Unitarity of strings and non-compact Hermitian symmetric spaces

Details Unitarity of strings and non-compact Hermitian symmetric spaces Unitarity of strings and non-compact Hermitian symmetric spaces

1998-06-05

arxiv.org/abs/hep-th/9806049v2

Phys.Lett. B435 (1998) 331-336

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex, two typos corrected and minor changes of wording. The final version is accepted for publication in Phys.Lett.

Scientific paper

10.1016/S0370-2693(98)00816-8

If G is a simple non-compact Lie group, with K its maximal compact subgroup, such that K contains a one-dimensional center C, then the coset space G/K is an Hermitian symmetric non-compact space. SL(2,R)/U(1) is the simplest example of such a space. It is only when G/K is an Hermitian symmetric space that there exists unitary discrete representations of G. We will here study string theories defined as G/K', K'=K/C, WZNW models. We will establish unitarity for such string theories for certain discrete representations. This proof generalizes earlier results on SL(2,R), which is the simplest example of this class of theories. We will also prove unitarity of G/K conformal field theories generalizing results for SL(2,R)/U(1). We will show that the physical space of states lie in the subspace of the G/K state space.

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