Are Moduli Vacuum Expectation Values or Parameters?

TL;DR

This paper proposes a method to distinguish different moduli vacuum expectation values from parameters by using black hole experiments, challenging previous views and suggesting that different moduli can correspond to different vacua.

Contribution

It introduces a new perspective on moduli as vacuum expectation values by using black hole experiments to differentiate vacua in string theory.

Findings

Black hole experiments can distinguish different moduli vacua.

Moduli values can vary over space, affecting observable spectra.

Different asymptotic moduli values can correspond to different vacua.

Abstract

Banks has argued that the moduli of string theory are not vacuum expectation values but parameters. We offer a different perspective on this question. Given two different points P and Q in the moduli space, we shall regard them as different vacua of the same underlying theory if in a theory where the asymptotic values of the moduli correspond to the point P, we can perform an experiment that can determine the spectrum and S-matrix of a theory where the asymptotic values of the moduli correspond to the point Q. We argue that in asymptotically flat space-time, this can be achieved by taking a charged black hole in the limit of large mass and charges. In this limit the local geometry at any point outside the horizon is indistinguishable from flat space-time. However the moduli vary slowly over the entire region so that their values at faraway points can differ by order unity. Therefore, by sending out experimental teams to different regions outside the horizon, an asymptotic observer can measure the spectrum and S-matrix for different values of the moduli.