Isotropy theorem for cosmological Yang-Mills theories

Isotropy theorem for cosmological Yang-Mills theories

We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a general...

Isotropy theorem for cosmological vector fields

We consider homogeneous Abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show—by making use of the virial theorem—that for an arbitrary potential and polarization pattern, the av...

Supersymmetric Yang-Mills Theories

In general, Picard-Fuchs systems in N = 2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independe...

From the Coleman-Mandula Theorem to Supersymmetric Yang-Mills Theories

Convergent Yang-Mills Matrix Theories

We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when D = 4, 6 and 10, and that correlation functions of degree k < kc = 2(D − 3) are convergent independently of the group. In the bosonic case we show that the part...