(The) field theoretic approach to high Tc superconductivity with abelian chern-simons term

Abstract

I start with a system involving O(3) nonlinear $\sigma$ -model and a Abelian Chern-Simons term. Since the latter is nonlocal in n field through A$\mu$, I rewrite the system into a CPI form which naturally appears a local gauge potential A$\mu$. And I also prove that CS term is locally the total divergence. the coefficient of CS term is fixed to n/4$\pi$, n=integer, by gauge invariance requirements on a three-dimensional manifold of the form $S^2\times{S^1}$. I find that the system is equivalent at low momenta to a system of n neutral fermions with strong Thirring type interactions between currents corresponding to different flavors, which cannot be fine-tuned to zero. Given that such system may be considered as long wave length limits of appropriate statistical systems describing high $T_c$ superconductors I relate these qualitative considerations to Lauglin``s ideas on pairing of spinons and (or) holones in order to explain the experimentally observed charge-2e order parameter.