Codimension Two Holography

TL;DR

This paper proposes a holographic duality between certain Ricci flat string backgrounds and a four-dimensional Euclidean conformal field theory defined on a codimension two submanifold, extending holographic principles to new geometric settings.

Contribution

It introduces a novel holographic interpretation for Ricci flat backgrounds of the form A_6×C_4, linking them to a 4D ECFT on a codimension two submanifold.

Findings

Holographic duality is extended to Ricci flat backgrounds.

A specific ECFT is conjectured to exist on a codimension two submanifold.

The central charge of the ECFT scales with the radius of curvature of the background.

Abstract

A holographic interpretation for some specific Ricci flat string backgrounds of the form $A_6\times C_4$ is proposed. The conjecture is that there is a Four-dimensional Euclidean Conformal Field Theory (ECFT) defined on a codimension two {\em submanifold} of the manifold $A_6$ (where one of the two remaining {\em holographic} coordinates of $A_6$ is timelike, and the other one spacelike), with central charge proportional to the radius of curvature of the six-dimensional manifold, $c\sim l^4$.