[Paper Review] Heterotic Coset Models of Microscopic Strings and Black Holes

Clifford V. Johnson|ArXiv.org|Jul 29, 2007

Black Holes and Theoretical Physics30 references17 citations

TL;DR

This paper proposes a heterotic coset conformal field theory (CFT) with target space AdS₃×S² as a microscopic description of fundamental heterotic strings in five dimensions, building on a conjecture by Lapan, Simons, and Strominger. The model is constructed via asymmetrically gauged WZW models, successfully capturing higher-order α′ corrections that resolve supergravity singularities and yield a smooth geometry consistent with black hole entropy calculations.

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.

Motivation & Objective

• To construct a consistent, anomaly-free heterotic CFT that describes the microscopic geometry of fundamental heterotic strings in five dimensions.
• To generalize the CFT construction to higher-dimensional heterotic strings with target space AdS₃×S^{D-3}.
• To provide a microscopic realization of the holographic dual to the core geometry of supersymmetric black holes formed by wrapped heterotic strings.
• To demonstrate that α′ corrections in the CFT yield a smooth, non-singular geometry (e.g., AdS₃×S²) consistent with supergravity and black hole entropy.
• To explore the viability of such CFTs as models for non-supersymmetric black holes via generalized coset constructions.

Proposed method

• Constructs the CFT as an asymmetrically gauged WZW model based on SL(2,ℝ)×SU(2) with a spacelike U(1) subgroup gauged.
• Uses analytic continuation of the SU(2) WZW model to obtain the SL(2,ℝ) WZW model, yielding AdS₃ geometry.
• Applies the same gauging procedure to the right-moving fermions to cancel quantum anomalies, ensuring consistency.
• Tensors the resulting coset model with a Q=0 GPS monopole theory to describe the S² factor, preserving supersymmetry.
• Extends the construction to higher dimensions by generalizing the coset to AdS₃×S^{D-3} via appropriate group continuations.
• Verifies consistency by checking that the classical and quantum anomalies cancel, particularly for k′=2 in the SL(2,ℝ) sector.

Experimental results

Research questions

• RQ1 Can a heterotic coset CFT be constructed that realizes the AdS₃×S² geometry conjectured to describe the core of a fundamental heterotic string?
• RQ2 How do α′ corrections in the CFT resolve the singularities present in the leading-order supergravity description of the heterotic string?
• RQ3 Can the CFT construction be generalized to describe higher-dimensional heterotic strings with target space AdS₃×S^{D-3}?
• RQ4 What is the role of anomaly cancellation in ensuring the consistency of the heterotic CFT with non-trivial spacetime geometry?
• RQ5 Can such CFTs serve as microscopic models for non-supersymmetric black holes via appropriate generalizations?

Key findings

• The proposed heterotic coset CFT with target space AdS₃×S² is anomaly-free and consistent, with quantum anomalies canceled by right-moving fermions.
• The model successfully reproduces the α′-corrected geometry AdS₃×S², resolving the core singularity of the classical supergravity solution.
• For the case of D=5, the CFT matches the conjectured geometry of the fundamental heterotic string, supporting its use as a microscopic description.
• The construction generalizes naturally to higher dimensions, yielding CFTs with target space AdS₃×S^{D-3} via analytic continuation of the group structure.
• The model provides a microscopic realization of the holographic dual to the black hole core geometry, consistent with entropy counting in heterotic string theory.
• The approach opens a path to studying non-supersymmetric black holes via CFTs with non-Abelian cosets and non-trivial dilaton profiles.