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Wrapped fivebranes and N=2 super Yang-Mills theory

Jerome P. Gauntlett, Nakwoo Kim, Dario Martelli, Daniel Waldram

Abstract

We construct D=10 supergravity solutions corresponding to type IIB fivebranes wrapping a two-sphere in a Calabi-Yau two-fold. These are related in the IR to the large N limit of pure N=2 SU(N) super Yang-Mills theory. We show that the singularities in the IR correspond to the wrapped branes being distributed on a ring. We analyse the dynamics of a probe fivebrane and show that it incorporates the full perturbative structure of the gauge theory. For a class of solutions the two-dimensional moduli space is non-singular and we match the result for the corresponding slice of the Coulomb branch of the gauge theory.

Wrapped fivebranes and N=2 super Yang-Mills theory

Abstract

We construct D=10 supergravity solutions corresponding to type IIB fivebranes wrapping a two-sphere in a Calabi-Yau two-fold. These are related in the IR to the large N limit of pure N=2 SU(N) super Yang-Mills theory. We show that the singularities in the IR correspond to the wrapped branes being distributed on a ring. We analyse the dynamics of a probe fivebrane and show that it incorporates the full perturbative structure of the gauge theory. For a class of solutions the two-dimensional moduli space is non-singular and we match the result for the corresponding slice of the Coulomb branch of the gauge theory.

Paper Structure

This paper contains 13 sections, 54 equations, 2 figures.

Table of Contents

  1. Introduction
  2. NS fivebranes wrapped on $S^2$ and ${\cal N}=2$ Yang--Mills theory
  3. Supergravity solution
  4. The gravity solution in $D=7$
  5. The supergravity solution in $D=10$
  6. Symmetries of the solution
  7. UV and IR behaviour of solutions
  8. Anomaly in $U(1)_R$
  9. D5 solution
  10. Probing the solution with fivebranes
  11. Comparison with gauge theory
  12. Discussion
  13. Orthonormal Frame

Figures (2)

  • Figure 1: Behaviour of $\mathrm{e}^{-2x}$ for different values of $k$.
  • Figure 2: Behaviour of the dilaton at $\theta=\pi/2$.