2D Seiberg-like dualities with an adjoint matter

Abstract

Abstract:We consider the analogue of Kutasov-Schwimmer-Seiberg duality for twodimensional N = (2, 2) U(k) gauge theory with one adjoint X with the superpotential Tr X l+1 and with fundamental and anti-fundamental chiral multiplets. We give the evidences for the proposed dualities by analytically proving that the elliptic genus of dual pair coincides with each other. For some of the dual pairs flowing to the superconformal field theory, we show the nonperturbative truncation of the chiral ring. For the theory with one adjoint and N f > k fundamental fields, we argue the theory exhibits mass gap.

On 3d Seiberg‐Like Dualities with Two Adjoints

“…We have two more chiral operators than the allowed monopole states. However, since we already have an imposed relation among those operators, (Tr 1 X) 2 |1, 1, 0, 0 , Tr 1 X 2 |1, 1, 0, 0 , (Tr 1 X) (Tr 2 X) |1, 1, 0, 0 , (Tr 2 X) 2 |1, 1, 0, 0 , Tr 2 X 2 |1, 1, 0, 0 (C. 26) while the allowed chiral operators composed of the lower dimensional monopole operators are (X 1 ) 2 W + 0 , X 2 W + 0 , X 1 V , which span the monopole states (C.26) together with composites of the lower dimensional monopole operators. We emphasize that while we don't specify the exact map between those two operators and the monopole states in (C.26), from the counting, we do know that those two, which carry global charges…”

A-twisted correlators and Hori dualities

“…In addition, new exact expressions were also obtained for correlation functions of certain half-BPS local operators in two-dimensional non-abelian gauge theories [10][11][12], generalizing the seminal results of [13][14][15]. See also [16][17][18][19][20][21][22][23][24][25][26][27][28] for related works.…”

“…In the dual theory, we find instead: 28) where the last factor is the contribution from the mesons M i j . For any pair of dual vacua {σ a } and {σ D a }, it is easy to see that:…”

2D Seiberg-like dualities for orthogonal gauge groups

“…Thus we have to work out each case separately so that check of the dualities are done for small rank of the gauge groups and small number of matter multiplets. Furthermore for the U (k) theory, equality of the elliptic genus of the dual pair can be shown analytically [10]. Here we manage to prove the equality of the elliptic genus of the dual pair for small k, N and numerically check the equality of the elliptic genus of the dual pair for more complicated cases.…”

“…Also additional difficulty arises when evaluating the elliptic genus of the theory with SO(k)/O(k) groups. For U (k) theory with fundamental flavors and adjoint chiral multiplets, the general formulae of the elliptic genus are known since the classification of the nontrivial JK-residues are possible [10]. However for the theory with SO(k)/O(k) gauge group with N fundamental multiplets, such general results are not known.…”