Exact spectrum of 4D conformal gauge theories from integrability

N. Gromov*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The spectrum of N = 4 super Yang-Mills theory can be studied using methods of integrability in the planar limit. We show that the exact spectrum is governed by a set of functional equations (Hirota equations) [1] (forumula Presented)) The set of functions Ta;s of the spectral parameter u belongs to an infinite lattice of a very particular shape called T-hook The Hirota equations by itself describe a classical integrable system. This allows further simplification of the solution. We describe how the infinite set of functional equations (75) can be recast into a finite set of nonlinear integral equations [2] (FiNLIE) which can be solved numerically or analyzed analytically in various limits. This new FiNLIE is in the perfect agreement with the previously obtained numerical results [2] based on the Thermodynamic Bethe Ansatz (TBA) approach. The presented solution of the spectral problem passes various very nontrivial tests. It agrees with extremely involved perturbative calculations in the gauge theory (up to five loops) as well as with the predictions of the string theory for the strong coupling limit (up two two loops).

Original languageEnglish
Title of host publicationXVIIth International Congress on Mathematical Physics
Subtitle of host publicationAalborg, Denmark, 6-11 August 2012
PublisherWorld Scientific Publishing Co.
Number of pages1
ISBN (Electronic)9789814449243
ISBN (Print)9789814449236
Publication statusPublished - 1 Jan 2013


  • Integrability
  • Quantum gauge theories


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