J. High Energy Phys. 01 (2022) 002 arXiv: 2103.15840
Three-point functions in ABJM and Bethe Ansatz
Peihe Yang1, Yunfeng Jiang2,3,4, Shota Komatsu4,5, Jun-Bao Wu1,6,7,*
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, P. R. China
2 School of physics, Southeast University, Nanjing 211189, P.R. China
3 Shing-Tung Yau Center of Southeast University, Nanjing 210096, P.R. China
4 Department of Theoretical Physics, CERN, 1 Esplanade des Particules, 1211 Meyrin, Switzerland
5 School of Natural Sciences, Institute for Advanced Study, 1 Einstein Dr. Princeton, NJ 08540, U.S.A.
6 Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, P. R. China
7 Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871, P. R. China
* Corresponding Authors
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.
