The R-map and the Coupling of N=2 Tensor Multiplets in 5 and 4 Dimensions

TL;DR

This paper explores the dimensional reduction of 5D N=2 supergravity theories with tensor multiplets to 4D, revealing new dualities, gauge group structures, and potential for stable de Sitter vacua.

Contribution

It provides a detailed analysis of the gauge group structures and dualities in reduced theories, including infinite families and topological terms, advancing understanding of supergravity compactifications.

Findings

4D theories involve first order interactions with mass terms.

Existence of infinite families with specific gauge group structures.

Scalar potentials suggest ingredients for stable de Sitter ground states.

Abstract

We study the dimensional reduction of five dimensional N=2 Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor multiplets. The resulting 4D theories involve first order interactions among tensor and vector fields with mass terms. If the 5D gauge group, K, does not mix the 5D tensor and vector fields, the 4D tensor fields can be integrated out in favor of 4D vector fields and the resulting theory is dual to a standard 4D YMESGT. The gauge group has a block diagonal symplectic embedding and is a semi-direct product of the 5D gauge group K with a Heisenberg group of dimension (2P+1), where 2P is the number of tensor fields in five dimensions. There exists an infinite family of theories, thus obtained, whose gauge groups are pp-wave contractions of the simple noncompact groups of type SO*(2M). If, on the other hand, the 5D gauge group does mix the 5D tensor and vector fields, the resulting 4D theory is dual to a 4D YMESGT whose gauge group does, in general,NOT have a block diagonal symplectic embedding and involves additional topological terms. The scalar potentials of the dimensionally reduced theories naturally have some of the ingredients that were found necessary for stable de Sitter ground states. We comment on the relation between the known 5D and 4D, N=2 supergravities with stable de Sitter ground states.