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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.

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天津大学理学院 量子交叉研究中心   地址:天津津南区 雅观路135号 天津大学北洋园校区32楼146 
Center for Joint Quantum Studies, School of Science, Tianjin University     Address : Yaguan Road 135, Jinnan District, 300350 Tianjin, P. R. China