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Time-like T-duality algebra
High Energy Physics - Theory · Submitted 22 Apr 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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)}. | background 1.00 | 0.09 | 0.15 | asserted 1.00 |
| s1 | We discuss how to compute the group H_n. | contribution 0.88 | 0.73 | 0.06 | asserted 0.74 |
| s2 | 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. | method 0.95 | 0.23 | 0.08 | asserted 0.98 |
| s3 | A few groups that have not appeared in the literature are found. | result 0.87 | 0.93 | 0.11 | asserted 1.00 |
| s4 | For n=9,10,11 we compute and describe the relevant real forms of E_n and H_n. | contribution 0.86 | 0.94 | 0.11 | asserted 1.00 |
| s5 | A given H_n can correspond to multiple signatures for the compact torus. | result 0.96 | 0.63 | 0.08 | asserted 0.95 |
| s6 | 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. | contribution 0.89 | 0.96 | 0.45 | asserted 1.00 |
| s7 | 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. | contribution 0.97 | 0.89 | 0.06 | asserted 0.99 |
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Original 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.
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Let us comment more on this issue.[See [ref] for more details on the generalised metric with the Lorentzian signature.]
Non-abelian U-duality at work · Spacetime signature · 0.93
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