Noboru Kawamoto

Geometric realization of conformal field theory on Riemann surfaces

Conformal field theory on a family of Riemann surfaces is formulated. We derive equations of motion of vacua which are parametrized by moduli of Riemann surfaces and show that these vacua are characterized uniquely by these equations. Our theory has a deep connection with Satos theory of KP equations.

Strong coupling analysis of the chiral phase transition at finite temperature

Abstract The finite-temperature chiral-symmetry-restoration phase transition in lattice gauge theories is investigated analytically in the strong coupling region, and predictions are made regarding the order of the phase transition. We discuss the temperature dependence of m π and ƒ π near the phase transition point. When the effect of baryons is ignored, we show explicitly how the phase transition is insensitive to the introduction of a chemical potential for quark densities. Finally, we derive the effective action for σ ∼ 〈 ψ ψ〉 with different numbers of flavours.

Even-dimensional generalization of Chern-Simons action and new gauge symmetry

We propose a new even-dimensional action which shares close algebraic similarities with the Chern-Simons action and thus possesses a topological nature. This action has a new type of gauge symmetry in the sense that adjoint representation is not enough to close the gauge transformation and gauge fermions are incorporated. “Quaternionic structure” emerges as a natural algebra to control the different natures of even forms, odd forms, bosons and fermions. We claim that the bundle structure in consideration is mathematically a new object.

Four-dimensional topological conformal gravity from even-dimensional generalized Chern-Simons action

Abstract We propose a new formulation of four-dimensional gravity as a gauge theory of special Clifford algebra by using a four-dimensional version of the generalized Chern-Simons action which we have proposed previously. We show that this gravity theory possesses a conformal symmetry as a gauge symmetry and induces a Weyl tensor vanishing condition as one of the equations of motion and can be reduced to Riemannian flat gravity. This gravity thus includes no dynamical degree of freedom, which is analogous to the three-dimensional gravity formulated by the standard Chern-Simons action. We find a new mechanism where two “hidden order parameters”, as constant classical solutions of zero form gauge field, differentiate the gravity phase and nongravity phase.

Modular invariance and the gravitational anomaly in type II superstring theory

Abstract By explicit calculations we show that the one-loop parity-violating amplitude with six external gravitons modular invariant and finite. As a natural consequence of the modular invariance and double periodicity of the amplitude with respect to torus parameters, the gravitational anomaly of type II superstring theory vanishes.

Gravitational anomaly cancellation type I superstring theory

Abstract By explicit calculations we show that the gravitational anomaly of type I superstring theory vanishes at the string level. There are contributions from four topologically different diagrams to the anomaly: annulus, Mobius strip, torus, and Klein bottle. We explicitly show how the non-trivial cancellation occurs between the open (annulus and Mobius strip) and closed (Klein bottle) sectors. The anomaly of the torus diagram has the same form of type II superstring theory and vanishes because of the modular invariance.

Topological particle field theory, general coordinate invariance and generalized Chern-Simons actions

We show that recently proposed generalized Chern-Simons action can be identified with the field theory action of a topological point particle. We find the crucial correspondence which makes it possible to derive the field theory actions from a special version of the generalized Chern-Simons actions. We provide arguments that the general coordinate invariance in the target space and the flat connection condition as a topological field theory can be accommodated in a very natural way. We propose series of new gauge invariant observables.

Internal geometry of two-dimensional gravity with C = −2 matter

Abstract We investigate numerically the internal geometry of dynamically triangulated two-dimensional quantum gravity coupled to c = −2 matter. The largest lattice consists of 5 × 10 6 triangles. Such a large lattice can be generated by applying a recursive sampling algorithm for the c = −2 model. The typical surfaces in our model are strongly branched and the number of these branches as a function of the internal geodesic distance shows a clear scaling behavior. Our results show that the internal fractal dimension of the model is approximately 3.55.

Ward identifies and differential equations of the N = 1,2 superconformal algebra on the supertorus

We derive Ward identities of correlation functions on the supertorus and differential equations of characters for N = 1,2 superconformal field theory.