Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
The M-theory 3-form and E8 gauge theory
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abstract
We give a precise formulation of the M-theory 3-form potential C in a fashion applicable to topologically nontrivial situations. In our model the 3-form is related to the Chern-Simons form of an E8 gauge field. This leads to a precise version of the Chern-Simons interaction of 11-dimensional supergravity on manifolds with and without boundary. As an application of the formalism we give a formula for the electric C-field charge, as an integral cohomology class, induced by self-interactions of the 3-form and by gravity. As further applications, we identify the M-theory Chern-Simons term as a cubic refinement of a trilinear form, we clarify the physical nature of Witten's global anomaly for 5-brane partition functions, we clarify the relation of M-theory flux quantization to K-theoretic quantization of RR charge, and we indicate how the formalism can be applied to heterotic M-theory.
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Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
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Symmetry TFTs from String Theory
Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.