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

Abstract

Abstract:We provide the reformulations of Yang-Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loop approximation.

Dreibein as Prepotential for Three-Dimensional Yang-Mills Theory

“…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.…”