New supersymmetric index of heterotic compactifications with torsion

Abstract

We compute the new supersymmetric index of a large class of N=2 heterotic compactifications with torsion, corresponding to principal two-torus bundles over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2) gauged linear sigma-model with torsion, we use supersymmetric localization techniques to provide an explicit expression of the index as a sum over the Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a geometrical formula that gives the new supersymmetric index in terms of bundle data, regardless of any particular choice of underlying two-dimensional theory.Comment: 53 pages. Version 2 to be published in JHEP: added proof of the geometrical formula for the quartic, few minor clarifications and typos correcte

From 6D superconformal field theories to dynamic gauged linear sigma models

“…The result is that such a gauge theory may a priori correspond to several distinct SCFTs, labelled by the choice of branch. 6 In addition, there are also a number of interesting examples of (2, 2) and (0, 2) abelian gauge theories with dynamical Fayet-Iliopoulos and θ-angle terms, for instance references [69][70][71][72][73][74].…”

Threshold corrections in heterotic flux compactifications

“…In this work, we have computed the one-loop threshold corrections to the gauge and gravitational couplings in a large class of N = 2 heterotic compactifications on non-Kähler manifolds with three-form flux. We have obtained the result from the new supersymmetric index that was computed in [10,11].…”

“…For the N = 2 torsional compactifications of interest, the new supersymmetric index was computed in [10], using a purposely designed gauged linear sigma model [7] and supersymmetric localization of the path integral [32]. A main difference with the conventional K3 × T 2 compactifications is that both the complex structure and complexified Kähler moduli of the two-torus fiber are now generically quantized.…”

“…The new supersymmetric index (2.3) was then computed in terms of this data in [10,11]. First, the dressed elliptic genus (2.6) can be written as a sum of three terms in the following way:…”

“…Localization techniques were then used by two of the present authors to compute the new supersymmetric index [10,11], which is, in the context of heterotic N = 2 compactifications, the building block that is used to compute the threshold corrections to the BPS-saturated couplings in the low energy four-dimensional N = 2 supergravity action [12].…”