Morse-Novikov theory, Heegaard splittings and closed orbits of gradient flows

The works of Donaldson and Mark make the structure of the Seiberg-Witten invariant of 3-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map on a 3-manifold. We study these invariants using the Morse-Novikov theory and Heegaard splitting for sutured manifolds, and make detailed computations for knot complements.Comment: 27 pages, 12 figure

Physical Meaning of the Current Vertex Corrections: DC and AC Transport Phenomena in High-Tc Superconductors

Famous non-Fermi liquid-like behaviors of the transport phenomena in high-Tc cuprates (Hall coefficient, magnetoresistance, thermoelectric power, Nernst coefficient, etc) are caused by the current vertex corrections in neary antiferromagnetic (AF) Fermi liquid, which was called the backflow by Landau. We present a simple explaination why the backflow is prominent in strongly correlated systems. In nearly AF Fermi liquid, R_H is enhanced by the backflow because it changes the effective curvature of the Fermi surfaces. Therefore, the relaxation time approximation is not appricalbe to a system near a magnetic quantum critical point (QCP).Comment: 2 pages, submitted to proceedings of LT24, Figure 1 has been change

A no-go theorem for the Majorana fermion on a lattice

A variant of the Nielsen--Ninomiya no-go theorem is formulated. This theorem states that, under several assumptions, it is impossible to write down a doubler-free Euclidean lattice action of a single Majorana fermion in $8k$ and $8k+1$ dimensions.Comment: 8 pages, uses PTPTeX. The final version to appear in Prog. Theor. Phy