Signature reversal invariance

TL;DR

This paper explores the signature reversal symmetry in various theories, revealing conditions under which it holds in chiral, Yang-Mills, and gravitational theories across different spacetime dimensions.

Contribution

It identifies specific dimensional and signature conditions for signature reversal invariance in chiral, Yang-Mills, and gravitational theories, clarifying its implications for supergravity and compactification.

Findings

Signature reversal symmetry exists only for certain dimensions and signatures.

Super Yang-Mills theories in 10D are not invariant under this symmetry.

In 10D supergravity, the symmetry applies to Type IIB but not Type IIA.

Abstract

We consider the signature reversing transformation of the metric tensor g_ab goes to -g_ab induced by the chiral transformation of the curved space gamma matrices gamma_a goes to gamma gamma_a in spacetimes with signature (S,T), which also induces a (-1)^T spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with S-T= 4k, with k integer. (2) Yang-Mills theories require dimensions D=4k with T even for which even rank antisymmentric tensor field strengths and mass terms are also allowed. For example, D=10 super Yang-Mills is ruled out. (3) Gravititational theories require dimensions D=4k+2 with T odd, for which the symmetry is preserved by coupling to odd rank field strengths. In D=10, for example, it is a symmetry of N=1 and Type IIB supergravity but not Type IIA. A cosmological term and also mass terms are forbidden but non-minimal R phi^2 coupling is permitted. (4) Spontaneous compactification from D=4k+2 leads to interesting but different symmetries in lower dimensions such as D=4, so Yang-Mills terms, Kaluza-Klein masses and a cosmological constant may then appear. As a well-known example, IIB permits AdS_5 x S^5.