Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT

Lima, A. A.; Sotkov, G. M.; Stanishkov, M.

doi:10.1007/jhep05(2022)106

Cited by 14 publications

(9 citation statements)

References 65 publications

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“…While the three-point functions are fundamental, providing the structure constants of the theory, the four-point functions allow one to check that all non-trivial structure constants have been found. There are many such examples of covering space maps for four-point functions [18,21,27,48,49]. Such investigations are critical when considering the shift in spectrum of operators in the presence of a deformation, as all fusions in the presence of a deformation operator between primary operators at the same weight must be considered: the exchange channels of a 4point function gives access to all of these at once.…”

Section: Discussionmentioning

confidence: 99%

Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$

Burrington¹,

Peet²

2022

Preprint

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We consider correlation functions in symmetric product (S N ) orbifold CFTs at large N with arbitrary seed CFT. Specifically, we consider correlators of descendant operators constructed using both the full Virasoro generators L m and fractional Virasoro generators ℓ m/n i . Using covering space techniques, we show that correlators of descendants may be written entirely in terms of correlators of ancestors, and further that the appropriate set of ancestors are those operators that lift to conformal primaries on the cover. We argue that the covering space data should cancel out in such calculations. To back this claim, we provide some example calculations by considering a three-point function of the form (4-cycle)-(2-cycle)-(5-cycle) that lifts to a three-point function of arbitrary primaries on the cover, and descendants thereof. In these examples we show that while the covering space is used for the calculation, the final descent relations do not depend on covering space data, nor on the details of which seed CFT is used to construct the orbifold, making these results universal.

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Section: Discussionmentioning

confidence: 99%

Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$

Burrington¹,

Peet²

2022

Preprint

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“…Our comparisons notably include an example in which the light operators in the symmetric orbifold CFT are twist-two. In this case, and as shown recently in [61,62], the Lunin-Mathur covering map used in the symmetric orbifold computation is different to the one appearing in the worldsheet computation, making the comparison highly non-trivial. Remarkably, both results agree exactly in the large N limit.…”

Section: Jhep03(2023)066 1 Introductionmentioning

confidence: 93%

“…(6.16) nevertheless matches with the symmetric orbifold CFT also in this case. The relevant four-point function was studied recently in [61,62,85] in the Sym N (T 4 ) CFT. At leading order in large N , the correlator is dominated by a contribution from a covering space with genus zero, where the copy indices of the light twist-two operator act on different JHEP03(2023)066 k-strands corresponding to the heavy state.…”

Section: Matching Between Worldsheet and Symmetric Product Orbifoldmentioning

confidence: 99%

Worldsheet computation of heavy-light correlators

Bufalini

Iguri

Kovensky

et al. 2023

J. High Energ. Phys.

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We compute a large collection of string worldsheet correlators describing light probes interacting with heavy black hole microstates. The heavy states consist of NS5 branes carrying momentum and/or fundamental string charge. In the fivebrane decoupling limit, worldsheet string theory on a family of such backgrounds is given by exactly solvable null-gauged WZW models. We construct physical vertex operators in these cosets, including all massless fluctuations. We compute a large class of novel heavy-light-light-heavy correlators in the AdS3 limit, where the light operators include those dual to chiral primaries of the holographically dual CFT. We compare a subset of these correlators to the holographic CFT at the symmetric product orbifold point, and find precise agreement in all cases, including for light operators in twisted sectors of the orbifold CFT. The agreement is highly non-trivial, and includes amplitudes that describe the analogue of Hawking radiation for these microstates. We further derive a formula for worldsheet correlators consisting of n light insertions on these backgrounds, and discuss which subset of these correlators are likely to be protected. As a test, we compute a heavy-light five-point function, obtaining precisely the same result both from the worldsheet and the symmetric orbifold CFT. This paper is a companion to and extension of [1].

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“…This was considered e.g. in [57,58]. However, on the string side this generalisation is non-trivial.…”

Section: Open Questionsmentioning

confidence: 99%

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

Dei

Eberhardt²

2022

SciPost Phys.

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We continue our study of string correlators on Euclidean \text{AdS}_3AdS3 with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show that correlators exhibit a simple behaviour near their singularities. The spacetime correlators are meromorphic functions in the \mathrm{SL}(2,\mathbb{R})SL(2,ℝ)-spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual \text{CFT}_2CFT2. Moreover, we also compute the residues of the spacetime correlators for some of the poles exactly and find again a perfect match with the proposal for the dual \text{CFT}_2CFT2, thereby checking the duality for some non-trivial four-point functions exactly. Our computations simplify drastically in the tensionless limit of \mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4AdS3×S3×𝕋4 where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.

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Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT

Cited by 14 publications

References 65 publications

Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$

Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$

Worldsheet computation of heavy-light correlators

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

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