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Integrability for the Full Spectrum of Planar AdS/CFT

Nikolay Gromov, Vladimir Kazakov, Pedro Vieira

TL;DR

The paper proposes a comprehensive Y-system for the planar spectrum of ${ m N}=4$ SYM based on AdS$_5 imes$S$^5$ integrability, linking it to the Hirota/T-system framework and the bound-state structure of the ABA. It demonstrates self-consistency with the asymptotic Bethe ansatz, enforces the crossing symmetry of the scalar dressing factor, and reproduces known weak-coupling wrapping corrections, while also generalizing the approach to the AdS$_4$/CFT$_3$ (ABJM) correspondence. By encoding finite-size effects in a universal set of functional equations, the work offers a unified, computationally practical route to anomalous dimensions of all local single-trace operators at any coupling. The explicit transfer-matrix construction and the handling of the dressing phase establish a robust foundation for extending integrability-based spectral analyses across AdS/CFT dualities.

Abstract

We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 SYM theory. It takes the form of a Y-system based on the integrability of the dual superstring sigma-model on the AdS_5xS^5 background. This Y-system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS_4/CFT_3 duality is also treated in a similar fashion.

Integrability for the Full Spectrum of Planar AdS/CFT

TL;DR

The paper proposes a comprehensive Y-system for the planar spectrum of SYM based on AdSS integrability, linking it to the Hirota/T-system framework and the bound-state structure of the ABA. It demonstrates self-consistency with the asymptotic Bethe ansatz, enforces the crossing symmetry of the scalar dressing factor, and reproduces known weak-coupling wrapping corrections, while also generalizing the approach to the AdS/CFT (ABJM) correspondence. By encoding finite-size effects in a universal set of functional equations, the work offers a unified, computationally practical route to anomalous dimensions of all local single-trace operators at any coupling. The explicit transfer-matrix construction and the handling of the dressing phase establish a robust foundation for extending integrability-based spectral analyses across AdS/CFT dualities.

Abstract

We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 SYM theory. It takes the form of a Y-system based on the integrability of the dual superstring sigma-model on the AdS_5xS^5 background. This Y-system passes some very important tests: it incorporates the full asymptotic Bethe ansatz at large length of operator L, including the dressing factor, and it confirms all recently found wrapping corrections. The recently proposed AdS_4/CFT_3 duality is also treated in a similar fashion.

Paper Structure

This paper contains 8 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Y-system for AdS/CFT
  3. Large $L$ solutions and ABA
  4. Asymptotic transfer matrices
  5. scalar factor from crossing
  6. Weak Coupling wrapping Corrections
  7. $AdS_4/CFT_3$ correspondence
  8. Appendix: Transfer Matrices

Figures (2)

  • Figure 1: T-shaped "fat hook" for Y- and T-systems footnote. The middle double line separates the two subgroups with extended $SU(2|2)_{L}$ and $SU(2|2)_{R}$ symmetries.
  • Figure 2: "Fat hook" for $AdS_4/CFT_3$. The $OSp(2,2|6)$ symmetry of the ABJM theory, with two momentum carrying nodes, and the $SU(2|2)$ subgroup is manifest in the diagram.