Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models

Abstract

We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of ${\mathbb{CP}}^1$ model by considering it as a specific decoupling limit of SQED${}_2$ model. This approach involves using a ${\mathbb{Z}}_3$ symmetry that leaves the supersymmetric parameter space of SQED${}_2$ model invariant to transform a pair of SQED${}_2$ holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED${}_2$ model and the two new transformed pairs turn out to be related by Stokes-like matrices. These three pairs of holomorphic blocks can be reduced to the known triplet of ${\mathbb{CP}}^1$ blocks in a particular decoupling limit where two of the chiral multiplets in the SQED${}_2$ model are made infinitely massive. This reduction then correctly reproduces the Stokes regions and matrices of the ${\mathbb{CP}}^1$ blocks. Along the way, we find six pairs of SQED${}_2$ holomorphic blocks in total, which lead to six Stokes-like regions covering uniquely the full parameter space of the SQED${}_2$ model.

arXiv comment28 pages, 4 figures; v2: 29 pages, discrete transformations identified as Z_3, text updated accordingly with no changes in final results, references added and typos corrected; v3: 31 pages, 6 figures (including a nontrivially colourful one), added analysis of Stokes regions for the SQED2 model itself, references updated and few more typos corrected (published version)

References in corpus (30)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Mirror Symmetry in Three Dimensional Gauge Theories
• The Exact Superconformal R-Symmetry Extremizes Z
• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
• Notes on SUSY Gauge Theories on Three-Sphere
• Multi-Matrix Models and Tri-Sasaki Einstein Spaces
• Supersymmetric Field Theories on Three-Manifolds
• Holomorphic Blocks in Three Dimensions
• N=2 supersymmetric theories on squashed three-sphere
• Factorisation of N = 2 theories on the squashed 3-sphere
• Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
• Supersymmetric partition functions and the three-dimensional A-twist
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Factorisation and holomorphic blocks in 4d
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Factorization of S^3/Z_n partition function
• Holomorphic blocks and the 5d AGT correspondence
• Boundaries, Vermas, and Factorisation
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Blocks and Vortices in the 3d ADHM Quiver Gauge Theory
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks

Cited by in corpus (1)

• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices