Kac-Moody and Borcherds symmetries of six-dimensional chiral supergravity

Abstract

Abstract:We investigate the conjectured infinite-dimensional hidden symmetries of sixdimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the F 4,4 symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space F ++ 4,4 /K(F ++ 4,4 ) using the level decomposition associated with the subalgebra gl(5) ⊕ sl(2) of F ++ 4,4 and show their equivalence with the bosonic equations of motion of six-dimensional chiral supergravity up to the level where the dual graviton appears. In particular, the self-duality condition on the chiral 2-form is automatically implemented in the sense that no dual potential appears for that 2-form, in contradistinction with what occurs for the non chiral p-forms. (ii) Second, we describe the p-form hierarchy of the model in terms of its V -duality Borcherds superalgebra, of which we compute the Cartan matrix.

Notes on generalized global symmetries in QFT

“…Examples of hyperbolic Kac‐Moody algebra actions on supergravity theories are discussed in a number of references including e.g . .…”

Forms and algebras in (half-)maximal supergravity theories

“…Another example is chiral supergravity in D " 6 coupled to two vector multiplets and two tensor multiplets, recently studied in[39].…”