Towards An N=1 SU(3)-Invariant Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity

TL;DR

This paper finds exact solutions describing supersymmetric membrane flows in eleven-dimensional supergravity, revealing interpolations between different fixed points and providing insights into the higher-dimensional lift of four-dimensional RG flows.

Contribution

It discovers exact 11D solutions for N=1 G_2-invariant flows using CP^2 internal space, advancing understanding of supersymmetric membrane flows in M-theory.

Findings

Exact solutions for N=1 G_2-invariant flow in 11D supergravity.

Interpolating solutions connecting UV and IR fixed points.

Insights into the 11D lift of 4D RG flows between fixed points.

Abstract

The M-theory lift of N=1 G_2-invariant RG flow via a combinatoric use of the 4-dimensional RG flow and 11-dimensional Einstein-Maxwell equations was found some time ago. The 11-dimensional metric, a warped product of an asymptotically AdS_4 space with a squashed and stretched 7-sphere, for SU(3)-invariance was found before. In this paper, by choosing the 4-dimensional internal space as CP^2 space, we discover an exact solution of N=1 G_2-invariant flow to the 11-dimensional field equations. By an appropriate coordinate transformation on the three internal coordinates, we also find an 11-dimensional solution of N=1 G_2-invariant flow interpolating from N=8 SO(8)-invariant UV fixed point to N=1 G_2-invariant IR fixed point. In particular, the 11-dimensional metric and 4-forms at the N=1 G_2 fixed point for the second solution will provide some hints for the 11-dimensional lift of whole N=1 SU(3) RG flow connecting this N=1 G_2 fixed point to N=2 SU(3) x U(1)_R fixed point in 4-dimensions.