Coset Character Identities in Superstring Compactifications

Abstract

We apply the coset character identities (generalization of Jacobi's abstruse identity) to compact and noncompact Gepner models. In the both cases, we prove that the partition function actually vanishes due to the spacetime supersymmetry. In the case of the compact models and discrete parts of the noncompact models, the partition function includes the expected vanishing factor. But the character identities used to the continuous part of the noncompact models suggest that these models have twice as many supersymmetry as expected. This fact is an evidence for the conjecture that the holographically dual of the string theory on an actually singular Calabi-Yau manifold is a super conformal field theory. The extra SUSY charges are interpreted as the superconformal S generators.

Coset construction of noncompact Spin(7) and G2 CFTs

“…Though we consider the Spin(7) compactifications, our models contain these factors. This fact is related to singularities of our models and enhanced spacetime superconformal symmetry appears in their dual models as indicated in [18].…”

“…When the target manifolds become singular, their dual field theories become interacting superconformal field theories. It suggests the "holographic dual" theories of these string models are superconformal as indicated in [18] and extra supercharges correspond to superconformal S generators in the dual theories. It is interesting to apply present approach to investigation of properties in dual field theories.…”

“…(2.6) have typically appeared in the partition functions of G 2 compactifications [4,5,18]. Though we consider the Spin(7) compactifications, our models contain these factors.…”

“…On the other hand ξ G 2 a 's (a = 0, 1) are defined by characters χ Tri h (τ ) of tri-critical Ising model with h = 0, 3/2, 7/16, 3/5, 1/10, 3/80 We make a remark here: Eqs. (2.6) have typically appeared in the partition functions of G 2 compactifications [4,5,18]. Though we consider the Spin(7) compactifications, our models contain these factors.…”