Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$

Abstract

We consider correlation functions in symmetric product ($S_N$) orbifold CFTs at large $N$ with arbitrary seed CFT, expanding on our earlier work arXiv:2211.04633 . Using covering space techniques, we calculate descent relations using fractional Virasoro generators in correlators, writing correlators of descendants in terms of correlators of ancestors. We first consider the case three-point functions of the form ($m$-cycle)-($n$-cycle)-($q$-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In these examples we show that the final descent relations do not depend on the covering space data, nor on the specific details of the seed CFT. This makes these descent relations universal in all $S_N$ orbifold CFTs. Next, we explore four-point functions of the form (2-cycle)-($n$-cycle)-($n$-cycle)-(2-cycle) which lift to arbitrary primaries on the cover, and descendants thereof. In such cases a single parameter in the map $s$ parameterizes both the base space cross ratio ${\zeta }_z$ and the covering space cross ratio ${\zeta }_t$. We find that the descent relations for the four point functions depend only on base space data and the parameter $s$, which we argue is tantamount to writing the descent relations in terms of the base space data and the base space cross ratio. These descent relations again do not depend on the covering space data, nor the specifics of the seed CFT, making these universal as well.

27 pages

References in corpus (17)

• Holography from Conformal Field Theory
• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• String Universality for Permutation Orbifolds
• Correlators of the symmetric product orbifold
• Emission from the D1D5 CFT
• Effect of the deformation operator in the D1D5 CFT
• Permutation orbifolds and holography
• Effect of the twist operator in the D1D5 CFT
• Bogoliubov coefficients for the twist operator in the D1D5 CFT
• Analyzing the squeezed state generated by a twist deformation
• Microstate Renormalization in Deformed D1-D5 SCFT
• Universal lifting in the D1-D5 CFT
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Intertwining Relations for the Deformed D1D5 CFT
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Bootstrapping the effect of the twist operator in symmetric orbifold CFTs

Cited by in corpus (1)

• Transport across interfaces in symmetric orbifolds