Heterotic Coset Models of Microscopic Strings and Black Holes

TL;DR

This work develops intrinsically heterotic coset models, formulated as asymmetrically gauged WZW theories, to describe the microscopic geometry of heterotic strings and their black hole realizations. It confirms that the GPS monopole construction yields an exact S^2 sector at k=2, which can be consistently tensored with an SL(2,ℝ) sector to realize AdS3×S2 as the microscopic geometry of the five-dimensional heterotic string core, with the levels fixed by central-charge constraints (k=2, k′=6) and with the Einstein-frame entropy matching the holographic/grey-body calculations. The construction is generalized to D dimensions by non-Abelian cosets, yielding AdS3×S^{D−3} target spaces with radii of order α′ and explicit relations between k and k′ governed by Coxeter numbers, suggesting a family of microscopic heterotic string geometries. The approach also extends to higher AdS geometries via analytic continuation and hints at rich applications to non-supersymmetric and twisted configurations, where α′ corrections and dilaton dynamics may play nontrivial roles. Overall, the paper provides a coherent CFT framework for understanding the microscopic structure of heterotic strings and their black hole cores.

Abstract

Following a recent conjecture by Lapan, Simons and Strominger, we revisit and discuss an intrinsically heterotic class of conformal field theories, emphasizing their Lagrangian construction as asymmetrically gauged WZW models, which may be useful in several applications to the study of supersymmetric strings and black holes in heterotic and type II string theory compactified on T^6 and K3 X T^2 respectively. In these cases, the leading supergravity geometry is singular, but higher order corrections remove this singularity in a way that is consistent with, for example the non-zero entropy for the black holes that these strings form after wrapping on an additional circle. The conformal field theories have the right structure to capture the features of the supergravity analysis, and possess precisely the microscopic target spaces required. We describe in detail the model with AdS_3 X S^2 geometry, which is conjectured by Lapan et. al. to represent a fundamental heterotic string in five dimensions, and then propose conformal field theories which are potential candidates for the microscopic geometry of heterotic strings in $D$ dimensions, with target space AdS_3 X S^{D-3}. We also discuss some conformal field theories that give microscopic AdS target spaces in various dimensions.