Abhishek Agarwal, V. P. Nair
A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N
\leq 4$ supersymmetry in terms of gauge-invariant variables is presented,
generalizing earlier work on nonsupersymmetric gauge theories. Special
attention is paid to the volume measure of integration (over the gauge orbit
space of the fields) which occurs in the inner product for the wave functions
and arguments relating it to the renormalization of the Chern-Simons level
number and to mass-gaps in the spectrum of the Hamiltonians are presented. The
expression for the integration measure is consistent with the absence of mass
gap for theories with extended supersymmetry (in the absence of additional
matter hypermultiplets), while for the minimally supersymmetric case, there is
a mass-gap, the scale of which is set by a renormalized level number, in
agreement with indications from existing literature. The realization of the
supersymmetry algebra and the Hamiltonian in terms of the gauge invariant
variables is also presented.
View original:
http://arxiv.org/abs/1201.6609
No comments:
Post a Comment