Abstract
We provide tests of dualities for three-dimensional $$ \mathcal{N}=4 $$ quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on S 3. The dualities are generated by SL(2, ℤ) transformations and Hanany-Witten 5-brane moves. These contain mirror symmetry as well as dualities identifiying fixed points of Yang-Mills quivers and Chern-Simons theories. The partition function is given by a matrix model, that can be nicely rearranged into a sequence of factors mimicking the brane realization. Identities obeyed by these elementary factors can be used to match the partition functions of dual theories, providing tests for the full web of dualities. In particular we are able to check mirror symmetry for linear and circular quivers with gauge nodes of arbitrary ranks. Our analysis also leads to a proof of a conjectured formula evaluating the matrix models of linear quiver SCFTs.
Highlights
N = 4 Yang-Mills theories in three dimensions admit infrared strongly coupled fixed points, subject to the mirror symmetry duality [1]
We provide tests of dualities for three-dimensional N = 4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on S3
The partition function is given by a matrix model, that can be nicely rearranged into a sequence of factors mimicking the brane realization
Summary
The second idea was to understand the full SL(2, Z) duality group of the three-dimensional quiver theories, inherited from type IIB string theory [16] It was shown in [17] that these more general dualities can map Yang-Mills fixed points to Chern-Simons theories coupled to matter. To test these dualities we decompose the matrix model which computes the partition function into a sequence of elementary factors, that can be associated to the 5-branes in the brane realization This approach was already developed in [25] for quiver with nodes of equal ranks and we generalize it to quivers of arbitrary ranks and including mass and FI deformation terms. The SCFTs arise in the infrared limit and the superconformal algebra is OSp(4|4)
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