arXiv subjects

S. G. Rajeev

Publications and source records attributed to S. G. Rajeev.

78 records · Page 5Linked to original sources

arXiv1992

Three Dimensional Quantum Chromodynamics

The subject of this talk was the review of our study of three ($2+1$) dimensional Quantum Chromodynamics. In our previous works, we showed the existence of a phase where parity is unbroken and the flavor group $U(2n)$ is broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective action for the theory and showed that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we studied the current algebra for this effective action and we found a co-homologically non trivial generalization of Kac-Moody algebras to three dimensions.

hep-th↗

arXiv1992

Two dimensional baryons in the large N limit

We propose a bilocal field theory for mesons in two dimensions obtained as a kind of non local bosonization of two dimensional QCD. Its semi-classical expansion is equivalent to the $1/N_c$ expansion of QCD. Using an ansatz we reduce the classical equation of motion of this theory in the baryon number one sector to a relativistic Hartree equation and solve it numerically. This (non topological) soliton is identified with the baryon.

hep-th↗

arXiv1992

Current Algebra in Three Dimensions

We study a three dimensional analogue of the Wess--Zumino--Witten model, which describes the Goldstone bosons of three dimensional Quantum Chromodynamics. The topologically non--trivial term of the action can also be viewed as a nonlinear realization of Chern--Simons form. We obtain the current algebra of this model by canonical methods. This is a three dimensional generalization of the Kac--Moody algebra.

hep-th↗

arXiv1992

The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

We consider the low energy limit of three dimensional Quantum Chromodynamics with an even number of flavors. We show that Parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern--Simons terms are necessary in the lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to be a model for quantum anti--ferromagnetism, our effective lagrangian can describe their long wavelength excitations (spin waves).

hep-th↗

arXiv1992

Baryons as Solitons in Three Dimensional Quantum Chromodynamics

We show that baryons of three dimensional Quantum Chromodynamics can be understood as solitons of its effective lagrangian. In the parity preserving phase we study, these baryons are fermions for odd $N_c$ and bosons for even $N_c$, never anyons. We quantize the collective variables of the solitons and there by calculate the flavor quantum numbers, magnetic moments and mass splittings of the baryon. The flavor quantum numbers are in agreement with naive quark model for the low lying states. The magnetic moments and mass splittings are smaller in the soliton model by a factor of $\log {F_π\over N_c m_π}$. We also show that there is a dibaryon solution that is an analogue of the deuteron. These solitons can describe defects in a quantum anti--ferromagnet.

hep-th↗

arXiv1992

$CP^N$ Model With a Chern-Simons Term

The $CP^N$ model in three euclidean dimensions is studied in the presence of a Chern-Simons term using the $1/N$ expansion. The $β$-function for the CS coefficient $θ$ is found to be zero to order $1/N$ in the unbroken phase by an explicit calculation. It is argued to be zero to all orders. Some remarks on the $θ$ dependence of the critical exponents are also made.

hep-th↗