Abstract
Searching for the simplest non-abelian 2d gauge theory with $\mathcal{N}=(0,2)$ supersymmetry and non-trivial IR physics, we propose a new duality for $SU(2)$ SQCD with $N_f = 4$ chiral flavors. The chiral algebra of this theory is found to be $\mathfrak{so}(8)_{-2}$, the same as in 4d $\mathcal{N}=2$ $SU(2)$ gauge theory with four hypermultiplets.
Highlights
Two-dimensional theories with N 1⁄4 ð0; 2Þ supersymmetry play an important role in string theory, quantum field theory, and connections with pure mathematics
They describe world sheet physics of heterotic strings. They can be found on two-dimensional objects in a 4D theory with N ≥ 1 supersymmetry and in 6D SCFTs with N ≥ ð1; 0Þ supersymmetry [in which case they support 2D (0,4) SUSY]
Given a possibility of a dynamical SUSY breaking, one might feel suspicious or, perhaps, even skeptical about the IR duality between SUð2Þ SQCD and the LG model (2). Such concerns are further supported by c-extremization [10], which leads to negative central charges on both sides of the duality and usually is a signal for either dynamical SUSY breaking or lack of a normalizable vacuum. We argue that both sides of the proposed duality do not break SUSY and, have equivalent IR physics, albeit are lacking the normalizable vacuum
Summary
Two-dimensional theories with N 1⁄4 ð0; 2Þ supersymmetry play an important role in string theory, quantum field theory, and connections with pure mathematics. Edge of dynamical SUSY breaking and, has nontrivial IR physics described by a (0,2) Landau-Ginzburg (LG) model with a cubic superpotential To build this theory we take the simplest non-Abelian gauge group SUð2Þ. We argue that both sides of the proposed duality do not break SUSY and, have equivalent IR physics, albeit are lacking the normalizable vacuum The latter aspect calls for better understanding of a noncompact IR dynamics in interacting two-dimensional quantum field theories. The result, is the hypersurface in C6, Φ12Φ34 − Φ13Φ24 þ Φ23Φ14 1⁄4 0: ð5Þ This is the same five-complex-dimensional space of vacua we found in SUð2Þ SQCD with Nf 1⁄4 4. The Pfaffian Calabi-Yau (6) is a noncompact analogue of a 2D N 1⁄4 ð2; 2Þ model considered in [14]
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