Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms

TL;DR

This paper computes gauge threshold corrections in N=2 heterotic local models with flux, revealing their connection to mock modular forms and non-localized states, and explores implications for dual type I models.

Contribution

It introduces a novel analysis of gauge threshold corrections governed by mock modular forms in heterotic models with flux, including their dependence on moduli and duality implications.

Findings

Threshold corrections are governed by the non-holomorphic completion of the Appell-Lerch sum.

Non-localized bulk states contribute to non-holomorphic corrections.

Explicit moduli dependence of one-loop corrections is determined, with implications for dual models.

Abstract

We determine threshold corrections to the gauge couplings in local models of N=2 smooth heterotic compactifications with torsion, given by the direct product of a warped Eguchi-Hanson space and a two-torus, together with a line bundle. Using the worldsheet CFT description previously found and by suitably regularising the infinite target space volume divergence, we show that threshold corrections to the various gauge factors are governed by the non-holomorphic completion of the Appell-Lerch sum. While its holomorphic Mock-modular component captures the contribution of states that localise on the blown-up two-cycle, the non-holomorphic correction originates from non-localised bulk states. We infer from this analysis universality properties for N=2 heterotic local models with flux, based on target space modular invariance and the presence of such non-localised states. We finally determine the explicit dependence of these one-loop gauge threshold corrections on the moduli of the two-torus, and by S-duality we extract the corresponding string-loop and E1-instanton corrections to the Kaehler potential and gauge kinetic functions of the dual type I model. In both cases, the presence of non-localised bulk states brings about novel perturbative and non-perturbative corrections, some features of which can be interpreted in the light of analogous corrections to the effective theory in compact models.