On three-point functions in ABJM and the latitude Wilson loop
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Springer
Received: May 20, Revised: July 6, Accepted: September 10, Published: October 13,
2020 2020 2020 2020
Marco S. Bianchi Instituto de Ciencias F´ısicas y Matem´ aticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile
E-mail: [email protected] Abstract: I consider three-point functions of twist-one operators in ABJM at weak coupling. I compute the structure constant of correlators involving one twist-one un-protected operator and two protected ones for a few finite values of the spin, up to two-loop order. As an application I enforce a limit on the gauge group ranks, in which I relate the structure constant for three chiral primary operators to the expectation value of a supersymmetric Wilson loop. Such a relation is then used to perform a successful five-loop test on the matrix model conjectured to describe the supersymmetric Wilson loop. Keywords: Chern-Simons Theories, Conformal Field Theory, Wilson, ’t Hooft and Polyakov loops, Integrable Field Theories ArXiv ePrint: 2005.09522
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)075
JHEP10(2020)075
On three-point functions in ABJM and the latitude Wilson loop
Contents 1 Introduction and summary
1
2 Matrix model
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4 Attempted perturbative check 4.1 Naive attempt 4.2 Regularization 4.3 The method and its potential issues 4.4 Other choices for a regulator 4.5 An example: the clover diagram
18 18 18 19 20 22
5 Extension to an operator with spin 5.1 Twist-one operators with spin 5.2 Two-loop correction to the two-point function 5.3 Two-loop correction to the structure constant 5.4 The final result for the structure constant
25 25 27 29 34
6 Conclusions
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1
Introduction and summary
In this note I approach the problem of computing quantum corrections to three-point functions of local twist-one operators in the ABJM theory [1] at weak coupling. Threepoint functions are central objects in conformal field theories. Their determination is notoriously hard from direct computation. These difficulties can be sidestepped in certain fortunate cases, for example retrieving information on them from the OPE decomposition of higher-point correlators [2] (usually of protected operators), which can sometimes be easier to determine. In the special case of N = 4 SYM theory in four dimensions, a novel approach consists in exploting the conjectured integrability of the theory for computing its three-point functions [3]. Since ABJM seems to share integrability properties of N = 4 SYM, at least for the planar spectral problem [4–6], there is hope that the integrability framework for threepoint functions could be eventually extended to ABJM. At a difference with N = 4 SYM,
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3 A three-point function from the matrix model 3.1 Colorful considerations at two loops 3.2 Color limit on the Wilson loop 3.3 Extracting the two-loop color limit of the three-point function 3.4 An aside: color limit of an extremal three-point function
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ABJM lacks any perturbative
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