Duality and confinement in 3d N=2 “chiral” SU(N) gauge theories

Abstract

We study the low-energy dynamics in three-dimensional N = 2 exceptional gauge theories with matters in a fundamental representation, especially focusing on confinement phases and on a quantum structure of the Coulomb branch in the moduli space of vacua. We argue that the confinement phases of these exceptional gauge theories have a single Coulomb branch. The 3d s-confinement phases for the exceptional gauge groups are associated with quantum-deformed moduli spaces of the corresponding 4d N = 1 exceptional gauge theories. * nii@itp.unibe.ch

“Chiral” and “non-chiral” 3d Seiberg duality

“…Next, we consider the Coulomb branch from the G 2 vector superfield. The G 2 Coulomb branch denoted by Z SU (2) was studied in [39,43]. When Z SU (2) obtains a non-zero expectation value, the gauge group is spontaneously broken to…”

3d “chiral” Kutasov-Schwimmer duality

“…While a lot of flat directions along the classical Coulomb branch are lifted by quantum corrections generated by monopole-instantons [26,27], some directions remain exactly massless. This situation is very different from the "vector-like" theories as noticed in [25]. (See also [12,24] where the chiral theory was partially studied.)…”

“…The low-energy theory for each SU(N i ) becomes the 3d N = 2 SU(N i ) gauge theory with F fundamentals andF anti-fundamentals. The dual of the "chiral" SU(N i ) SQCD was proposed in [25] and given by the SU(F − N i ) gauge theory. On the magnetic side, the similar breaking takes place and we obtain the SU(Ñ i ) gauge theory with k i=1Ñ i = kF − N. By identifying N i = F − N i , the "chiral" Kutasov-Schwimmer duality correctly reduces to the "chiral" Seiberg duality [25] for each SU(N i ) factor.…”

“…Now, the breaking pattern is very symmetric and hence the CS term k U (1) 1 U (1) 1 ef f , which is for instance generated by the 1-loop diagrams of ( , 1, 1) 1,a and (1, , 1) −1,a , is canceled out. Therefore, the "chiral" theory can have this type of the flat directions [25].…”

“…The U(1) 2 charge of Y bare a is proportional to k U (1) 1 U (1) 2 ef f and it becomes −a(N − a)(F −F ) which is negative for F >F . In order to construct the gauge invariant operator from it, we can multiply it by the massless component (1, 1, ) 0,(N −a) of the antifundamental matters [25,[28][29][30]. Since this component is charged under the remaining SU(2a) gauge group, the bare Coulomb branch should be dressed by the generalized antibaryon operatorsB (n 0 ,··· ,n k−1 ) :=Q n 0 (XQ) n 1 · · · (X k−1Q ) n k−1 , n ℓ = 2a (2.7)…”