New 3d dualities are obtained by T-duality reduction of 4d mezzanine and balcony models, with partition function matching after double scaling limit and a proof of required confining dualities via tensor deconfinement.
Chiral Rings, Singularity Theory and Electric-Magnetic Duality
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abstract
We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e.\ singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges ``trivial'' classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.
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Nilpotent-direction analysis on the moduli space supports duality for W_{A_k} superpotentials but shows the duality conjecture fails for W_{D_{k+2}} models in N=1 SUSY gauge theories.
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Overlooking 3d dualities from mezzanines and balconies
New 3d dualities are obtained by T-duality reduction of 4d mezzanine and balcony models, with partition function matching after double scaling limit and a proof of required confining dualities via tensor deconfinement.
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The Potency of Nilpotence
Nilpotent-direction analysis on the moduli space supports duality for W_{A_k} superpotentials but shows the duality conjecture fails for W_{D_{k+2}} models in N=1 SUSY gauge theories.