Janus solutions in six-dimensional gauged supergravity

TL;DR

This paper explores supersymmetric domain wall solutions in six-dimensional gauged supergravity, finding that regular Janus solutions exist under specific parameter conditions, providing insights into holographic duals of 5d superconformal defects.

Contribution

It demonstrates the existence of regular Janus solutions in 6D gauged supergravity with specific scalar profiles, extending the understanding of holographic duals to 5d superconformal defects.

Findings

Supersymmetric domain walls require non-trivial scalar profiles charged under SU(2).

Numerical solutions are mostly singular, but certain parameters yield regular Janus solutions.

Regular Janus solutions correspond to specific fine-tuned boundary conditions.

Abstract

Motivated by an analysis of the sub-superalgebras of the five-dimensional superconformal algebra $F(4)$, we search for the holographic duals to co-dimension one superconformal defects in 5d CFTs which have $SO(4,2) \oplus U(1)$ bosonic symmetry. In particular, we look for domain wall solutions to six-dimensional $F(4)$ gauged supergravity coupled to a single vector multiplet. It is found that supersymmetric domain wall solutions do not exist unless there is a non-trivial profile for one of the vector multiplet scalars which is charged under the gauged $SU(2)$ R-symmetry. This non-trivial profile breaks the $SU(2)$ to $U(1)$, thus matching expectations from the superalgebra analysis. A consistent set of BPS equations is then obtained and solved numerically. While the numerical solutions are generically singular and thought to be dual to boundary CFTs, it is found that for certain fine-tuned choices of parameters regular Janus solutions may be obtained.