Poincare Duality and G+++ algebra's

TL;DR

This paper explores how infinite-dimensional G+++ algebras encode dualities in theories with gravity, clarifying the role of Poincare duality and Weyl invariance in understanding these symmetries across different spacetime signatures.

Contribution

It demonstrates that Poincare duality constraints can be algebraically encoded within G+++ algebras and introduces Weyl-invariant quantities for analyzing these symmetries.

Findings

Poincare duality leads to algebraic constraints invariant under Weyl groups.

Weyl-invariant quantities can extract information from G+++ algebras.

Dualities in theories with gravity are captured by properties of G+++ algebras.

Abstract

Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of ``exotic dualities''. Upon inclusion of time-like directions in the reductions one can dualize to theories in different space-time signatures. We clarify the nature of these dualities and show that they are well captured by the properties of infinite-dimensional symmetry algebra's (G+++ algebra's), but only after taking into account that the realization of Poincare duality leads to restrictions on the denominator subalgebra appearing in the non-linear realization. The correct realization of Poincare duality can be encoded in a simple algebraic constraint, that is invariant under the Weyl-group of the G+++ algebra, and therefore independent of the detailed realization of the theory under consideration. We also construct other Weyl-invariant quantities that can be used to extract information from the G+++ algebra without fixing a level decomposition.