Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds

TL;DR

This paper constructs superstring vacua on non-compact special holonomy manifolds with conical singularities using superconformal field theories, revealing a correspondence between worldsheet and spacetime supersymmetry and analyzing deformations that resolve singularities.

Contribution

It introduces a systematic CFT-based approach to model superstring vacua on non-compact special holonomy manifolds with conical singularities, linking geometry and worldsheet theories.

Findings

Matching spacetime and worldsheet SUSY counts.

Construction of superstring vacua using affine Lie algebras.

Analysis of marginal deformations resolving singularities.

Abstract

We study aspects of superstring vacua of non-compact special holonomy manifolds with conical singularities constructed systematically using soluble N = 1 superconformal field theories (SCFT's). It is known that Einstein homogeneous spaces G/H generate Ricci flat manifolds with special holonomies on their cones R_+ x G/H, when they are endowed with appropriate geometrical structures, namely, the Sasaki-Einstein, tri-Sasakian, nearly Kahler, and weak G_2 structures for SU(n), Sp(n), G_2, and Spin(7) holonomies, respectively. Motivated by this fact, we consider the string vacua of the type: R^{d-1,1} x (N = 1 Liouville) x (N=1 supercoset CFT on G/H) where we use the affine Lie algebras of G and H in order to capture the geometry associated to an Einstein homogeneous space G/H. Remarkably, we find the same number of spacetime and worldsheet SUSY's in our ``CFT cone'' construction as expected from the analysis of geometrical cones over G/H in many examples. We also present an analysis on the possible Liouville potential terms (cosmological constant type operators) which provide the marginal deformations resolving the conical singularities.