Abstract
We propose some new infra-red dualities for 2d mathcal{N} = (0, 2) theories. The first one relates a USp(2N) gauge theory with one antisymmetric chiral, four fundamental chirals and N Fermi singlets to a Landau-Ginzburg model of N Fermi and 6N chiral fields with cubic interactions. The second one relates SU(2) linear quiver gauge theories of arbitrary length N − 1 with the addition of N Fermi singlets for any non-negative integer N. They can be understood as a generalization of the duality between an SU(2) gauge theory with four fundamental chirals and a Landau-Ginzburg model of one Fermi and six chirals with a cubic interaction. We derive these dualities from already known 4d mathcal{N} = 1 dualities by compactifications on {mathbbm{S}}^2 with suitable topological twists and we further test them by matching anomalies and elliptic genera. We also show how to derive them by iterative applications of some more fundamental dualities, in analogy with similar derivations for parent dualities in three and four dimensions.
Highlights
A complete understanding of an organizing principle behind the currently known IR dualities in two, three and four dimensions hasn’t been achieved yet
The second one relates SU (2) linear quiver gauge theories of arbitrary length N −1 with the addition of N Fermi singlets for any non-negative integer N. They can be understood as a generalization of the duality between an SU (2) gauge theory with four fundamental chirals and a Landau-Ginzburg model of one Fermi and six chirals with a cubic interaction
This precisely coincides with the alternative version of the duality between SU (2) with 4 chirals and the LG model of 6 chirals and one Fermi fields with a cubic interaction of [11, 18] we presented at the end of subsection 2.1, where we already noticed the decoupling of the U (1)d symmetry in the IR on the side of theory TA
Summary
We review some known results that will be important in our discussion. The non-compact directions are parametrized by five out of the six chirals Φab because of the constraint (2.10) Since these six chirals belong to the same representation of the SU (4)u global symmetry, we must require that they all have zero R-charge and this fixes the mixing coefficient to Rs = 0. This result can’t be correct, as the central charges are negative for any N We interpret this as due to the fact that the theories have a non-compact target space, since the number of chirals on the gauge theory side is large enough to expect no SUSY breaking in the IR (see footnote 6). With qx being the charge under U (1)x and Rx the mixing coefficient of U (1)x with the R-symmetry, while on the WZ side they are fixed by the superpotential This duality can be derived by iterative applications of the Intriligator-Pouliot duality in the confining case. In subsubsection 3.3.2 we will present a similar derivation for the 2d version of the duality that we are going to discuss
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