arXiv subjects

Jake Stedman

Publications and source records attributed to Jake Stedman.

3 recordsLinked to original sources

arXiv2026

Hamiltonian Analysis of Doubled 4d Chern-Simons

Motivated by a conjecture that doubled four-dimensional Chern-Simons produces new integrable models, we perform its Hamiltonian analysis and find the theory's Poisson algebra. This requires carefully accounting for a set of boundary conditions that identify two gauge fields. Two methods for doing so are given, one of which is based on edge-modes and the other on a recharacterisation of the boundary conditions as constraints. We find that the Poisson algebra is that of an affine Gaudin model subject to a constraint, generalising the Goddard-Kent-Olive construction (from conformal field theory) to the world of integrable models. We also conjecture the existence of extended quantum groups and a generalisation of the affine Harish-Chandra Isomorphism.

hep-th↗

arXiv2023

Simplifying the Type $A$ Argyres-Douglas Landscape

A well-established organisational principle for Argyres--Douglas-type $\mathcal{N}=2$ superconformal field theories in four dimensions is to characterise such theories by the data defining a(n irregular) Hitchin system on $\mathbb{CP}^1$. The dictionary between Hitchin system data and various features of the corresponding SCFT has been studied extensively, but the overall structure of the resulting space of SCFTs still appears quite complicated. In this work, we systematically delineate a variety of simplifications that arise within this class of constructions due to several large classes of isomorphisms between SCFTs associated with inequivalent Hitchin system data (and their exactly marginal gaugings). We restrict to the most studied class of theories, namely the type $A$ theories without outer automorphism twists.

hep-th↗

arXiv2021

Four-Dimensional Chern-Simons and Gauged Sigma Models

In this paper, we introduce a new method for constructing gauged $\sigma$-models from four-dimensional Chern-Simons (4d CS) gauge theory. We begin with a review of recent work by several authors on the classical generation of integrable $\sigma$-models from 4d CS. In this approach, a gauge field is required to satisfy certain boundary conditions on two-dimensional defects inserted into the bulk. Using these boundary conditions, the equations of motion are solved, and the result is substituted back into the action. This yields a $\sigma$-model whose integrability is guaranteed because the 4d CS field is gauge equivalent to a Lax connection. Using a theory consisting of two 4d CS fields coupled together on new classes of ``gauged'' defects, we construct gauged $\sigma$-models and identify a unifying action. These models are conjectured to be integrable because the 4d CS fields remain gauge equivalent to two Lax connections. Finally, we consider two examples: the gauged Wess-Zumino-Witten model and the nilpotent gauged Wess-Zumino-Witten models. This latter model is of note as one can find the conformal Toda models from it.

hep-th↗