Kazuo Fujikawa

Gauge symmetry in extended objects and the stability of compactified membranes

A large number of gauge degrees of freedom inherent in relativistic extended objects often cause dynamical instability. This problem is studied by taking bosonic membranes and balls as examples. The bosonic membrane with two spatial coordinates compactified is examined in detail, and it is pointed out that the compactification produces a stabilizing potential barrier for the variables orthogonal to the compactified spaces. By gauge transforming away the variables in the compactified spaces, we suggest a possible confinement of unstable modes in compactified spaces.

Topological conformal algebra and BRST algebra in non-critical string theories

Abstract The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = −2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = −2 is examined by replacing the string coordinate by a fermionic matter with c = −2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = −2 string theory and two-dimensional topological gravity.

Nambu-Goto action in D=2 and topological field theories

Abstract The Nambu-Goto theory in D = 2 dimensions is canonically transformed to study topological aspects of the theory. Using the Batalin-Fradkin-Vilkovisky formalism, it is shown that the transformed theory, which is quantum mechanically consistent, is related to various topological theories in two dimensions including topological gravity. It is emphasized that the bosonic coordinates X a ( τ , σ ) play quite different roles in string theory and in topological theory.