Exploring 6D origins of 5D supergravities with Chern-Simons terms

TL;DR

The paper investigates whether five-dimensional supergravity theories with Abelian vectors and ungauged scalars can originate from circle compactifications of anomaly-free six-dimensional theories with $ (1,0) $ or $ (2,0) $ supersymmetry. It argues that classical and one-loop Chern-Simons terms encode the essential information relating 5D couplings to six-dimensional anomaly data, enabling testable necessary conditions for lifts. For the $\mathcal{N}=2$ case, the authors derive gravitational anomaly constraints in terms of CS coefficients: $24\, k_0 = - a^\alpha \Omega_{\alpha\beta} a^\beta = T-9$ and $24\, \kappa_0 = a^\alpha \Omega_{\alpha\beta} a^\beta + 3 = 12 - T$. In the $\mathcal{N}=4$ case, a lift to Abelian $ (2,0) $ requires $T=21$ and $\kappa_0 = 1/4$, reflecting a purely one-loop origin for the gravitational CS term. Overall, the work provides a first systematic framework to assess the six-dimensional origin of 5D theories via CS terms, while outlining paths to extend the analysis to non-Abelian $(2,0)$ theories and other dimensional reductions.

Abstract

We consider five-dimensional supergravity theories with eight or sixteen supercharges with Abelian vector fields and ungauged scalars. We address the question under which conditions these theories can be interpreted as effective low energy descriptions of circle reductions of anomaly free six-dimensional theories with (1,0) or (2,0) supersymmetry. We argue that classical and one-loop gauge- and gravitational Chern-Simons terms are instrumental for this question.

Figures (1)

• Figure 1: Five dimensional effective low-energy theories coupled to gravity which arise through compactification of anomaly-free six-dimensional theories form a subset of all apparently quantum-consistent theories.