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Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (1505.06745v1)

Published 25 May 2015 in hep-th

Abstract: We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and possibly higher-point correlators. These newborn hexagons are more elementary and easier to deal with than the three-point functions. Moreover, they can be entirely constructed using integrability, by means of a suitable bootstrap program. In this letter, we present our main results and conjectures for these vertices, and match their predictions for the three-point functions with both weak and strong coupling data available in the literature.

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Summary

  • The paper presents a novel hexagon framework that efficiently computes structure constants in planar N=4 SYM through a non-perturbative approach.
  • It leverages integrability to decompose three-point functions into manageable geometric hexagon patches, simplifying complex operator interactions.
  • Validation against both weak and strong coupling regimes underscores the robustness of the method and its potential to advance gauge theory research.

Integrable Bootstrap and Structure Constants in Planar N=4\mathcal{N}=4 SYM Theory

The paper, titled "Structure Constants and Integrable Bootstrap in Planar N=4\mathcal{N}=4 SYM Theory," provides a significant advancement in the calculation methodologies for three-point functions within the planar N=4\mathcal{N}=4 Supersymmetric Yang-Mills (SYM) theory, exploring the synergy between integrability and the paper of correlation functions. This research introduces a novel non-perturbative framework designed for the computation of structure constants related to single-trace operators in N=4\mathcal{N}=4 SYM, focusing on large NN scenarios. Grounded in the principles of integrability, this methodology proposes a geometric approach involving hexagonal patches, or hexagons, which can replace the traditional three-point functions for assembling correlators. This technique leverages the fundamental properties of integrable systems to devise efficient bootstrapping procedures.

The hexagon framework distinctively allows the decoupling of the problem into more elementary components by mapping the interaction of three-point functions into manageable hexagonal geometries. These hexagons are considered to be simpler to manipulate, and one's ability to bootstrap them entirely through integrability showcases an innovative stride away from traditional perturbative techniques. The methodology further relates the structure constants with finite volume two-point functions of these hexagon-constructed operators, marking a critical improvement in analytical tractability.

Where numerical results are concerned, the comparison of these computations with existing data, from both weak and strong coupling regimes, exhibits a robust correspondence, thus validating the paper's claims. The novelty of the approach is underscored by its capability to recover previously elusive structure constants that play a pivotal role in understanding operator production expansion (OPE) in the planar N=4\mathcal{N}=4 SYM context.

Furthermore, the paper provides insights into the extension of integrable bootstrap concepts, recognizing the potential of integrating higher symmetry groups, such as PSU(22)PSU(2|2), as a way to impose constraints that dramatically simplify these complex calculations. The results, rooted deep in mathematical physics and integrable models, have potential implications on how theoretical physicists interpret the dynamics of gauge theory correlators.

While the implications of this work could extend towards speculative applications in string theory, especially around the AdS/CFT correspondence, the immediate horizon seems focused on broadening the scope of integrable models further and potentially uncovering a unified framework that relates these findings with form factor theories in lower dimensional settings. Moreover, it speculates on future engagements with the Quantum Spectral Curve (QSC) and its potentiality in interpreting quantum levels of these interactions.

Thus, the paper enriches the current landscape of integrable systems and N=4\mathcal{N}=4 SYM theory by laying down a pathway for further explorations into non-perturbative dynamics, enveloped in the geometrically intuitive hexagonal structure. This path offers promising foresight into how traditionally intricate quantum field theory problems might be tackled using the aesthetics and rigor of integrability.

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