According to the conventional notion, if a system has strict gauge symmetry, the mass of gauge field in the lagrangian must be zero [1 ]. With the development of the gauge theory, this notion has already been changed. In the gauge theory developed by Wu [2 ], under the precondition that the system has strict gauge symmetry, the theory contains massive gauge bosons. In fact, this result holds no...

We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. This is done without prescribing the space states in definition theory.

Apply the T-duality and smeared twist to the D3-brane solution one can construct the supergravity backgrounds which may dual to supersymmetric or non-supersymmetric noncommutative dipole field theory. We introduce D7-brane probe into the dual supergravity background to study the chiral dynamics and meson spectrum therein. We first find that the non-commutative dipole field does not induce the c...

We develop a supersymmetric extension of Chern-Simons theory and Chern-Simons-LandauGinzburg theory for the supersymmetric quantum Hall liquid. Supersymmetric counterparts of topological and gauge structures peculiar to the Chern-Simons theory are inspected in the supersymmetric Chern-Simons theory. We also explore an effective field theoretical description for the supersymmetric quantum Hall l...

This is a pedagogical introduction to D-branes, addressed to graduate students in field theory and particle physics and to other beginners in string theory. I am not going to review the most recent results since there are already many good papers on web devoted to that. Instead, I will present some old techniques in some detail in order to show how some basic properties of strings and branes as...