Quantum symmetries and exceptional collections

TL;DR

This paper explores the relationship between quantum symmetries in Calabi-Yau compactifications and D-brane monodromy identities, revealing that these identities often derive from a fundamental mathematical principle.

Contribution

It demonstrates that monodromy identities linked to quantum symmetries can be universally derived from a single mathematical statement across various Calabi-Yau models.

Findings

Monodromy identities follow from a unifying mathematical principle.

Quantum symmetries impose specific constraints on D-brane monodromies.

The approach applies to both local and compact Calabi-Yau examples.

Abstract

We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the Z_5 symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.