Classical Hamiltonian Reduction On $D(2|1;\alpha)$ Chern-Simons Gauge Theory and Large N=4 Superconformal Symmetry

TL;DR

This paper explores the Hamiltonian reduction of $D(2|1;\alpha)$ Chern-Simons theory, revealing connections to large N=4 superconformal symmetry and linking 3d gauge theory with 2d superconformal field theories.

Contribution

It introduces a novel Hamiltonian reduction framework for $D(2|1;\alpha)$ Chern-Simons theory, connecting it to large N=4 superconformal algebra and characterizing Hilbert states.

Findings

Hilbert states relate to characters of large N=4 SCFT

Constraints on $D(2|1;\alpha)$ CS theory establish new links to 2d superconformal symmetry

Hamiltonian reduction provides a new perspective on gauge theory and CFT connection

Abstract

3d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;\alpha)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in $D(2|1;\alpha)$ CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties.