We study three-dimensional gauge dynamics by using type IIB superstring brane configurations, which can be obtained from the M-theory configuration of M2-branes stretched between two M5-branes with relative angles. Our construction of brane configurations includes (p, q)5-brane and gives a systematic classification of possible threedimensional gauge theories. The explicit identification of gauge theories are made and their mirror symmetry is discussed. As a new feature, our theories include interesting Maxwell-Chern-Simons system whose vacuum structure is also examined in detail, obtaining results consistent with the brane picture.

We study the creation of a fundamental string between D4-branes at angles in string theory. It is shown that R(−1) F part of the one-loop potential of open string changes its sign due to the change of fermionic zero-mode vacua when the branes cross each other. As a result the effective potential is independent of the angles when supersymmetry is partially unbroken, and leads to a consistent picture that a fundamental string is created in the process. We also discuss the s-rule in the configuration. The same result is obtained from the one-loop potential for the orthogonal D4-branes with non-zero field strength. The result is also confirmed from the tension obtained by deforming the Chern-Simons term on one D4-brane, which is induced by another tilted D4

We study the 3D field theory on one D3-brane stretched between (r, s) and (p, q)5branes. The boundary conditions are determined from the analysis of NS5 and D5 charges of the two 5-branes. We carry out the mode expansions for all the fields and identify the field theory as Maxwell-Chern-Simons theory. We examine the mass spectrum to determine the conditions for unbroken supersymmetry (SUSY) in this field theory and compare the results with those from the brane configurations. The spectrum is found to be invariant under the Type IIB SL(2, Z)-transformation. We also discuss the theory with matters and its S-dual configuration. The result suggests that the equivalence under S-duality may be valid if we include all the higher modes in the theories with matters. We also find an interesting phenomenon that SUSY enhancement happens in the field theory after dimensional reduction from 3D to 2D.

We study low-energy effective superpotentials for the phase with a confined photon in N = 1 supersymmetric gauge theories with an adjoint matter Φ and fundamental flavors Q,Q. Arbitrary classical gauge groups are considered. The results are used to derive the hyperelliptic curves which describe the Coulomb phase of N = 2 supersymmetric QCD with classical gauge groups. These curves are in agreement with those proposed earlier by several authors. Our results also produce the curves relevant to describe the Coulomb phase of N = 1 theories with a superpotential of the formQΦ l Q.

We derive the singularity conditions of the N = 1 generalized (general yukawa couplings and quark masses) form of hyperelliptic curves of SU(N c ) with N f flavors. The results reproduce the known form of N = 2 curves when the yukawa couplings and the quark masses reduce to those of N = 2. We obtained these curves by determining the dependence of the unbroken SU(2) gaugino condensation on the couplings in the moduli source terms which break N = 2 SQCD to N = 1 SU(N c ) gauge theory with the quarks and the adjoint matter, Φ. The degenerate component of the diagonalized classical vacuum expectation value of Φ is shown to be explicitly written in terms of these couplings, which enables us to determine the form of the gaugino condensation.