Wednesday, June 28, 2023
10:00 a.m. (sharp)
Zoom Web Conference
PhD Candidate: Surya Raghavendran
Co-Supervisors: Kevin Costello/Marco Gualtieri
Thesis title: Twisted eleven-dimensional supergravity and exceptional
simple infinite dimensional super-Lie algebras
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We study a class of formal moduli problems associated to eleven-manifolds with a rank 6 transversely holomorphic foliation and a transverse Calabi-Yau structure. On R×C5, the (−1)-shifted tangent complex of this formal moduli problem is L∞-equivalent to a Lie-2 extension of an infinite dimensional exceptional simple super-Lie algebra called E(5|10). In the first part of the thesis, we equip this formal moduli problem with the structure of a perturbative classical field theory in the Batalin- Vilkovisky formalism. Conjecturally, this theory describes the minimal twist of eleven-dimensional supergravity. We present strands of evidence for this conjecture by computing dimensional reductions and comparing with expected descriptions of twists of supergravity in lower dimensions, and by identifying the residual symmetries of the putative twist of eleven-dimensional supergravity within the symmetries of our theory.
In the second half of the thesis, we construct particular backgrounds for our theory which we conjecture are twisted avatars of the AdS4×S7 and AdS7×S4 backgrounds of eleven-dimensional supergravity. To justify this conjecture, we study spaces of supergravity states on these backgrounds. We find that their characters match with prior expressions enumerating multi-gravitons in AdS4×S7 and AdS7×S4 respectively, and also admit specializations recovering generating functions of representation theoretic and enumerative significance, such as the MacMahon function. We study a decomposition of the state spaces we construct that exhibits them as direct sums of modules for two other exceptional linearly compact super-Lie algebras, E(1|6) and E(3|6) respectively. We conclude with some speculations about how our results can be used as input for holographic techniques.
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The draft of the thesis can be found here: main
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