Complex Chern-Simons and Gribov

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 theorie...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: Amaral, M M, Lemes, V E R, Ventura, O S, Vilar, L C Q
Format: Article
Language:English
Subjects:
Condensates
Mathematical analysis
Operators (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.05093