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Title: Three-point functions in $$\mathrm{ABJM}$$ and Bethe Ansatz

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [4]
  1. Tianjin University (China); Tianjin Univ. (China)
  2. Southeast University, Nanjing (China); European Organization for Nuclear Research (CERN), Meyrin (Switzerland)
  3. European Organization for Nuclear Research (CERN), Meyrin (Switzerland); Institute for Advanced Study, Princeton, NJ (United States)
  4. Tianjin University (China); Peng Huangwu Center for Fundamental Theory, Hefei (China); Peking University, Beijing (China)
+ Show Author Affiliations

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.

Research Organization:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Natural Science Foundation of China; Natural Science Foundation of Tianjin
Grant/Contract Number:
SC0009988
OSTI ID:
1976423
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

1/N Expansion
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AdS-CFT Correspondence
Bethe Ansatz
integrable field theories