Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity

TL;DR

This paper demonstrates how combining specific topological quantum field theories in 8 dimensions can reproduce N=2 supergravity and its lift to 11-dimensional supergravity, highlighting the role of topological symmetries in supersymmetry origins.

Contribution

It shows that combining TQFTs with different gauge fields yields N=2 D=8 supergravity and its lift to D=11, extending previous work on N=1 supergravity from TQFTs.

Findings

N=2 D=8 supergravity derived from combined TQFTs

Lift to N=1 D=11 supergravity via higher-dimensional TQFTs

Topological symmetry as origin of local supersymmetry

Abstract

In a previous work, it was shown that the 8-dimensional topological quantum field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1 D = 8 supergravity. It is shown here that, the combination of this TQFT with that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated dimensional reduction of N = 1 D = 11 supergravity. Our construction holds for 8-dimensional manifolds with Spin(7) \subset SO(8) holonomy. We suggest that the origin of local Poincare supersymmetry is the gravitational topological symmetry. We indicate a mechanism for the lift of the TQFT in higher dimensions, which generates Chern-Simons couplings.