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On AGT Conjecture for Pure Super Yang-Mills and W-algebra

Masato Taki

Abstract

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.

On AGT Conjecture for Pure Super Yang-Mills and W-algebra

Abstract

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal blocks associated with the conformal algebra. Likewise, a counterpart in pure super Yang-Mills theory exists in conformal field theory. We propose a simple relation between the Shapovalov matrix of the W_3-algebra and the Nekrasov partition function of N=2 SU(3) Yang-Mills theory.

Paper Structure

This paper contains 16 sections, 94 equations.

Table of Contents

  1. Introduction
  2. Non-conformal AGT Conjecture and Virasoro Algebra
  3. Alday-Gaiotto-Tachikawa conjecture
  4. Gaiotto conjecture (non-conformal AGT conjecture)
  5. $SU(3)$ Pure Super Yang-Mills and $\mathcal{W}_3$-algebra
  6. Nekrasov formula
  7. $\mathcal{W}_3$-algebra and $SU(3)$ Nekrasov formula
  8. Derivation from AGT conjecture
  9. AGT-W relation for $N_c=3$, $N_f=6$ gauge theory
  10. decoupling limit of massive hypermultiplets
  11. Conclusion
  12. Acknowledgement
  13. Conformal Symmetry and Conformal Blocks
  14. structure of correlators
  15. conformal block of Virasoro algebra
  16. ...and 1 more sections