Global anomalies in 8d supergravity

Abstract

We study gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds. Possible global gauge anomalies are classified by spin bordism groups Ω spin 9 (BG) which we determine by spectral sequence techniques, and we also identify their explicit generator manifolds. It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in 8d N = 1 supergravity theory, have anomalies. We discuss how a 2-form field, which also appears in supergravity, produces anomalies which cancel against these fermion anomalies in a certain class of supergravity theories. In another class of theories, the anomaly of the gravitino is not cancelled by the 2-form field, but by topological degrees of freedom. It gives a restriction on the topology of spacetime manifolds which is not visible at the level of differential-form analysis.

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

“…The anomaly theory A d+1 has been significantly developed and applied in recent years in the high energy, condensed matter, and mathematics communities. This includes results for familiar continuous global symmetries [214][215][216][217][218][219][220], discrete global symmetries [221][222][223][224][225]56,[226][227][228][229][230], higher-form and higher-group symmetries [52,54,58,59,231,74], and subsystem symmetries [144,147,148], families of quantum field theories [232][233][234][235][236][237][238][239][240][241], as well as structural developments [242-244, 40, 99, 245-249, 55, 250, 251].…”