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

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

2009-07-02

arxiv.org/abs/0907.0380v1

Phys.Rev.D80:065017,2009

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1103/PhysRevD.80.065017

We provide an algebraic study of the local composite operators A_\mu A_\nu-\delta_{\mu\nu}/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_\mu A_\nu into 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 \neq 0, together with =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 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.

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