Flowing with Eight Supersymmetries in M-Theory and F-theory

TL;DR

This paper explores holographic RG flows with eight supersymmetries in M-theory and F-theory, revealing new solutions with hyper-Kahler slices and their geometric structures, including a novel M-theory flow with branes on Eguchi-Hanson space.

Contribution

It introduces a new M-theory flow solution with hyper-Kahler geometry, obtained via gauged supergravity and uplifted to eleven dimensions, applicable to orbifold theories.

Findings

New M-theory flow solution with Eguchi-Hanson moduli space

Hyper-Kahler slice encodes Seiberg-Witten coupling in IIB

Extension of hyper-Kahler structure to G-structure in eight-manifold

Abstract

We consider holographic RG flow solutions with eight supersymmetries and study the geometry transverse to the brane. For both M2-branes and for D3-branes in F-theory this leads to an eight-manifold with only a four-form flux. In both settings there is a natural four-dimensional hyper-Kahler slice that appears on the Coulomb branch. In the IIB theory this hyper-Kahler manifold encodes the Seiberg-Witten coupling over the Coulomb branch of a U(1) probe theory. We focus primarily upon a new flow solution in M-theory. This solution is first obtained using gauged supergravity and then lifted to eleven dimensions. In this new solution, the brane probes have an Eguchi-Hanson moduli space with the M2-branes spread over the non-trivial 2-sphere. It is also shown that the new solution is valid for a class of orbifold theories. We discuss how the hyper-Kahler structure on the slice extends to some form of G-structure in the eight-manifold, and describe how this can be computed.