Complex Chern-Simons and the Gribov Scenario for Confinement
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PARTICLES AND FIELDS
Complex Chern-Simons and the Gribov Scenario for Confinement M. M. Amaral1,2 · V. E. R. Lemes1 · O. S. Ventura3
· L. C. Q. Vilar1
Received: 13 January 2020 © Sociedade Brasileira de F´ısica 2020
Abstract We show that BLG-ABJM type of theories, discovered in the context of the AdS/CFT correspondence, generates gauge propagators with the complex pole structure prescribed by the Gribov scenario for confinement, which was developed in the context of Yang-Mills theories. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive K¨all´en-Lehmann spectral representation for their two-point functions. Therefore, these operators satisfy the criteria to describe glueball condensates. We calculate the (first-order) contribution to the two-point function of the gauge invariant condensate in the ABJM framework. We show that the correlator can be interpreted as a physical composite particle state in terms of the K¨all´en-Lehmann representation. Keywords Supersymmetry · Gribov · K¨all´en-Lehmann · Yang-Mills
1 Introduction Three-dimensional gauge theory is an interesting laboratory for many studies in non-perturbative aspects of gauge field theories such as color confinement [1–3] or topological properties such as obtained from Chern-Simons action [4– 6]. Also, the three-dimensional Yang-Mills theory has local degrees of freedom and the coupling constant has dimension of mass. These properties indicate that this theory can be seen as an approximation for the high temperature phase of QCD with the mass gap in the role of the M. M. Amaral
[email protected] V. E. R. Lemes [email protected] O. S. Ventura [email protected] L. C. Q. Vilar [email protected] 1
Instituto de F´ısica, Universidade do Estado do Rio de Janeiro, Rua S˜ao Francisco Xavier 524, Maracan˜a, Rio de Janeiro, RJ, 20550-013, Brazil
2
Institute for Gravitation and the Cosmos & Physics Department, The Pennsylvania State University, University Park, PA 16802, USA
3
Centro Federal de Educac¸a˜ o Tecnol´ogica do Rio de Janeiro, Av. Maracan˜a 249, 20271-110, Rio de Janeiro, RJ, Brazil
magnetic mass [2]. In particular, one of the mechanisms to study color confinement comes from the analysis of Gribov copies [7], known generally as Gribov ambiguity, with special emphasis on the Gribov-Zwanziger model (GZ) [8–11] and its refined version (RGZ) [12]. One of the Gribov mechanism properties is that it generates propagators for gauge fields with complex poles, known as i-particles [13, 14]. The i-particles can not be identified with the propagation of simple massive particles but they provide the possibility to obtain condensates that behave like massive particles. This property is interpreted as confinement and known generally as a Gribov-Zwanziger scenario. The Gribov ambiguity is a general characteristic of the quantization of Yang-Mills theories and a general property of all local covariant renormalizable gauge fixing procedures [15]. It is importan
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