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

We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $$ \mathbbm{CP} $$ CP 1 model by considering it as a specific decoupling limit of SQED2 model. This approach involves using a ℤ3 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 $$ \mathbbm{CP} $$ 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 $$ \mathbbm{CP} $$ 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.

D-modules of pure Gaussian type and enhanced ind-sheaves

Differential systems of pure Gaussian type are examples of D-modules on the complex projective line with an irregular singularity at infinity, and as such are subject to the Stokes phenomenon. We employ the theory of enhanced ind-sheaves and the Riemann–Hilbert correspondence for holonomic D-modules of D’Agnolo and Kashiwara to describe the Stokes phenomenon topologically. Using this description, we perform a topological computation of the Fourier–Laplace transform of a D-module of pure Gaussian type in this framework, recovering and generalizing a result of Sabbah.

A note on the Stokes phenomenon in flow under an elastic sheet

The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue ‘Stokes at 200 (part 2)’.