Quantum Background Independence In String Theory

TL;DR

This paper explores the concept of background independence in string theory, revealing that the holomorphic anomaly provides a quantum perspective where the exact partition function maintains background independence in an auxiliary quantum space.

Contribution

It offers a novel interpretation of the holomorphic anomaly as a quantum form of background independence in string theory, connecting anomalies to an auxiliary quantum Hilbert space.

Findings

Holomorphic anomaly explains background independence issues.

Exact partition function interpreted as a state in a quantum Hilbert space.

Background independence holds at the exact level, not perturbatively.

Abstract

Not only in physical string theories, but also in some highly simplified situations, background independence has been difficult to understand. It is argued that the ``holomorphic anomaly'' of Bershadsky, Cecotti, Ooguri, and Vafa gives a fundamental explanation of some of the problems. Moreover, their anomaly equation can be interpreted in terms of a rather peculiar quantum version of background independence: in systems afflicted by the anomaly, background independence does not hold order by order in perturbation theory, but the exact partition function as a function of the coupling constants has a background independent interpretation as a state in an auxiliary quantum Hilbert space. The significance of this auxiliary space is otherwise unknown.