Multi-Brane Recombination and Standard Model Flux Vacua

In a previous work, we noted that vacua with higher flux could be obtained by recombination of a small set of hidden-sector branes, numbering up to the Kahler degrees of freedom left to be fixed in the problem. Here, we discuss the general construction of Type IIB Standard Model flux vacua in which multiple branes participate in brane recombination in the hidden sector. We present several models with 4, 5 and 10 branes in a stack. They are complete with Pati-Salam gauge group, Standard Model chiral matter, and a hidden sector that combines with nonzero flux to satisfy RR tadpole constraints. We also illustrate a puzzle: within the 4-brane recombination approach, we are unable to find a formal cutoff on the number of Standard Model flux vacua. Nevertheless, we show that phenomenological considerations are sure to cut off the number of vacua, albeit at an extraordinarily large value. We comment on the possibility that more formal constraints could further reduce the number of vacua.