ar X iv : h ep - t h / 06 05 27 3 v 3 2 3 O ct 2 00 6 hep - th / 0605273 Signature reversal invariance

We consider the signature reversing transformation of the metric tensor g µν → −g µν induced by the chiral transformation of the curved space gamma matrices γ µ→ γγ µ 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 Rφ 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 × S 5 .