Time-like T-duality algebra

Abstract

When compactifying M- or type II string-theories on tori of indefinite space-time signature, their low energy theories involve sigma models on E_{n(n)}/H_n, where H_n is a not necessarily compact subgroup of E_{n(n)} whose complexification is identical to the complexification of the maximal compact subgroup of E_{n(n)}. We discuss how to compute the group H_n. For finite dimensional E_{n(n)}, a formula derived from the theory of real forms of E_n algebra's gives the possible groups immediately. A few groups that have not appeared in the literature are found. For n=9,10,11 we compute and describe the relevant real forms of E_n and H_n. A given H_n can correspond to multiple signatures for the compact torus. We compute the groups H_n for all compactifications of M-, M*-, and M'-theories, and type II-, II*- and II'-theories on tori of arbitrary signature, and collect them in tables that outline the dualities between them. In an appendix we list cosets G/H, with G split and H a subgroup of G, that are relevant to timelike toroidal compactifications and oxidation of theories with enhanced symmetries.

LaTeX, 37 pages, 1 eps-figure, uses JHEP.cls; v2. corrected typo's in tables 16 and 17, minor changes to text

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Cited by in corpus (10)

• M-theory and Type IIB from a Duality Manifest Action
• An E9 multiplet of BPS states
• Supersymmetric Domain Walls
• Non-abelian U-duality at work
• Dualities and signatures of G++ invariant theories
• Poincare Duality and G+++ algebra's
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• M-Theory Solutions in Multiple Signatures from E_11
• Timelike duality, $M^{\prime }$-theory and an exotic form of the Englert solution