Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs

Abstract

We consider states of the D1-D5 CFT where only the left-moving sector is excited. As we deform away from the orbifold point, some of these states will remain BPS while others can `lift'. The lifting can be computed by a path integral containing two twist deformations; however, the relevant 4-point amplitude cannot be computed explicitly in many cases. We analyze an older proposal by Gava and Narain where the lift can be computed in terms of a finite number of 3-point functions. A direct Hamiltonian decomposition of the path integral involves an infinite number of 3-point functions, as well the first order correction to the starting state. We note that these corrections to the state account for the infinite number of 3-point functions arising from higher energy states, and one can indeed express the path-integral result in terms of a finite number of 3-point functions involving only the leading order states that are degenerate. The first order correction to the supercharge ${\bar{G}}^{(1)}$ gets replaced by a projection ${\bar{G}}^{(P)}$; this projected operator can also be used to group the states into multiplets whose members have the same lifting.

arXiv comment42 pages, 4 figures

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Cited by in corpus (15)

• 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
• Conformal Perturbation Theory for Twisted Fields
• Universal lifting in the D1-D5 CFT
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• 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
• Fortuity and Supergravity
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure
• A New Supersymmetry Index for the D1-D5 CFT
• The Resolved Elliptic Genus and the D1-D5 CFT