Applications of functional bosonization and infinite-dimensional gauge theories to the study of quantum transport phenomena

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As seen from the observation of Skyrmion excitations in quantum Hall systems, low-dimensional electron systems offer a realistic place to test and apply various ideas and techniques of gauge theories. Under a Grant-in-Aid over the past three years we have studied various aspects of the fractional quantum Hall effect (FQHE), such as composite bosons/fermions, collective excitations, and inter-layer coherence in bilayer systems, and, as a new subject, an interplay of supersymmetry and topological excitations.1. Combined use of the single-mode approximation and nonlinear realization of the W_∞ algebra enabled us to construct a long-wavelength effective theory of the FQHE, that relies on the incompressible nature of the quantum Hall states without referring to the standard composite-boson or composite-fermion picture of the FQHE. We applied it to study, in particular, some characteristic features of the collective excitations inherent in bilayer Hall systems.2. In certain supersymmetric theories topological (or central) charges acquire a new type of quantum anomalies, which play an important role in the presence of topological excitations. In academic 2003 I developed a superfield formulation of the central-charge anomalies for solitons and discussed their origins and role. I extended a superspace analysis to domain walls and vortices during academic 2004. The superspace approach tells us that the problem of central-charge anomalies is essentially the problem of the supertrace of the supercurrent, and reveals a dual (bosonic/fermionic) character of these anomalies.