An N=1 Supersymmetric G_2-invariant Flow in M-theory

TL;DR

This paper constructs an exact M-theory solution representing a supersymmetric RG flow between two critical points with different symmetries, using a G_2-invariant flow in four-dimensional supergravity and lifting it to eleven dimensions.

Contribution

It provides the first explicit M-theory lift of a G_2-invariant RG flow connecting two supersymmetric fixed points.

Findings

Derived the M-theory lift of the G_2-invariant RG flow.

Found an exact eleven-dimensional solution with varying scalars.

Confirmed the consistency of the flow along the entire RG trajectory.

Abstract

It was found that deformation of S^7 gives rise to renormalization group(RG) flow from N=8, SO(8)-invariant UV fixed point to N=1, G_2-invariant IR fixed point in four-dimensional gauged N=8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G_2-invariant RG flow equations for both scalar fields and domain-wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G_2-invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein-Maxwell equations. The nontrivial r(that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values becomes consistent with not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional three-form gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein-Maxwell equations corresponding to the M-theory lift of the G_2-invariant RG flow.