Complex Chern-Simons and Gribov

TL;DR

This paper connects contact point between contact point between two approaches to confinement, showing that certain gauge theories generate propagators with complex poles consistent with the Gribov scenario, enabling the definition of physical glueball operators.

Contribution

It demonstrates that BLG-ABJM like theories produce gauge propagators with complex poles, facilitating the construction of physical glueball operators with positive spectral representation.

Findings

Gauge propagators exhibit complex pole structure consistent with Gribov scenario.

Constructed gauge-invariant operators with positive Källén-Lehmann spectral representation.

Calculated the two-point function of a gauge-invariant condensate showing its particle interpretation.

Abstract

We explore a contact point between two distinct approaches to the confinment problem. We show that BLG-ABJM like theories generate gauge propagators with just the complex pole structure prescribed by the Gribov scenario for confinemnt. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive K\"{a}ll\'{e}n-Lehmann spectral representation for their two-point functions . Then, these operators satisfy the criteria to describe glue-ball condensates. We calculate the (first order) contribution to the two-point function of the gauge invariant condensate in an ABJM environment, showing its interpretation as a physical particle along K\"{a}ll\'{e}n-Lehmann. In the meantime, we argue for the necessity of absorbing Witten's work on holomorphic complex theories in order to settle the physical interpretation of this non-perturbative scenario.