Supercoset CFT’s 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 (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 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: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.

Generalised discrete torsion and mirror symmetry for G2manifolds

“…Mirror symmetry of the flux backgrounds should then induce mirror symmetry of these G 2 manifolds. Finally, it would be interesting to study this mirror symmetry for other G 2 manifolds for which a conformal field theory description is available [13,[22][23][24][25][26][27][28]. It may also be interesting to see whether there is a similar construction for Spin(8) manifolds.…”

The Topological G₂ String

“…It is also perhaps worthwhile to investigate more concrete world-sheet models of theories based on the G 2 algebra, for example using minimal models and discrete torsion, see e.g. [15,16,17,18,19,20,21,22,23]. It is also interesting to extend this construction to more general setting which involve turning on the NS-NS background fields.…”

“…For more about type II strings on G 2 manifolds and their mirror symmetry, see e.g. [13,14,15,16,17,18,19,20,21,22,23]. A review of M-theory on G 2 manifolds with many references can be found in [24].…”

More on superstrings inAdS3× Script N

“…Recently, the work in ref. [27] implies that if the SCFT N contains a tri-critical Ising model, then N = 1 supersymmetry can be constructed in the boundary dual of AdS 3 . A new family of examples of this sort is N = SO(7) k ′ /(G 2 ) k ′ +1 , which leads to precisely N = 1 two dimensional supersymmetry in spacetime 13 .…”