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Warping and vacua of $(S)YM_{3+1}$

Iosif Bena, Aleksey Nudelman

TL;DR

This work extends the AdS/CFT-inspired dielectric-brane framework to a nonconformal 2+1D gauge theory on D2 branes by introducing fermion-mass perturbations. Higgs vacua arise from D2 polarization into D4 branes, while confining vacua come from D2 polarization into NS5 branes; three equal masses preserve ${\cal N}=2$ SUSY and yield Higgs phases, whereas a fourth mass fully breaks SUSY and produces confinement. The authors construct explicit string-theory duals for domain walls, condensates, baryon vertices, flux tubes, and glueballs, analyze the Kahler potential structure, and perform a nontrivial consistency check of the NS5-brane action in a D2 background. They further discuss flows to M-theory and the absence of naked singularities, delineating a coherent picture of Higgs–confinement dynamics in 3D YM from dielectric-brane physics.

Abstract

We use dielectric branes to find non singular string theory duals of a perturbed 2+1 dimensional gauge theory living on D2 branes. By adding fermion masses we obtain theories with reduced supersymmetry. The Higgs vacua of the perturbed theory correspond to polarization of the D2 branes into D4 branes. The confining vacua correspond to polarization of the D2 branes into NS5 branes. We consider different mass perturbations. Adding three equal masses preserves N=2 supersymmetry. In this case there are no confining vacua. By adding a fourth fermion mass we break all the supersymmetry, and find confining vacua. We also obtain duals for domain walls, condensates, baryon vertices, glueballs and flux tubes. We comment on the Kahler potentials for the Higgs and confining phases. In the course of the calculations we also find a nontrivial consistency check of the NS5 brane action in a D2 brane background.

Warping and vacua of $(S)YM_{3+1}$

TL;DR

This work extends the AdS/CFT-inspired dielectric-brane framework to a nonconformal 2+1D gauge theory on D2 branes by introducing fermion-mass perturbations. Higgs vacua arise from D2 polarization into D4 branes, while confining vacua come from D2 polarization into NS5 branes; three equal masses preserve SUSY and yield Higgs phases, whereas a fourth mass fully breaks SUSY and produces confinement. The authors construct explicit string-theory duals for domain walls, condensates, baryon vertices, flux tubes, and glueballs, analyze the Kahler potential structure, and perform a nontrivial consistency check of the NS5-brane action in a D2 background. They further discuss flows to M-theory and the absence of naked singularities, delineating a coherent picture of Higgs–confinement dynamics in 3D YM from dielectric-brane physics.

Abstract

We use dielectric branes to find non singular string theory duals of a perturbed 2+1 dimensional gauge theory living on D2 branes. By adding fermion masses we obtain theories with reduced supersymmetry. The Higgs vacua of the perturbed theory correspond to polarization of the D2 branes into D4 branes. The confining vacua correspond to polarization of the D2 branes into NS5 branes. We consider different mass perturbations. Adding three equal masses preserves N=2 supersymmetry. In this case there are no confining vacua. By adding a fourth fermion mass we break all the supersymmetry, and find confining vacua. We also obtain duals for domain walls, condensates, baryon vertices, glueballs and flux tubes. We comment on the Kahler potentials for the Higgs and confining phases. In the course of the calculations we also find a nontrivial consistency check of the NS5 brane action in a D2 brane background.

Paper Structure

This paper contains 25 sections, 102 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Perturbation of the bulk
  3. Polarization into D4 branes wrapped on $S^2$.
  4. D4 brane probes
  5. The full problem
  6. The near shell solution
  7. NS5 brane probes
  8. The NS5 brane action
  9. The NS5 brane probe
  10. NS5 brane warping
  11. Unequal masses
  12. SO(4) invariant non supersymmetric solutions
  13. The near shell metric of an NS5 brane wrapped on a 3-ellipsoid
  14. The near shell metric of an NS5 brane wrapped on a 3-sphere
  15. Gauge Theory
  16. ...and 10 more sections

Figures (2)

  • Figure 1: Effective potential as a function of $r$. The local maximum is at $r=\frac{2\sqrt{g_s A m}}{3}\sqrt{1-\frac{1}{\sqrt{7}}}$ . The local minimum is at $r_0=\frac{2\sqrt{g_s A m}}{3}\sqrt{1+\frac{1}{\sqrt{7}}}$.
  • Figure 2: Squashed $4$ ellipsoid in the $(w_1,w_2,w_3,w_4)$ plane. We calculate $Z$ at points 1 and 2.