Correlation functions of composite Ramond fields in deformed D1-D5 orbifold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>SCFT</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Abstract

We study two families of composite twisted Ramond fields (made by products of two operators) in the $\mathcal{N}=(4,4)$ supersymmetric D1-D5 ${\mathrm{SCFT}}_{2}$ deformed by a marginal modulus operator away from its $({T}^{4}{)}^{N}/{S}_{N}$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance operator product expansion limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists ${m}_{1}$ and ${m}_{2}$: protected states, for which ${m}_{1}+{m}_{2}=N$, and ``lifted'' states for which ${m}_{1}+{m}_{2}&lt;N$. The latter require an appropriate renormalization. We also derive the leading order corrections to their two-point functions, and to their three-point functions with the deformation operator.

Topics & Concepts