AdS solutions in gauge supergravities and the global anomaly for the product of complex two-cycles

A. A. Bytsenko, E. Elizalde

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    2 Citations (Scopus)

    Abstract

    Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of solutions is proposed, the Hilbert modular varieties, which consist of the 2n-fold product of the two-spaces Hn/Γ (where Hn denotes the product of n upper half-planes, H2, equipped with the co-compact action of Γ ⊂ SL(2,R)n) and (Hn)∗/Γ (where (H2)∗ = H2 ∪ {cusp of Γ } and Γ is a congruence subgroup of SL(2,R)n). The cohomology groups of the Hilbert variety, which inherit a Hodge structure (in the sense of Deligne), are analyzed, as well as bifiltered sequences, weight and Hodge filtrations, and it is argued that the torsion part of the cuspidal cohomology is involved in the global anomaly condition. Indeed, in the presence of the cuspidal part, all cohomology classes can be mapped to the boundary of the space and the cuspidal contribution can be involved in the global anomaly condition.
    Original languageEnglish
    Article number1592
    JournalEuropean Physical Journal C
    Volume71
    Issue number3
    DOIs
    Publication statusPublished - 1 Jan 2011

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