String Theory and the CPT Theorem on the World-Sheet

TL;DR

This paper investigates the CPT theorem within two-dimensional conformal field theories on arbitrary Riemann surfaces, demonstrating its implications for string theory scattering matrices and extending known results to higher genus surfaces.

Contribution

It extends the CPT theorem to conformal field theories on arbitrary Riemann surfaces and links this to hermiticity properties of string scattering matrices at all loop orders.

Findings

CPT theorem holds on arbitrary Riemann surfaces.

String scattering T-matrix is formally hermitean at all loops.

Extension of the CPT theorem from sphere to higher genus surfaces.

Abstract

We study the CPT theorem for a two-dimensional conformal field theory on an arbitrary Riemann surface. On the sphere the theorem follows from the assumption that the correlation functions have standard hermiticity properties and are invariant under the transformation $z \rightarrow 1/z$. The theorem can then be extended to higher genus surfaces by sewing. We show that, as a consequence of the CPT theorem on the world-sheet, the scattering $T$-matrix in string theory is {\sl formally\/} hermitean at any loop order.