Two Phases of Supersymmetric Gluodynamics

We argue that supersymmetric gluodynamics has two phases with equivalent infrared behavior, one of which is asymptotically free and another one is superstrongly coupled in the ultraviolet domain.Comment: Plain LaTeX, 6 pages, 2 figures in a uuencoded file Final version which appeared in Phys. Rev. Let.75;2085-2087,1995 Corrected references and some Comments with no effect on conclusion

The Dual of Supersymmetric SU(2k) with an Antisymmetric Tensor and Composite Dualities

We suggest a dual to an $SU(2k)$ Susy gauge theory containing an antisymmetric tensor, \nf fundamentals and \nfb anti-fundamentals. This is done by expanding the theory into an equivalent description with two gauge groups and then performing known duality tranformations on each gauge group separately. Chiral operators, mass perturbations and flat directions are discussed.Comment: 17 pages, Harvma

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde

The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD

We analyze in detail the moduli space of vacua of N=2 SUSY QCD with n_c colors and n_f flavors. The Coulomb branch has submanifolds with non-Abelian gauge symmetry. The massless quarks and gluons at these vacua are smoothly connected to the underlying elementary quarks and gluons. Upon breaking N=2 by an N=1 preserving mass term for the adjoint field the theory flows to N=1 SUSY QCD. Some of the massless quarks and gluons on the moduli space of the N=2 theory become the magnetic quarks and gluons of the N=1 theory. In this way we derive the duality in N=1 SUSY QCD by identifying its crucial building blocks---the magnetic degrees of freedom---using only semiclassical physics and the non-renormalization theorem.Comment: 46 pages harvmac, 3 figures included using epsf.te

On the Low-Energy Effective Action of N=2 Supersymmetric Yang-Mills Theory

We investigate the perturbative part of Seiberg's low-energy effective action of N=2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on $U(1)_R$ anomaly and non-perturbative $\beta$-function arguments.Comment: 27 pages, RevTex, no figure

The Moduli Space and Monodromies of the N=2N=2 Supersymmetric Yang-Mills Theory with any Lie Gauge Groups

We propose a unified scheme for finding the hyperelliptic curve of $N=2$ SUSY YM theory with any Lie gauge groups. Our general scheme gives the well known results for classical gauge groups and exceptional $G_2$ group. In particular, we present the curve for the exceptional gauge groups $F_4, E_{6,7,8}$ and check consistency condition for them. The exact monodromies and the dyon spectrum of these theories are determined. We note that for any Lie gauge groups, the exact monodromies could be obtained only from the Cartan matrix.Comment: 17 pages, LaTeX fil

Geodesics and BPS States in N=2 Supersymmetric QCD

Conformal mapping techniques are used to determine analytically the geodesics on the Seiberg-Witten Riemann surface which correspond to the BPS dyon states in N=2 SUSY QCD with gauge group SU(2) and up to three flavors of massless fundamental matter. The results are exact for zero and two flavors, and approximate in the weak-coupling limit for one and three flavors. The presence of states of magnetic charge 2, in the three-flavor case only, is confirmed.Comment: 14 pages, 6 eps figures, LaTeX2e using packages amsmath, graphicx, float, captio

Towards Mirror Symmetry as Duality for Two-Dimensional Abelian Gauge Theories

Superconformal sigma models with Calabi--Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror symmetry for this class of Calabi--Yau spaces as a duality in the abelian gauge theory, giving the explicit mapping relating the two Lagrangians. The duality relates inequivalent theories which lead to isomorphic theories in the low-energy limit. This formulation suggests that mirror symmetry could be derived using abelian duality. The application of duality in this context is complicated by the presence of nontrivial dynamics and the absence of a global symmetry. We propose a way to overcome these obstacles, leading to a more symmetric Lagrangian. The argument, however, fails to produce a derivation of the conjecture.Comment: 14 pages, latex, no figure

Nonholomorphic Corrections to the One-Loop N=2 Super Yang-Mills Action

In addition to the familiar contribution from a holomorphic function \FF, the K\"ahler potential of the scalars in the nonabelian $N=2$ vector multiplet receives contributions from a real function \HH. We determine the latter at the one-loop level, taking into account both supersymmetric matter and gauge loops. The function \HH characterizes the four-point coupling of the $N=2$ vector-multiplet vectors for constant values of their scalar superpartners. We discuss the consequences of our results.Comment: 11 pages, Latex, one Postscript figure. Corrections to equation (24): 1 missing term added and one pair of indices interchange