Modifying the Sum Over Topological Sectors and Constraints on Supergravity

TL;DR

This paper demonstrates how the sum over topological sectors in quantum field theory can be modified without altering local degrees of freedom, impacting the quantization of parameters in supergravity.

Contribution

It introduces a way to restrict the sum over instantons, affecting the understanding of topological sums and parameter quantization in supergravity theories.

Findings

Sum over instantons can be restricted without changing local degrees of freedom.

FI-terms and Kahler forms are quantized in supergravity.

Provides a new derivation of linearized supergravity results.

Abstract

The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual theta-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kahler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.