Entropy bounds and Cardy–Verlinde formula in Yang–Mills theory

Abstract

Using gauge formulation of gravity the three-dimensional SU(2) YM theory equations of motion are presented in equivalent form as FRW cosmological equations. With the radiation, the particular (periodic, big bangbig crunch) three-dimensional universe is constructed. Cosmological entropy bounds (so-called Cardy-Verlinde formula) have the standard form in such universe. Mapping such universe back to YM formulation we got the thermal solution of YM theory. The corresponding holographic entropy bounds (Cardy-Verlinde formula) in YM theory are constructed. This indicates to universal character of holographic relations.

Reformulations of Yang–Mills theories with space–time tensor fields

“…The Lagrangian L is divided into three parts in the above. The L (4) part is not new, as it has been given in [12] in a Hamiltonian analysis of the SU (2) Yang-Mills theory and recently in [25,26] through the similar approach as we just presented in the above. Because we have decomposed A a µ into two parts in Eq.…”

“…Because we have decomposed A a µ into two parts in Eq. (2.2), compared to the results in [12,25,26], we obtain two additional parts L (2) and L (0) . From the view of effective field theory, the terms L (2) and L (0) are both relevant operators.…”

Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

“…The first clear proposal to use the dreibein came from Haagensen and Johnson [1] in the context of Hamiltonian formalism in 3 + 1 dimensions. (References [2][3][4][5][6][7][8] are some other works on Yang-Mills theory involving various constructions of the metric.) The defining equation for the dreibein is the condition for the dreibein to be torsion-free with respect to a connection one-form.…”

“…Then Haagensen et al [9] followed it up with a deformation of the defining equation for the dreibein, removing the deformation at the end. References [5][6][7][8] have used the original defining equation for the dreibein as in [1] and not the deformation of it. In this work also, we use the original defining equation of [1].…”

“…Examples of this on the gravity side include the Chern-Simons formulation of 2 + 1 gravity [17], Ashtekar and loop gravity formulation [18], and the pure connection formulation of general relativity [19]. We have already cited several works which attack gauge theory using gravity [1][2][3][4][5][6][7][8][9]; a recent work is [20]. In spite of all this, our approach gives a new way to attack the exotic features of Yang-Mills theory.…”