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.
Highlights
Manifold and the stable holomorphic vector bundle
As usual going to Wess-Zumino gauge is convenient in order to exhibit the physical degrees of freedom; in the present situation one should not forget that the theory is not classically gauge invariant, such gauge choice only makes sense in the path integral of the full quantum theory, including the base gauged linear sigma-models (GLSMs), as will be clear below when supersymmetric localization will be put into action
Our goal is to extend these results to the new supersymmetric index of Fu-Yau compactifications using the torsion gauged linear sigma-models
Summary
We review the construction of torsion gauged linear sigma-models proposed in [7]. These are gauge theories in two-dimensions with (0, 2) supersymmetry which are expected to flow in the infrared to (0, 2) non-linear sigma-models whose target space corresponds to Fu-Yau compactifications; a brief presentation of these non-Kahler heterotic solutions is given in appendix C. One cancels instead the anomalous variation of the functional measure against a classically non-gauge-invariant Lagrangian for a torsion multiplet modeling the T 2 principal bundle, thereby realizing the Green-Schwarz mechanism on the worldsheet
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