Linear Models for Flux Vacua

Abstract

We construct worldsheet descriptions of heterotic flux vacua as the IR limits of N = 2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz mechanism in which a doublet of axions cancels a oneloop gauge anomaly. Manifest (0, 2) supersymmetry and the compactness of the gauge theory instanton moduli space suggest that these models, which include Fu-Yau models, are stable against worldsheet instantons, implying that they, like Calabi-Yaus, may be smoothly extended to solutions of the exact beta functions. Since Fu-Yau compactifications are dual to KST-type flux compactifications, this provides a microscopic description of these IIB RR-flux vacua.

Local Heterotic Torsional Models

“…Alternatively, one would like to have a worldsheet conformal field theory description of the geometrical model. Such has been presented in [22] using the gauged linear sigma model formalism of [23].…”

Summing the instantons in half-twisted linear sigma models

“…The half-twisted correlators should still be amenable to solution via localization, and phenomenologically interesting examples should merely require a more involved notation and book-keeping. It is less clear how to apply our ideas to heterotic compactifications with torsion and non-Kähler target-space, but a careful study of the half-twisted theories based on the linear model constructed in [23] should be a useful first step.…”

Some recent advances in gauged linear sigma models

“…In the limit r ≫ 0, standard analyses imply that this is described at low energies by a nonlinear sigma model on P 3 [2,2]. In the opposite limit r ≪ 0, we have argued that it is described by a nonlinear sigma model on a branched double cover of CP 1 , branched over a degree four locus, which is another T 2 .…”

“…As our first example, let us analyze the GLSM for a complete intersection of two quadrics in CP 3 , denoted P 3 [2,2]. This is a two-torus T 2 , the simplest Calabi-Yau.…”

“…[2,3,4,5,6,7,8,9,10] and references therein) to new developments in Calabi-Yau compactifications, including realizations of non-complete-intersection target spaces [11,12,13,14,15], non-birational phases [11,12,15,16,17,18,19,20] (leading to modern conjectures that all phases of GLSM's are related by a new notion known as "homological projective duality" [17,18,19,20,21,22,23]), nonperturbative realizations of geometry [11,12,15,16,24,25,26], realizations of noncommutative resolutions [12,16,25,26], and localization techniques [27,28]. Those localization techniques have been applied to deduce new methods for computing Gromov-Witten invariants [24,29], computations of elliptic genera directly in GLSM's [30,31,…”