Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents

TL;DR

This paper investigates how deforming symmetric product orbifolds of 2D $ abla=2$ CFTs affects higher spin currents, revealing universal lifting behavior and non-universal details related to central charge and marginal operators, with implications for AdS/CFT.

Contribution

It demonstrates that higher spin currents are universally lifted under deformation and explores the non-universal aspects depending on central charge and specific operators.

Findings

Higher spin currents are universally lifted by marginal deformations.

The lifting process depends on the central charge and the chosen marginal operator.

Results support the holographic nature of symmetric product orbifolds of $ abla=2$ minimal models.

Abstract

We analyze how deforming symmetric product orbifolds of two-dimensional $\mathcal{N}=2$ conformal field theories by an exactly marginal operator lifts higher spin currents present at the orbifold point. We find on the one hand that these currents are universally lifted regardless of the underlying CFT. On the other hand the details of the lifting are surprisingly non-universal, with dependence on the central charge of the underlying CFT and the specific marginal operator in use. In the context of the AdS/CFT correspondence, our results illustrate the mechanism by which the stringy spectrum turns into a supergravity spectrum when moving through the moduli space. They also provide further evidence that symmetric product orbifolds of $\mathcal{N}=2$ minimal models are holographic.