4-D gauged supergravity analysis of Type IIB vacua on $K3\times T^2/Z_2$

TL;DR

The authors cast Type IIB compactifications on $K3\times T^2/\mathbb{Z}_2$ with three-form fluxes into four-dimensional gauged $N=2$ supergravity, showing that the resulting vacua include $N=2$, $N=1$, and $N=0$ no-scale configurations. They construct the quaternionic moduli space $M_q=SO(4,20)/(SO(4)\times SO(20))$ as a fibration over $SO(3,19)/(SO(3)\times SO(19))$, and embed the vector sector in a symplectic frame without a prepotential to realize partial SUSY breaking. By gauging translational isometries corresponding to the 22 axions (via flux-induced couplings $f_{m,\Lambda}, h_{a,\Lambda}$), they reproduce the Tripathy–Trivedi vacua and elucidate the Higgs mechanism that absorbs axions into massive vector multiplets. The analysis also identifies general no-scale non-supersymmetric vacua and a truncation to $N=1$ with a rich moduli space, highlighting the role of the no-prepotential symplectic frame in enabling SUSY breaking without a cosmological term. These results connect string flux constructions to effective gauged supergravity and suggest avenues for including branes and broader fluxes in no-scale setups.

Abstract

We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the $K3$ moduli space together with the special geometry of the NS and R-R dilatons and of the $T^2$-complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N=2, D=4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.