MSSM GUT String Vacua, Split Supersymmetry and Fluxes

TL;DR

This work constructs explicit non-supersymmetric string vacua in toroidal IIA orientifolds with intersecting D6-branes that fully cancel RR tadpoles while preserving MSSM-like chiral content within a Pati-Salam (and later Left-Right) gauge structure. A distinct N′=1 messenger sector is added to mediate SUSY breaking string-theoretically, yielding a gauge-mediated, split-SUSY–style spectrum at a high scale with universal scalar masses and a potentially Higgsino- or Higgsino–Wino–like LSP. The authors demonstrate gauge coupling unification at the string scale M_s ≈ 2.04 × 10^{16} GeV (sin^2(θ_W)_{M_s} = 3/8) and show how RR, NS, and metric fluxes can stabilize many moduli, fixing real parts of S, U, and T while leaving certain axionic components unfixed. The framework integrates flux-induced moduli stabilization with a realistic MSSM sector, ensuring proton stability and a mechanism for lifting all exotics through Yukawa couplings and SS/deformations, thus providing a concrete, string-theoretic realization of a split MSSM landscape.

Abstract

We show that previous proposals to accommodate the MSSM with string theory N=0 non-supersymmetric compactifications coming from intersecting D6-branes may be made fully consistent with the cancellation of RR tadpoles. In this respect we present the first examples of non-supersymmetric string Pati-Salam model vacua with starting observable gauge group $SU(4)_c \t SU(2)_L \t SU(2)_R$ (SU(2) from Sp(2)'s) that accommodate the spectrum of the 3 generation MSSM with a gauged baryon number with all extra exotics (either chiral or non-chiral) becoming massive and all MSSM Yukawas realized. The N=1 supersymmetry of the visible sector is broken by an extra supersymmetry messenger breaking sector that preserves a different N$^{\prime}$=1 susy, exhibiting the first examples of stringy gauge mediated models. Due to the high scale of the models, these models are also the first realistic examples of carriers of stringy split supersymmetry exhibiting universal slepton/squark masses, massive string scale gauginos, {\em unification of SU(3), SU(2) gauge couplings at} $2.04 \times 10^{16}$ GeV, a stable proton and the appearance of a landscape split SM with chiral fermions and only Higgsinos below the scale of susy breaking; the LSP neutralino candidate could also be only Higgsino or Higgsino-Wino mixture. We also add RR, NS and metric fluxes as every intersecting D-brane model without fluxes can be accommodated in the presence of fluxes. The addition of metric fluxes in the toroidal lattice also stabilizes the expected real parts of all in AdS closed string moduli (modulo D-term affects), leaving unfixed only the imaginary parts of Kähler moduli.