Stokes phenomena in 3d N $$ \mathcal{N} $$ = 2 SQED2 and CP $$ \mathbbm{CP} $$ 1 models

Abstract

Abstract We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of CP $$ \mathbbm{CP} $$ 1 model by considering it as a specific decoupling limit of SQED2 model. This approach involves using a ℤ 3 symmetry that leaves the supersymmetric parameter space of SQED2 model invariant to transform a pair of SQED2 holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED2 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 CP $$ \mathbbm{CP} $$ 1 blocks in a particular decoupling limit where two of the chiral multiplets in the SQED2 model are made infinitely massive. This reduction then correctly reproduces the Stokes regions and matrices of the CP $$ \mathbbm{CP} $$ 1 blocks. Along the way, we find six pairs of SQED2 holomorphic blocks in total, which lead to six Stokes-like regions covering uniquely the full parameter space of the SQED2 model.

Keywords

• Chern-Simons Theories
• Supersymmetric Gauge Theory
• Nonperturbative Effects