Abstract
We develop a novel nonperturbative approach to a class of three-point functions in planar mathcal{N} = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS5×S5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large N collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of g-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state g-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.
Highlights
Understanding the low-energy physics of Quantum Chromodynamics (QCD) is an important theoretical challenge with diverse physical implications
We develop a novel nonperturbative approach to a class of three-point functions in planar N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA)
It is rather interesting that the partially-contracted Giant Graviton (PCGG) approach leads directly to a two-point function of single-trace operators, which can be immediately recast as an overlap of two spin-chain states, while the semi-classical approach gives a matrix-trace representation (3.28), which can be interpreted as an expectation value of the operator in the presence of the emergent classical background
Summary
Understanding the low-energy physics of Quantum Chromodynamics (QCD) is an important theoretical challenge with diverse physical implications. In the past fifteen years, significant progress has been made in computing the spectrum and the correlation functions of single-trace operators This was achieved largely by the successful application of integrability techniques [5], which were originally developed in the study of two-dimensional quantum field theories. As we will show in this paper, the worldsheet topology for the threepoint function of determinants and a single-trace operator is a disk with one puncture, which is topologically equivalent to a semi-infinite cylinder (see figure 4) This is the topology relevant for the standard analysis of the spectrum in integrable QFTs based on Thermodynamic Bethe Ansatz (TBA).
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