N=1 SUPERSYMMETRIC SPIN-CHARGE SEPARATION IN EFFECTIVE GAUGE THEORIES OF PLANAR MAGNETIC SUPERCONDUCTORS

Abstract

We present an N=1 supersymmetric extension of a spin-charge separated effective SU (2)× U S(1) "particle-hole" gauge theory of excitations about the nodes of the gap of a d-wave planar magnetic superconductor. The supersymmetry is achieved without introducing extra degrees of freedom, as compared to the nonsupersymmetric models. The only exception, the introduction of gaugino fields, finds a natural physical interpretation as describing interlayer coupling in the statistical model. The low-energy continuum theory is described by a relativistic (2+1)-dimensional supersymmetric CP1 σ-model with Gross–Neveu–Thirring-type four-fermion interactions. We emphasize the crucial role of the CP1 constraint by inducing a nontrivial dynamical mass generation for fermions (and thus superconductivity), in a way compatible with manifest N=1 supersymmetry. We also give a preliminary discussion of nonperturbative effects. We argue that supersymmetry suppresses the danger of superconductivity instanton contributions to the mass of the perturbatively massless gauge boson of the unbroken U(1) subgroup of SU(2). Finally, we point out the possibility of applying these ideas to effective gauge models of spin-charge separation in one-space dimensional superconducting chains of holons, which, for example, have recently been claimed to be important in the stripe phase of underdoped cuprates.