Complete gauge threshold corrections for intersecting fractional D6-branes: The and Standard Models

Abstract

We perform a complete analysis of one-loop threshold corrections to the gauge couplings of fractional D6-branes. This includes besides SU(N) also symplectic, orthogonal and massless Abelian gauge factors and the full computation of contributions from discrete and continuous Wilson lines and brane displacements. Two classes of globally consistent supersymmetric compactifications with Standard Model spectra on T 6 /Z 6 and T 6 /Z ′ 6 are presented in detail with the latter exhibiting the potential of supersymmetry breaking via a hidden sector gaugino condensate. The T 6 /Z ′ 6 Standard Models are completely classified, and it turns out that out of 768 distinct D6-brane configurations only 16 different sets of massless spectra and ten distinct values of gauge couplings at one-loop arise. The gauge threshold corrections enhance the diversity to 196 nonequivalent models.

Rigid D6-branes on $ {{{{T^6}}} \left/ {{\left( {{Z_2} \times {Z_{2M}} \times \Omega \mathcal{R}} \right)}} \right.} $ with discrete torsion

“…More details on this expression can be found in appendix A.1 of [79] in the context of T 6 /Z 2N models. In order to compute the multiplicites of chiral antisymmetric and symmetric representations, one also needs the intersection number with the orientifold planes,…”

“…Details for T 6 /(Z 2 × Z 2M × ΩR) without and with discrete torsion are given in appendix B, where again the discussion follows the one for T 6 /Z 2N in [79].…”

“…In [68,69,79], two classes of supersymmetric models on aAB on T 6 /Z 6 were analysed with complex structure parameters ≡ √ 3 R 2 R 1 = 1 ω and ω = 1 for the models with hidden sectors and ω = 2 for the model without hidden sector. The representants per orbifold and orientifold orbit, as discussed at the end of section 5.1, are listed in table 29.…”

“…We can thus use the extensive inspection of gauge thresholds on T 6 /Z 2N performed in [79] to find beta function coefficients on T 6 /Z 2 × Z 2M without and with discrete torsion and compare with the field theoretic expression for the beta function coefficients…”

“…In the context of fractional D6-branes on T 6 /Z 2N backgrounds, a method of deriving the complete matter spectrum from the beta function coefficients, which are computed along with the gauge thresholds, 3 has been derived [79], on which we will heavily rely after appropriate modifications to T 6 /Z 2 × Z 2M . This method will in particular be used to confirm the absence of adjoint matter, i.e.…”