3d mirror symmetry as a canonical transformation

Abstract

We generalize the free Fermi-gas formulation of certain 3d $\mathcal{N}=3$ supersymmetric Chern-Simons-matter theories by allowing Fayet-Iliopoulos couplings as well as mass terms for bifundamental matter fields. The resulting partition functions are given by simple modifications of the argument of the Airy function found previously. With these extra parameters it is easy to see that mirror-symmetry corresponds to linear canonical transformations on the phase space (or operator algebra) of the 1-dimensional fermions.

11 pages, 2 figures. v2: figure added - version published in JHEP

References in corpus (4)

• Gluon and Wilson loop TMDs for hadrons of spin $\le$ 1
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
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Cited by in corpus (15)

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• Partition functions of 3d $\hat{D}$-quivers and their mirror duals from 1d free fermions
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• ABJM on ellipsoid and topological strings
• Exact relations between M2-brane theories with and without Orientifolds
• Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas
• Exact Instanton Expansion of ABJM Partition Function
• Localization at large N in Chern-Simons-matter theories
• Large N behavior of mass deformed ABJM theory
• On Three-Dimensional Quiver Gauge Theories of Type B
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$
• Exact partition function in $U(2)\times U(2)$ ABJM theory deformed by mass and Fayet-Iliopoulos terms
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• 3d dualities with decoupled sectors and brane transitions