CPT Invariance of String Models in a Minkowski Background

We study the space-time CPT properties of string theories formulated in a flat Minkowski background of even dimension. We define CPT as a world-sheet transformation acting on the vertex operators and we prove the CPT invariance of the string S-matrix elements. Some related issues, including the connection between spin and statistics of physical string states, are also considered. † Supported by a MURST Fellowship. ‡ Supported by the Carlsberg Foundation. Introduction and Summary Recently there has been some interest in the question of possible CPT nonconservation in string theory. Indeed, some mechanisms have been proposed that would lead to CPT-breaking effects that might be detected in the next generation of experiments [1,2]. If observed, these effects could give the first experimental evidence of the existence or non-existence of strings. Accordingly the issue of CPT invariance in string theory is quite interesting both from a theoretical and an experimental point of view. From a theoretical point of view, not too much is known and published on the space-time CPT properties of string theory. Sonoda [3] discussed and proved the space-time CPT theorem at the level of string perturbation theory for ten-dimensional heterotic strings in a Minkowski background. Kostelecky and Potting [1] proved the dynamical CPT invariance of the open bosonic and super string field theories, formulated in flat backgrounds –but they also suggested a method whereby CPT might be broken spontaneously, based on the possibility of a CPT non-invariant ground state. For more complicated string models no general analysis has appeared. With this paper, we would therefore like to start a detailed investigation of the space-time CPT properties of general string theories. Should we always expect some kind of space-time CPT theorem to hold? Let us start by reviewing the situation in field theory. The CPT theorem [4,5,6,7] 1 asserts that any quantum field theory is invariant under CPT transformations assuming that it satisfies the following very mild assumptions [6]: a) Lorentz invariance, b) The energy is positive definite and there exists a Poincaré-invariant vacuum, unique up to a phase factor, 1 For a general discussion of the CPT theorem in field theory see for example ref. [8].