Vacuum Instability in Chern-Simons Theory, Null Vectors and Two-Dimensional Logarithmic Operators

TL;DR

This paper explores the connection between 2D conformal field theories and 3D topologically massive gauge theories, revealing how non-unitary states induce vacuum instability and how logarithmic operators relate to Jordan structures in the Hamiltonian.

Contribution

It establishes a new relation linking non-unitary states in 2D CFTs to supercritical charges and vacuum instability in 3D gauge theories, highlighting the role of logarithmic operators.

Findings

Non-unitary descendants correspond to supercritical charges causing vacuum instability.

Logarithmic operators are associated with zero energy ground states and Jordan structures.

A novel connection between 2D CFTs and 3D topologically massive gauge theories is demonstrated.

Abstract

A new relation between two-dimensional conformal field theories and three-dimensional topologically massive gauge theories is found, where the dynamical nature of the 3d theory is ultimately important. It is shown that the those primary states in CFT which have non-unitary descendants correspond in the 3d theory to supercritical charges and cause vacuum instability. It is also shown that logarithmic operators separating the unitary sector from a non-unitary one correspond to an exact zero energy ground state in which case the 3d Hamiltonian naturally has a Jordan structure.