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

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+ × G/H , when they are endowed with appropriate geometrical structures, namely, the Sasaki-Einstein, triSasakian, nearly Kähler, and weak G2 structures for SU(n), Sp(n), G2, and Spin(7) holonomies, respectively. Motivated by this fact, we consider the string vacua of the type: Rd−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 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.