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 S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 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.
Highlights
Two classes of 2d CFTs with moduli spaces are known in the literature: 1. CFTs with a u(1) global symmetry, where the exactly marginal operator is the JJoperator
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 find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space
Summary
We will use a convention where R = 1 corresponds to the self-dual point (the SU(2) WZW model), d2z is normalized so that the integral over the worldsheet torus gives τ2, and the free boson φ is periodic as φ ≡ φ + 2π. With these conventions, the action is given by. Let us consider how the twist changes when perturbing by the exactly marginal operator ∂φ∂ ̄φ, S(λ) = S + λ d2z∂φ∂ ̄φ. For the free boson on S1, we have a closed form expression for the perturbation series, which we can use as a toy model for questions about the density of rational points
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