Sp(N_c) Gauge Theories and M Theory Fivebrane

Abstract

We analyze M theory fivebrane in order to study the moduli space of vacua of N=1 supersymmetric $Sp(N_c)$ gauge theories with $N_f$ flavors in four dimensions. We show how the N=2 Higgs branch can be encoded in M theory by studying the orientifold which plays a crucial role in our work. When all the quark masses are the same, the surface of the M theory spacetime representing a nontrivial ${\mathbf{S}}^1$ bundle over ${\mathbf{R}}^3$ develops $A_{N_f-1}$ type singularities at two points where D6 branes are located. Furthermore, by turning off the masses, two singular points on the surface collide and produce $A_{2N_f-1}$ type singularity. The sum of the multiplicities of rational curves on the resolved surface gives the dimension of N=2 Higgs branch which agrees with the counting from the brane configuration picture of type IIA string theory. By rotating M theory fivebranes we get the strongly coupled dynamics of N=1 theory and describe the vacuum expectation values of the meson field parameterizing Higgs branch which are in complete agreement with the field theory results. Finally, we take the limit where the mass of adjoint chiral multiplet goes to infinity and compare with field theory results. For massive case, we comment on some relations with recent work which deals with N=1 duality in the context of M theory.

25 pages, Latex:We clarified the discussion of Higgs and Coulomb branch on page 14. This final version will appear in Phys. Rev. D

References in corpus (30)

• Solutions Of Four-Dimensional Field Theories Via M Theory
• Branes, Superpotentials and Superconformal Fixed Points
• Branes And The Dynamics Of QCD
• Branes and N=1 Duality in String Theory
• Brane Dynamics and N=1 Supersymmetric Gauge Theory
• Branes and N=2 Theories in Two Dimensions
• Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• Orientifolds, Branes, and Duality of 4D Gauge Theories
• Branes and Six Dimensional Fixed Points
• Geometry of N=1 Dualities in Four Dimensions
• M Theory And Seiberg-Witten Curves: Orthogonal and Symplectic Groups
• Type IIA Superstrings, Chiral Symmetry, and N=1 4D Gauge Theory Dualities
• Comments on the M Theory Approach to N=1 SQCD and Brane Dynamics
• Rotated Branes and N=1 Duality
• Monopole Condensation and Confining Phase of N=1 Gauge Theories Via M Theory Fivebrane
• Brane Configurations and 4D Field Theory Dualities
• Four-dimensional BPS-spectra via M-theory
• Chiral Symmetry from Type IIA Branes
• Geometry, D-branes and N=1 Duality in Four Dimensions with Product Gauge Group
• N = 1 Field Theory Duality from M-theory
• Non-Abelian Conifold Transitions and N=4 Dualities in Three Dimensions
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
• Duality in Sp and SO Gauge Groups from M Theory
• Dualities in 4D Theories with Product Gauge Groups from Brane Configurations
• From M-theory to F-theory, with Branes
• On the Orientifolding of Type II NS-Fivebranes
• Geometry, D-Branes and N=1 Duality in Four Dimensions I
• Superpotentials of N=1 Supersymmetric Gauge Theories from M-theory
• Geometry, D-Branes and N=1 Duality in Four Dimensions II

Cited by in corpus (14)

• Brane Dynamics and Gauge Theory
• M-theory Lift of Meta-Stable Brane Configuration in Symplectic and Orthogonal Gauge Groups
• Open/Closed String Dualities and Seiberg Duality from Geometric Transitions in M-theory
• M Theory, Type IIA String and 4D N=1 SUSY SU(N_L) X SU(N_R) Gauge Theory
• Meta-Stable Brane Configuration with Orientifold 6 Plane
• M Theory Fivebrane and Confining Phase of N=1 $SO(N_c)$ Gauge Theories
• Meta-Stable Brane Configuration and Gauged Flavor Symmetry
• Supersymmetric Gauge Theories with Classical Groups via M Theory Fivebrane
• Supersymmetric SO(N)/Sp(N) Gauge Theory from Matrix Model:Exact Mesonic Vacua
• A cascading N=1 Sp(2N+2M)xSp(2N) gauge theory
• Comments on $SO/Sp$ Gauge Theories from Brane Configurations with an O6 Plane
• M theory and the ``integrating in'' method with an antisymmetric tensor
• M-Theory Five-brane Wrapped on Curves for Exceptional Groups
• Aspects of Confinement and Screening in M theory