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.
Highlights
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 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 focus on the computation at weak coupling and show that the treelevel structure constants of two determinant operators and one single-trace operator can be computed by overlaps between a matrix product state and a Bethe eigenstate in an integrable spin chain
We studied the tree-level structure constants of a single-trace non-BPS operator and two sub-determinant operators in ABJM theory in the planar limit
Summary
A distinguishing feature of ABJM theory (as compared to N = 4 SYM) is that it admits two different large N limits: the first limit is called the M-theory limit and can be defined by N → ∞ with k fixed This limit has attracted much attention since it is dual to a M-theory on AdS4 × S7/Zk and provides one of the most concrete non-perturbative definitions of the M-theory currently available. There are two classes of giant gravitons in AdS4 × CP 3 known in the literature which are conjectured to be dual to 1/3 BPS operators.. The other class is the D4 branes which are point-like in AdS4 and extended in the CP 3 direction [83, 87, 90,91,92,93,94] They are dual to antisymmetric Schur polynomials and are the subject of this paper. In the upcoming paper [31], we will study the correlation functions from these holographic perspectives
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