A five-brane modulus in the effective N=1 supergravity of M-theory

Five-branes lead in four dimensions to massless N = 1 supermultiplets if M-theory is compactified on S-1/Z (2)x (a Calabi-Yau threefold). One of them describes the modulus associated with the position of the five-brane along the circle S-1. 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 22 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. (C) 2001 Elsevier Science B.V. All rights reserved.