler metric is independent of flavor but depends on the fluxes, 4D dilaton, K\"{a}hler moduli and complex structure moduli, and will be always positive definite if an induced Ramond-Ramond charge of the D-branes on which matters are living are positive. We read the superpotential from an F-term scalar quartic interaction derived from the ten dimensional action and the contribution of the new matter K\"{a}hler metric to the scalar potential which we derive turns out to be consistent with the supergravity formulation.