Quantum Symmetries and Stringy Instantons

TL;DR

This paper investigates how string theory configurations preserve quantum symmetries in ext{LG} orbifolds despite instanton effects, revealing cancellations that impose new constraints on spectra and moduli mixing.

Contribution

It demonstrates that string theory instanton configurations preserve quantum symmetries through non-trivial cancellations, leading to new spectral constraints and moduli mixing conditions.

Findings

Instanton effects are canceled by other configurations in string theory.

Quantum symmetry is preserved in ext{LG} orbifolds due to these cancellations.

Constraints on spectra and moduli mixing are derived from these effects.

Abstract

The quantum symmetry of many \LG\ orbifolds appears to be broken by Yang-Mills instantons. However, isolated Yang-Mills instantons are not solutions of string theory: They must be accompanied by gauge anti-instantons, gravitational instantons, or topologically non-trivial configurations of the $H$ field. We check that the configurations permitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effects due to the various types of instantons. These cancellations indicate new constraints on \LG\ orbifold spectra and require that the dilaton modulus mix with the twisted moduli in some \LG\ compactifications. We point out that one can find similar constraints at all fixed points of the modular group of the moduli space of vacua.