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arXiv · 2011.07062

On Rational Points in CFT Moduli Spaces

Nathan Benjamin·Christoph A. Keller·Hirosi Ooguri·Ida G. Zadeh
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Abstract

Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with $S^1$ target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the $S^1$ example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory.

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Nathan Benjamin, Christoph A. Keller, Hirosi Ooguri, Ida G. Zadeh. 2020-11-13. On Rational Points in CFT Moduli Spaces. https://doi.org/10.1007/jhep04(2021)067

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