Infinite number of MSSMs from heterotic line bundles?

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

“…In order to have a way of comparing the model building potential of the various heterotic theories on the various geometries, we have preformed computer-aided scans for all cases for a fixed period of time. The total model search duration seems to be arbitrarily chosen; indeed, as was pointed out in [56], there does not seem to be a clear-cut bound on the line bundle input data. Consequently, we arbitrarily constrained the duration of scans to the same period of time for each heterotic theory on the various geometries under consideration.…”

“…As emphasized in [56], there seems not to exist a clear bound for the range of the entries K ij left undetermined by the simultaneous solution of the Bianchi identities and the DUY equations. This range needs for sure to be at least such that the second Chern class contribution with mostly c 2i ≥ 0 can be compensated.…”

“…of four weeks was mostly dictated by our requirement to obtain representative statistical results and not by some upper bound on the total number of inequivalent GUT-like/MSSM-like models we were able to spot. Furthermore, as explained in [56] for smooth compactifications with line bundles there seems to be no clear theoretical bound on the total number of models supported on a given manifold inside the validity of the supergravity approximation. In that sense, we think that the very notion of exhaustive scans is not well-defined on those smooth manifolds and we have thus concentrated primarily on generic statistical findings.…”

Uncovering a Spinor-Vector Duality on a Resolved Orbifold

“…(For translations to other characterizations see e.g. [33].) Often it is convenient to split the line bundle vectors in contributions in the first and second E 8 as:…”

Taming Triangulation Dependence of T6/Z2xZ2 Resolutions

“…In particular, to exploit the richness of the moduli space beyond the target space singularities, these singularities need to be deformed and/or resolved to form smooth Calabi-Yau compactifications with vector bundles [18]. A variety of effective field theory and cohomology methods have been developed to study the resulting theories [19][20][21][22][23][24][25][26][27][28][29]. In particular, methods to resolve orbifold singularities using well-established toric geometry methodology have been worked out in many cases [30][31][32][33][34][35][36][37].…”