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Spin chain sigma models with fermions

Rafael Hernandez, Esperanza Lopez

Abstract

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.

Spin chain sigma models with fermions

Abstract

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.

Paper Structure

This paper contains 6 sections, 30 equations.

Table of Contents

  1. Introduction
  2. ${\cal N}=4$ operators with fermions
  3. The $SU(1|3)$ spin chain
  4. The superstring action
  5. The $SU(2|3)$ spin chain
  6. Conclusions