Gravity, Duality and Conformal Symmetry

TL;DR

This paper explores the possibility of a non-lagrangian 6D superconformal (4,0) theory as a strong coupling limit of 5D supergravity, examining BPS states in M-theory for evidence.

Contribution

It proposes a test for the existence of a (4,0) superconformal theory based on the presence of specific BPS states in M-theory compactifications.

Findings

Identifies BPS states as key indicators for the conjecture.

Suggests these states are related to gravitational instantons.

Provides a criterion to validate or falsify the conjecture.

Abstract

The (4,0) supermultiplet in 6 dimensions contains a 4th rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32+32 supersymmetries. Dimensional reduction on a circle gives the 5D N=8 supergravity multiplet, with the 4th rank tensor reducing to the graviton. If there is an interacting (4,0) theory it should reduce to the full N=8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual 2-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacting (4,0) superconformal theory arises from a strong coupling limit of 5D supergravity (suitably embedded in M-theory) describing M-theory at energies beyond the Planck scale. A key test for this is identified: M-theory toroidally compactified to 5D should have certain BPS states carrying a singlet central charge. These 1/2 BPS states are not related to any of the standard BPS states by dualities and do not correspond to non-singular soliton solutions -- they appear to correspond to singular solutions related to gravitational instantons. Such states are needed to provide the Kaluza-Klein modes for the compactified 6D theory. If there are no such states, then the conjecture is false, while the presence of such states would be strong indication that the conjecture could be true.