Abstract
It is known that matrix models computing the partition functions of three-dimensional mathcal{N} = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.
Highlights
Consisting of D3-branes with one direction compactified, an NS5-brane and a (1, k)5-brane in type IIB string theory
It is known that matrix models computing the partition functions of threedimensional N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks
Our method can be applied to a wide class of rank deformations since we provided the computation method for deformed factors, which are parts of matrix models
Summary
We present brane configurations in type IIB string theory which we deal with in this paper. We briefly review matrix models computing the partition functions of the worldvolume theories of the brane configurations. We explain our strategy to apply the Fermi gas formalism to these matrix models. We review the way we rewrite the matrix models as the partition functions of ideal Fermi gases for simple examples including the ABJ theory. [fa,b]Aa,×b B denotes an A × B matrix whose (a, b) element is fa,b
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