Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD

TL;DR

This paper compares r duality and Seiberg duality in N=1 supersymmetric QCD, revealing their equivalence in certain vacua and differences in others, highlighting a triality phenomenon across coupling regimes.

Contribution

It systematically analyzes the relationship between r duality and Seiberg duality in N=1 theories, demonstrating their equivalence in some vacua and differences in others, and introduces the concept of triality.

Findings

r and Seiberg dualities coincide in r=N vacua.

In (2/3)N_f < r < N vacua, the dualities do not match, indicating a triality.

Seiberg's duality at weak coupling reappears at r < N_f - N < (1/3)N_f.

Abstract

Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term \mu for the adjoint matter, eventually decoupling the adjoint matter in the limit of large \mu. If one starts from a large value of the parameter \xi\sim\mu m, where the original theory is at weak coupling, and decreases \xi one hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$.