Supercoset CFTs for string theories on non-compact special holonomy manifolds

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 (SCFTs). It is known that Einstein homogeneous spaces G/ H generate Ricci flat manifolds with special holonomies on their cones ≃ R +×G/H , when they are endowed with appropriate geometrical structures, namely, the Sasaki–Einstein, tri-Sasakian, nearly Kähler, 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×( N=1 Liouville)×( 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 SUSYs 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.