5 M ay 1 99 8 U ( 1 ) × SU ( 2 ) Chern – Simons gauge

The Chern-Simons bosonization with U(1)× SU(2) gauge field is applied to the 2-D t− J model in the limit t ≫ J , to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average – a coexisting flux phase and s + id-like RVB state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V , the holon field is a fermion and the spinon field is a hard– core boson. Within this approximation we show that the B field produces a π flux phase for the holons, converting them into Dirac–like fermions, while the V field, taking into account the feedback of holons produces a gap for the spinons vanishing in the zero doping limit. The nonlinear σ-model with a mass term describes the crossover from the short-ranged antiferromagnetic (AF) state in doped samples to long range AF order in reference compounds. Moreover, we derive a low–energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. Neglecting the gauge fluctuations, the holons are described by the Fermi liquid theory with a Fermi surface consisting of 4 “half-pockets” centered at (±2 ,±2 ) and one reproduces the results for the electron spectral function obtained in the mean field approximation, in agreement with the photoemission data on underdoped cuprates. The gauge fluctuations are not confining due to coupling to holons, but nevertheless yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalisation effects due to gauge fluctuations give rise to non–Fermi liquid behaviour for the composite electron, in certain temperature range showing the linear in T resistivity. This