Abstract
We obtain new constraints on the anomaly coefficients of 6D mathcal{N}=left(1,0right) supergravity theories using local and global anomaly cancellation conditions. We show how these constraints can be strengthened if we assume that the theory is well-defined on any spin space-time with an arbitrary gauge bundle. We distinguish the constraints depending on the gauge algebra only from those depending on the global structure of the gauge group. Our main constraint states that the coefficients of the anomaly polynomial for the gauge group G should be an element of 2H4(BG; ℤ) ⊗ ΛS where ΛS is the unimodular string charge lattice. We show that the constraints in their strongest form are realized in F-theory compactifications. In the process, we identify the cocharacter lattice, which determines the global structure of the gauge group, within the homology lattice of the compactification manifold.
Highlights
A long-standing question is whether all consistent quantum gravity theories are string theories
We note that all non-trivial six-dimensional SCFTs with N = (1, 0) supersymmetry constructed in F-theory have a tensor branch, whose effective theory can be described in terms of the massless multiplets reviewed [47,48,49,50]
We do not know whether there are lowenergy constraints in six-dimensional supergravity imposing this constraint on the gravitational anomaly coefficient
Summary
A long-standing question is whether all consistent quantum gravity theories are string theories. We use local and global [16, 26] anomaly cancellation, as well as the quantization of the string charges, to derive new constraints on the anomaly coefficients of six-dimensional supergravity theories. The string charge quantization condition is used along with the assumption that all spin spacetime manifolds and all gauge bundles should be included in the “path integral” of the supergravity theory This assumption can be seen as a strong version of the completeness hypothesis of [27,28,29], which states that all charges allowed by Dirac quantization are realized in a consistent quantum gravity theory.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
