The asymmetry of the dimension 2 gluon condensate: the zero temperature case

Abstract

We provide an algebraic study of the local composite operators A_μA_ν-δ_{μν}/d A^2 and A^2, with d=4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A_μA_νinto its trace and traceless part. We present explicit results for the relevant renormalization group functions to three loop order, accompanied with various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for <A^2> \neq 0, together with <A_μA_ν-δ_{μν}/d A^2>=0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the <A^2> condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase diagram.

25 pages

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• 1/q^2 Corrections and Gauge/String Duality
• Magnetic component of Yang-Mills plasma
• Dimension-two gluon condensate from large-Nc Regge models
• Electric-magnetic asymmetry of the A^2 condensate and the phases of Yang-Mills theory
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Cited by in corpus (7)

• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• The asymmetry of the dimension 2 gluon condensate: the finite temperature case
• The Dynamics and Thermodynamics of Soft-Wall AdS/QCD
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• The Thermodynamics of a 5D Gravity-Dilaton-Tachyon Solution
• Aspects of the Gribov problem in Euclidean Yang-Mills theories