Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory

TL;DR

This paper explores how string theory moduli spaces can be used to construct classical solutions with arbitrary asymptotic values, implying that observable data at infinity do not uniquely determine the moduli's asymptotic behavior.

Contribution

It demonstrates that in certain string theories, the asymptotic moduli values can be arbitrarily chosen without affecting the local physics, challenging the notion of unique boundary conditions.

Findings

Classical solutions can interpolate between different asymptotic moduli values.

Observables at finite times cannot determine asymptotic moduli values.

Implications for holography in flat space-time are discussed.

Abstract

N=2, 4 and 8 supersymmetric string theories in four dimensional flat space-time have moduli space of vacua. We argue that starting from a theory where the moduli approach a particular moduli space point A at infinity, we can construct a classical solution that contains an arbitrarily large space-time region where the moduli take values corresponding to any other moduli space point B of our choice to any desired accuracy. Therefore the observables of a theory with a given set of asymptotic values of the moduli will have complete information on the observables for any other asymptotic values of the moduli. Also it is physically impossible for any experiment, performed over a finite time, to determine the asymptotic values of the moduli. We point out the difference between asymptotically flat space-time and asymptotically AdS space-time in this regard and discuss the possible implication of these results for holographic duals of string theories in flat space-time. For N=2 supersymmetric theories, A and B could correspond to compactifications on topologically distinct Calabi-Yau manifolds related by flop or conifold transitions.