Abstract
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this reduction. We translate the identity between indices of the dual 4d theories to 3d. This produces various new identities between partition functions of 3d dual phases.
Highlights
Exact results in supersymmetry, as from the recent progress in localisation, lead to efficient tests of dualities
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions
We study the dimensional reduction of SQCD with an adjoint [11] at the level of the index and the partition function
Summary
The magnetic phase is an SU(kNf − Nc) gauge theory, with Nf dual (anti-) fundamentals q and qand one adjoint Y. By gauging the non-anomalous global U(1)B in the electric and in the magnetic phase one can extend the duality to the unitary gauge groups U(Nc) and U(kNf − Nc). This is the case considered in this paper. The magnetic phase is a U(kNf −Nc) YM gauge theory with Nf dual (anti-) fundamentals q and qand one adjoint Y. In 3d we have additional 2k gauge singlets, tj,±, corresponding to the electric monopole operators (2.4) They couple to the magnetic theory through the superpotential k−1 k−1. The Coulomb branch is lifted and no monopole operators appear in the description of the low energy theory
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