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.
Monnier and G.W
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abstract
We construct the Green-Schwarz terms of six-dimensional supergravity theories on spacetimes with non-trivial topology and gauge bundle. We prove the cancellation of all global gauge and gravitational anomalies for theories with gauge groups given by products of $U(n)$, $SU(n)$ and $Sp(n)$ factors, as well as for $E_8$. For other gauge groups, anomaly cancellation is equivalent to the triviality of a certain 7-dimensional spin topological field theory. We show in the case of a finite Abelian gauge group that there are residual global anomalies imposing constraints on the 6d supergravity. These constraints are compatible with the known F-theory models. Interestingly, our construction requires that the gravitational anomaly coefficient of the 6d supergravity theory is a characteristic element of the lattice of string charges, a fact true in six-dimensional F-theory compactifications but that until now was lacking a low-energy explanation. We also discover a new anomaly coefficient associated with a torsion characteristic class in theories with a disconnected gauge group.
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Eleven new anomaly-free 6D supergravity spectra with G_non-Abelian × U(1)_R are exhibited that satisfy Green-Schwarz factorization and global consistency conditions, together with lattice-embeddability theorems for the anomaly coefficients.
Upper bounds are placed on the order of enhanced discrete gauge symmetries in supersymmetric supergravity theories with 8 or more supercharges, with some bounds saturated by string theory examples.
Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.
citing papers explorer
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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.
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Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity
Eleven new anomaly-free 6D supergravity spectra with G_non-Abelian × U(1)_R are exhibited that satisfy Green-Schwarz factorization and global consistency conditions, together with lattice-embeddability theorems for the anomaly coefficients.
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Bounds on Discrete Gauge Symmetries in Supergravity
Upper bounds are placed on the order of enhanced discrete gauge symmetries in supersymmetric supergravity theories with 8 or more supercharges, with some bounds saturated by string theory examples.
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Dai-Freed anomalies and level matching in heterotic asymmetric orbifolds
Dai-Freed anomalies for chiral fermion actions in heterotic asymmetric orbifolds recover the level-matching constraints plus mod-2 conditions for even m.