No-scale N=4 supergravity coupled to Yang-Mills: the scalar potential and super-Higgs effect

TL;DR

The work derives the complete scalar potential for no-scale $N=4$ supergravity coupled to Yang-Mills in the presence of fluxes and D3-brane coordinates, clarifying how fluxes and non-abelian branes shape moduli and vacuum structure. The potential is organized as a sum of squares mixing flux-derived $F^{IJK-}$ and brane-induced $C^{IJK-}$, plus an axion-related term, which explains cancellations that yield vanishing vacuum energy in the no-scale setting. Coupling to Yang-Mills enlarges the gauge sector to $12+n$ generators, triggers a Higgs mechanism that eats 12 axions and leaves $6+6n$ flat directions, and yields a moduli space that factorizes into three copies of the $CP^{n+1}$ sigma-model. In the $N=2$ sector, a two-flux example demonstrates possible $N=2\to N=1$ partial breaking within a frame lacking a prepotential, illustrating the threefold $SU(1,1)/U(1)$ moduli structure and the role of symplectic frames in determining vacua.

Abstract

We derive the scalar potential of the effective theory of type IIB orientifold with 3-form fluxes turned on in presence of non abelian brane coordinates. N=4 supergravity predicts a positive semidefinite potential with vanishing cosmological constant in the vacuum of commuting coordinates, with a classical moduli space given by three radial moduli and three RR scalars which complete three copies of the coset (U(1,1+n)/U(1)\otimes U(1+n)), together with 6n D3-branes coordinates, n being the rank of the gauge group G. Implications for the super Higgs mechanism are also discussed.