Integral cubic form of 5D minimal supergravities and non-perturbative anomalies in 6D (1,0) theories

[摘要] A five-dimensional minimal supergravity theory coupled to vector and hypermultiplets is specified by a set of trilinear couplings, given by an intersection form CIJK, and gravitational couplings specified by an integer-valued vector aI and is consistent when these data define an integral cubic form. For every Calabi-Yau threefold reduction of M-theory, this condition is satisfied automatically. Via suitable redefinitions of the basis of 5D vectors, this is also shown to be the case for the circle reductions of six-dimensional anomaly-free (1,0) theories. When the 6D theory has a ℤk gauge symmetry, we point out that the consistency of the circle reduction with nontrivial ℤk holonomy is closely related to 6D constraints derived by Monnier and Moore. These constraints are extended to semidirect products with continuous gauge groups ℤk ⋉ G and CHL-like circle compactifications. When ℤk acts on anti-self-dual tensor fields of 6D supergravity there should be a nontrivial action of holonomy on the topological Green-Schwarz terms.

[发布日期] 2026-09-03

[关键词] Anomalies in Field and String Theories;F-Theory;Supersymmetry and Duality