Conformal Perturbation Theory for Twisted Fields

Abstract

We investigate second order conformal perturbation theory for ${\mathbb{Z}}_2$ orbifolds of conformal field theories in two dimensions. To evaluate the necessary twisted sector correlation functions and their integrals, we map them from the sphere to its torus double cover. We discuss how this relates crossing symmetry to the modular group, and introduce a regularization scheme on the cover that allows to evaluate the integrals numerically. These methods do not require supersymmetry. As an application, we show that in the torus orbifold of 8 and 16 free bosons, ${\mathbb{Z}}_2$ twist fields are marginal at first order, but stop being marginal at second order.

arXiv comment29pp, v2: minor corrections + references added

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• Narain to Narnia
• Lifting at higher levels in the D1D5 CFT
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Lifting of level-1 states in the D1D5 CFT
• Microstate Renormalization in Deformed D1-D5 SCFT
• The Stranger Things of Symmetric Product Orbifold CFTs
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Dynamical evolution in the D1D5 CFT
• Bootstrapping the effect of the twist operator in symmetric orbifold CFTs
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• On Rational Points in CFT Moduli Spaces
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Searching for strongly coupled AdS matter with multi-trace deformations