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 (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.

Superconformal algebras for twisted connected sums and G2 mirror symmetry

“…In spite of this, we have explained in this paper how to take advantage of relations like (28) and inspiration from already existing realisations of the Shatashvili-Vafa G 2 SCA [15,19] to establish a realisation for twisted connected sums. Our realisation could perhaps seem unsurprising based on the mathematically established existence of Ricci-flat metrics on TCSs, which suggests a fixed point of the RG flow.…”

Heterotic strings on homogeneous spaces

“…We will consider the A n case in the discussion, although it's pretty much the same for the other classical Lie algebras. An abelian super-coset G × SO(#g − d)/U (1) d , (withĝ at level k − g * ) must be supplemented with the definition of the action of the abelian subgroup in g, corresponding to a choice of a particular sub-lattice of Γ ∈ √ kM (these issues have been discussed in [30] for symmetric supercosets of type II superstrings). In our construction, the left-coset structure will require that, in order to achieve modular invariance, the lattice behaves covariantly as some combination of right-moving fermions of the gauge sector of the heterotic string.…”

“…It was shown in [13] that a large class of these linear dilaton theories are dual to singular CY manifolds in the decoupling limit. An extensive review of the different possibilities in various dimensions has been given in [30] with all the possible G/H cosets. The left cosets that we constructed allow to find new solutions of this type in heterotic strings, with a different geometrical interpretation since our cosets differ from ordinary gauged wzw model.…”

“…which corresponds in the classification of [30] to a non-compact manifold of SU (4) holonomy once the proper projection is done on the left N = 2 charges. This solution is asymptotically conformal to a cone over the Einstein space SU (3)/U (1).…”

“…For the symmetrically gauged wzw models, this has been studied in[30].c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim…”