## Abstract

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 language | English |
---|---|

Title of host publication | XVIIth International Congress on Mathematical Physics |

Subtitle of host publication | Aalborg, Denmark, 6-11 August 2012 |

Publisher | World Scientific Publishing Co. |

Pages | 683 |

Number of pages | 1 |

ISBN (Electronic) | 9789814449243 |

ISBN (Print) | 9789814449236 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

## Keywords

- Integrability
- Quantum gauge theories