Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory

Isachenkov, Mikhail; Schomerus, Volker

doi:10.1007/jhep07(2018)180

Cited by 62 publications

(94 citation statements)

References 124 publications

(241 reference statements)

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“…It will be interesting to better understand our closed-form expression (13), such as the connections to higher order differential equations [26,35] and integrability [44,45]. One can further compute the subleading terms in the lightcone expansion using the Casimir equations.…”

Section: Resultsmentioning

confidence: 99%

Closed-form expression for cross-channel conformal blocks near the lightcone

2020

J high energy phys

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In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalars. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We also derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our approach and results may shed light on the complete analytic structure of conformal blocks.

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Section: Resultsmentioning

confidence: 99%

Closed-form expression for cross-channel conformal blocks near the lightcone

2020

J high energy phys

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“…Notice that we are working in one-dimensional theory and did not assume that it is a holomorphic part of a two-dimensional theory. This is why our conventions for the relation between the parameters a, b with the external conformal weights differ from the standard ones by a factor of two, see [56].…”

Section: The Supergroup and Hamiltonian Reductionmentioning

confidence: 99%

Superconformal blocks: general theory

Burić

Schomerus

Sobko

2020

J. High Energ. Phys.

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In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number N of supersymmetries. The central new ingredient is a universal construction of the relevant Casimir differential equations. In order to find these equations, we model superconformal blocks as functions on the supergroup and pick a distinguished set of coordinates. The latter are chosen so that the superconformal Casimir operator can be written as a perturbation of the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent) term. Solutions to the associated eigenvalue problem can be obtained through a quantum mechanical perturbation theory that truncates at some finite order so that all results are exact. We illustrate the general theory at the example of d = 1 dimensional theories with N = 2 supersymmetry for which we recover known superblocks. The paper concludes with an outlook to 4-dimensional blocks with N = 1 supersymmetry.

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“…Hence, one would expect that a universal set of Casimir equations for long multiplets of superconformal groups can be derived in any dimension. Moreover, by exploiting the integrability of Calogero-Sutherland Hamiltonians it should be possible to develop a systematic solution theory [104,105], without the need for an Ansatz that decomposes superblocks in terms of bosonic ones.…”

Section: Jhep10(2017)119mentioning

confidence: 99%

Long multiplet bootstrap

Cornagliotto

Lemos

Schomerus

2017

J. High Energ. Phys.

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Applications of the bootstrap program to superconformal field theories promise unique new insights into their landscape and could even lead to the discovery of new models. Most existing results of the superconformal bootstrap were obtained form correlation functions of very special fields in short (BPS) representations of the superconformal algebra. Our main goal is to initiate a superconformal bootstrap for long multiplets, one that exploits all constraints from superprimaries and their descendants. To this end, we work out the Casimir equations for four-point correlators of long multiplets of the two-dimensional global N = 2 superconformal algebra. After constructing the full set of conformal blocks we discuss two different applications. The first one concerns two-dimensional (2,0) theories. The numerical bootstrap analysis we perform serves a twofold purpose, as a feasibility study of our long multiplet bootstrap and also as an exploration of (2,0) theories. A second line of applications is directed towards four-dimensional N = 3 SCFTs. In this context, our results imply a new bound c 13 24 for the central charge of such models, which we argue cannot be saturated by an interacting SCFT.

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Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory

Cited by 62 publications

References 124 publications

Closed-form expression for cross-channel conformal blocks near the lightcone

Closed-form expression for cross-channel conformal blocks near the lightcone

Superconformal blocks: general theory

Long multiplet bootstrap

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