Type IIB Orientifolds with NS-NS Antisymmetric Tensor Backgrounds

TL;DR

The paper studies six-dimensional ${\cal N}=1$ Type IIB orientifolds with a quantized NS-NS background $B_{ij}$, showing that the rank of both the $99$ and $55$ gauge groups is reduced by $2^{b/2}$ where $b=\mathrm{rk}(B_{ij})$. It demonstrates that a non-zero $B$-field induces a multiplicity $2^{b/2}$ for the $59$ open-string sector and can generate extra tensor multiplets in the ${\bf Z}_2$ twisted sector, with detailed accounting ensuring anomaly cancellation via $n_H-n_V=244-29n_T$. The analysis of the ${\bf Z}_2$ case reveals how $oxed{\,b=2\,}$ yields $n_T=4$ additional tensors and a gauge group reduction to $U(8)\times U(8)$, while $oxed{\,b=4\,}$ gives $n_T=6$ and $U(4)\times U(4)$, with analogous but more constrained behavior for other ${\bf Z}_N$ models. The work connects these orientifolds to F-theory duals and maps them onto moduli spaces, enriching the landscape of consistent six-dimensional vacua and illustrating the interplay between background fluxes, tadpole cancellation, and anomaly constraints.

Abstract

We consider six dimensional N=1 space-time supersymmetric Type IIB orientifolds with non-zero untwisted NS-NS sector B-field. The B-field is quantized due to the requirement that the Type IIB spectrum be left-right symmetric. The presence of the B-field results in rank reduction of both 99 and 55 open string sector gauge groups. We point out that in some of the models with non-zero B-field there are extra tensor multiplets in the Z_2 twisted closed string sector, and we explain their origin in a simple example. Also, the 59 open string sector states come with a multiplicity that depends on the B-field. These two facts are in accord with anomaly cancellation requirements. We point out relations between various orientifolds with and without the B-field, and also discuss the F-theory duals of these models.