Holographic RG flows in six dimensional F(4) gauged supergravity

TL;DR

The paper investigates holographic RG flows in six-dimensional $F(4)$ gauged supergravity coupled to three vector multiplets to uncover a new supersymmetric fixed point and an analytic flow between fixed points in AdS$_6$/CFT$_5$. By restricting to symmetry-invariant subsectors, it derives the scalar potential, identifies a maximally supersymmetric UV point and a novel IR fixed point with $SO(3)_R\times SO(3)\to SO(3)_{\mathrm{diag}}$ symmetry, and constructs an explicit BPS flow interpolating between them. The flow is driven by vacuum expectation values of dimension-3 operators corresponding to hypermultiplet mass terms, and the dual CFT features an enhanced $E_1\sim SU(2)$ global symmetry in the UV, broken to a diagonal subgroup in the IR. The work also notes a non-supersymmetric RG flow in pure $F(4)$ gravity, found numerically and shown to be unstable when matter multiplets are included, contributing a concrete AdS$_6$/CFT$_5$ example with potential uplifts to massive type IIA string theory. Overall, it provides an analytically tractable instance of holographic RG flows in $AdS_6$/CFT$_5$ and insights into the structure of 5d fixed points with enhanced global symmetry.

Abstract

We study critical points of $F(4)$ gauged supergravity in six dimensions coupled to three vector multiplets. Scalar fields are described by $\mathbb{R}^+\times \frac{SO(4,3)}{SO(4)\times SO(3)}$ coset space, and the gauge group is given by $SO(3)_R\times SO(3)$ with $SO(3)_R$ being the R-symmetry. The maximally supersymmetric critical point with all scalars vanishing preserves the full $SO(3)_R\times SO(3)$ symmetry. This is dual to a superconformal field theories (SCFT$_5$) arising from a near horizon geometry of the D4-D8 brane system in type I$'$ theory with an enhanced global symmetry $E_1\sim SU(2)$. Apart from this trivial critical point, we identify a new supersymmetric critical point preserving the full supersymmetry with the $SO(3)_R\times SO(3)$ symmetry broken to its diagonal subgroup. This critical point should correspond to a new SCFT in five dimensions. We study an RG flow solution interpolating between the SCFT with $E_1$ symmetry and the new supersymmetric critical point. The flow describes a supersymmetric deformation driven by a vacuum expectation value of relevant operators of dimension $3$. We identify the dual operators with the mass terms for hypermultiplet scalars in the dual field theory. The solution provides an example of analytic supersymmetric RG flows in AdS$_6$/CFT$_5$ correspondence.

Figures (1)

• Figure 1: $\phi(r)$ solution in pure $F(4)$ gauged supergravity.