Speaker
Mr
Grigory Vartanov
(Joint Institute for Nuclear Research)
Description
We demonstrate how one can construct renormalizable
perturbative expansion in formally nonrenormalizable higher
dimensional field theories. It is based on $1/N$-expansion and
results in a logarithmically divergent perturbation theory in
arbitrary high space-time dimension. First, we consider a simple
example of $N$-component scalar filed theory and then extend this
approach to Abelian and non-Abelian gauge theories with $N_f$
fermions. In the latter case, due to self-interaction of
non-Abelian fields the proposed recipe requires some modification
which, however, does not change the main results. The resulting
effective coupling is dimensionless and is running in accordance
with the usual RG equations. The corresponding beta function is
calculated in the leading order and is nonpolynomial in effective
coupling. It exhibits either UV asymptotically free or IR free
behaviour depending on the dimension of space-time. The original
dimensionful coupling plays a role of a mass and is also
logarithmically renormalized. We analyze also the analytical
properties of a resulting theory and demonstrate that in general
it acquires several ghost states with negative and/or complex
masses. In the former case, the ghost state can be removed by a
proper choice of the coupling. As for the states with complex
conjugated masses, their contribution to physical amplitudes
cancels so that the theory appears to be unitary.
Authors
Prof.
Dmitri Kazakov
(Joint Institute for Nuclear Research)
Mr
Grigory Vartanov
(Joint Institute for Nuclear Research)
