Transitions in the web of heterotic vacua

Abstract

We analyze transitions between heterotic vacua with distinct gauge bundles using two complementary methods -the effective four-dimensional field theory and the corresponding geometry. From the viewpoint of effective field theory, such transitions occur between flat directions of the potential energy associated with heterotic stability walls. Geometrically, this branch structure corresponds to smooth deformations of the gauge bundle coupled to the chamber structure of Kähler moduli space. We demonstrate how such transitions can change important properties of the effective theory, including the gauge symmetry and the massless spectrum. Geometrically, this study is divided into deformations of the vector bundle which preserve the rank of the gauge bundle and those which change the rank. In the latter case, our results provide explicit solutions to a class of Li-Yau type deformation problems. Finally, we use the framework of stability walls and their effective theory to study Donaldson-Thomas invariants on Calabi-Yau threefolds.

The moduli space of heterotic line bundle models: a case study for the tetra-quadric

“…For our example model, we will consider both approaches as well as the relation between them. Similar studies have been undertaken in [15][16][17]. An important question in this context concerns the fate of the Higgs doublet pair.…”

The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications

“…If we change the Kähler class, it could be that no solution to this equation will exist. This is associated with the D-term breaking of supersymmetry at so-called stability walls, and was discussed [47] and in detail in recent work by the authors [48,49,50,51].…”

“…Previous work [46]- [51] investigated the constraints arising from g ab F ab = 0, the slope-stability condition [52] on V , and the conditions this places on the combined Kähler and vector bundle moduli spaces.…”

“…Of the three approaches to complex structure stabilization illustrated in Section 4, here we use the effective field theory [50,51] and geometric methods associated with the bundle (7.1). As in Section 4.3,…”

Matter in transition

“…It would be interesting to further explore the physical consequences of these massive abelian symmetries in the low-energy theory away from the stable degeneration limit. Particularly in 4D compactifications, it is expected that the discrete remnants of such massive symmetries can significantly affect the structure of the theory -including Yukawa couplings, Kähler potentials and the vacuum structure of the theory [50,[90][91][92][93].…”