Quark Number Fractionalization in N=2 Supersymmetric $SU(2) \times U(1)^{N_f}$ Gauge Theories

We consider evidence for the existence of gauge configurations with fractional charge in pure N=1 supersymmetric Yang-Mills theory . We argue that these field configurations are singular and have to be treated as distributions. It is shown that the path integral representation of constant Green's functions can be reduced to a finite dimensional integral. The fractional configurations are essentially the zero size limit of the usual instantons and they have a reduced number of...

We derive the central charge and BPS equations from the low-energy effective action for N=2 SU(2) Yang-Mills theory in the Coulomb phase, using a systematic, canonical procedure. We then obtain solutions for monopole and dyon BPS states, whose core structure is described by a dual Lagrangian containing the monopole or dyon as a fundamental field. Spherically symmetric states possess a shell of charge at a characteristic radius.

We analyze the Coulomb phase of theories of $N=2$ SQCD with $SU(N_c)$ gauge groups which are conjectured to have exact electric-magnetic duality. We discuss the duality transformation of the particle spectrum, emphasizing the differences between the general case and the $SU(2)$ case. Some difficulties associated with the definition of the duality transformation for a general gauge group are discussed. We compute the classical monopole spectrum of these theories, and when it i...

We show that the baryon number of N=2 supersymmetric QCD can be twisted in order to couple the topological field theory of non-abelian monopoles to $Spin^c$-structures. To motivate the construction, we also consider some aspects of the twisting procedure as a gauging of global currents in two and four dimensions, in particular the role played by anomalies.

Electric-magnetic duality allows to calculate the central charges of N=2 supersymmetric theories with massless hypermultiplets as derivatives of simple modular forms. The procedure reproduces the Seiberg-Witten results for N_f=0,2,3 in a uniform way, but indicates open problems for N_f=1.

A new discrete symmetry is shown to govern and simplify low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary gauge group. Each element of the related symmetry group S_r, r being the rank of the gauge group, represents a permutation of r electric charges available in the theory accompanied by a concurrent permutation of r monopoles, provided the sets of charges and monopoles are chosen properly. The superpotential is symmetric under S_r. This symmetry...

The parallel roles of modular symmetry in ${\cal N}=2$ supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -- magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of ${\cal N}=2$ supersymmetric Yang-Mills in 3+1 dimensions, scaling f...

We propose a method for the evaluation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics. We rederive a known result for the SU(2) gauge group and generalize it to any SU(N) gauge group.

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavors of quarks in the vector representation are constructed. The quantum moduli spaces for $2N_f < N_c-1$ are determined completely by imposing $R$-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue calculations. The quantum moduli spaces for $2N_f\geq N_c-1$ t...

We present an explicit non-perturbative solution of N=2 supersymmetric SU(N_c) gauge theory with N_f \le 2N_c flavors generalizing results of Seiberg and Witten for N_c=2.