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An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills

Timothy J. Hollowood, S. Prem Kumar

Abstract

We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade and calculate precisely how quantum effects deform the classical moduli space by replacing the conifold singularities with three-cycles of finite size. Locally the structure is that of the deformed conifold, but the global geometry is different. This desingularized quantum deformed geometry is the moduli space of probe D3-branes at the end of a duality cascade realized on the worldvolume of (fractional) D3-branes placed at the isolated conifold singularities in the deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.

An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills

Abstract

We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade and calculate precisely how quantum effects deform the classical moduli space by replacing the conifold singularities with three-cycles of finite size. Locally the structure is that of the deformed conifold, but the global geometry is different. This desingularized quantum deformed geometry is the moduli space of probe D3-branes at the end of a duality cascade realized on the worldvolume of (fractional) D3-branes placed at the isolated conifold singularities in the deformation of the orbifold C^3/Z_n x Z_n with discrete torsion.

Paper Structure

This paper contains 20 sections, 145 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Classical Vacuum Structure
  3. The case $q=-1$ with cubic deformation
  4. The general case $n>2$
  5. The Classical Effective Action and RG Cascade
  6. The case $q=-1$ with cubic deformation
  7. The case $n>2$ with quadratic deformation
  8. Engineering the Quantum Geometry from the Matrix Model
  9. Saddle point condition
  10. The general solution
  11. The case $q=-1$ with cubic deformation
  12. The case $n>2$ with quadratic deformation
  13. Relation to periods of the Calabi-Yau geometry
  14. A Generalization
  15. Conclusions
  16. ...and 5 more sections

Figures (3)

  • Figure 1: The branch cuts of $t(x)$ and the gluing conditions on them lead to a parameterization in terms of a torus $E_{\tilde{\tau}}$ with complex structure parameter $\tilde{\tau}$.
  • Figure 2: The one-cycles on the $u$-plane which lift to the compact 3-cycles of the Calabi-Yau geometry.
  • Figure 3: The Riemann surface for $t(u)$ in the case $n=3$. The two one-cycles on the $u$-plane lift to compact 3-cycles of the Calabi-Yau space.