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Negative branes, supergroups and the signature of spacetime. (English) Zbl 1387.81311

Summary: We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0\(| N\)) supergroup theories are holographically dual to an exotic variant of type IIB string theory on \( {\mathrm{dS}}_{3,2}\times {\overline{\mathrm{S}}}^5 \), for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov’s instanton calculus, all of which agree, we derive the Seiberg-Witten curve for \( \mathcal{N}=2 \) SU(\(N | M\)) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E30 String and superstring theories in gravitational theory
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