Competing orders in high-T_c superconductors

Within a (2+1)-dimensional U(1) gauge field theory, after calculating the Dyson-Schwinger equation for fermion self-energy we find that chiral symmetry breaking (CSB) occurs if the gauge boson has a very small mass but is suppressed when the mass is larger than a critical value. In the CSB phase, the fermion acquires a dynamically generated mass, which leads to antiferromagnetic (AF) long-range order. Since in the superconducting (SC) state the gauge boson acquires a finite mass via Anderson-Higgs mechanism, we obtain a field theoretical description of the competition between the AF order and the SC order. As a compromise of this competition, there is a coexistence of these two orders in the bulk material of cuprate superconductors.