Abstract
We study a class of two-dimensional ${\cal N}=(0, 4)$ quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d ${\cal N}=2$ theories of class ${\cal S}$, labelled by a Riemann surface ${\cal C}$. The dual descriptions arise from various pair-of-pants decompositions, that involves an analog of the $T_N$ theory. Especially, we find the superconformal index of such theories can be written in terms of a topological field theory on ${\cal C}$. We interpret this class of SCFTs as the ones coming from compactifying 6d ${\cal N}=(2, 0)$ theory on $\mathbb{CP}^1 \times {\cal C}$
Highlights
Was shown that a large class of N = (0, 2) theories possess dualities reminiscent to Seiberg dualities in four dimensions
We study a class of two-dimensional N = (0, 4) quiver gauge theories that flow to superconformal field theories
We show that many statements about N = 2 theories in 4d can be translated into statements about analogous N = (0, 4) theories
Summary
The first theory is a linear quiver gauge theory, and the second one contains trifundamental hypermultiplet coupled to three SU(2) gauge groups One can consider another example of duality between two distinct 2d (0,4) theories that follows from the crossing symmetry as depicted in figure 5. The index of such theory can be understood as the 2d TQFT partition function of a genus two Riemann surface. Let us note that cL > 2cR/3 when g > 0 This is because, unlike in the case when quiver has no loops, unbroken directions of the gauge group give rise to a non-empty complex rank 2g bundle E of left-moving Fermions, the only remnant of the usual Coulomb branch that would appear for (4, 4) theories. In the UV we only see the diagonal of these two symmetries, SU(2)+R, with anomaly coefficient being half the difference of affine algebras levels, (nh − nv)/2
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