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- Title
Three-point functions in ABJM and Bethe Ansatz.
- Authors
Yang, Peihe; Jiang, Yunfeng; Komatsu, Shota; Wu, Jun-Bao
- Abstract
We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.
- Subjects
MATRIX multiplications; OPERATOR theory; OPERATOR functions; STRUCTURAL frames
- Publication
Journal of High Energy Physics, 2022, Vol 2022, Issue 1, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP01(2022)002