A Five-brane Modulus in the Effective N=1 Supergravity of M-Theory

TL;DR

This paper derives the effective four-dimensional supergravity theory involving a five-brane modulus in M-theory compactified on a Calabi-Yau threefold, highlighting its coupling to bulk fields and its impact on gauge couplings and potential.

Contribution

It presents the first derivation of the effective supergravity including the five-brane modulus and its couplings, respecting all M-theory symmetries and self-duality constraints.

Findings

The five-brane modulus couples to bulk moduli and matter fields.

Corrections to gauge couplings are constrained by self-duality.

The brane contribution resembles string one-loop corrections.

Abstract

Five-branes lead in four dimensions to massless N=1 supermultiplets if M-theory is compactified on S1/Z2 x (a Calabi-Yau threefold). One of them describes the modulus associated with the position of the five-brane along the circle S1. We derive the effective four-dimensional supergravity of this multiplet and its coupling to bulk moduli and to Yang-Mills and charged matter multiplets located on Z2 fixed planes. The dynamics of the five-brane modes is obtained by reduction and supersymmetrization of the covariant five-brane bosonic action. Our construction respects all symmetries of M-theory, including the self-duality of the brane antisymmetric tensor. Corrections to gauge couplings are strongly constrained by this self-duality property. The brane contribution to the effective scalar potential is formally similar to a renormalization of the dilaton. The vacuum structure is not modified. Altogether, the impact of the five-brane modulus on the effective supergravity is reminiscent of string one-loop corrections produced by standard compactification moduli.