Kenichiro Aoki

Unitarity of closed superstring perturbation theory

Abstract The scattering amplitudes for the covariant formulation of closed Type II and heterotic superstrings are shown to be equivalent, order-by-order in string perturbation theory, to those of the light-cone interacting string picture. This establishes the unitarity of covariant superstring perturbation theory and the Lorentz invariance of the light-cone superstring.

Topological supergravity in two dimensions

Abstract The topological theory of OSp(2|1; R ) flat gauge connections is shown to be equivalent to two-dimensional supergravity. By choosing a particular gauge fixing of the SL(2; R ) (OSp(2|1; R ) invariance we make contact with the Liouville theory approach to two-dimensional gravity (supergravity). We discuss the scaling and multriritical behavior of two-dimensional supergravity.

ON THE LIOUVILLE APPROACH TO CORRELATION FUNCTIONS FOR 2D QUANTUM GRAVITY

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods.

CORRELATION FUNCTIONS OF MINIMAL MODELS COUPLED TO TWO-DIMENSIONAL QUANTUM SUPERGRAVITY

We compute the three-point functions of Neveu-Schwarz primary fields of the minimal models on the sphere when coupled to supergravity in two dimensions. The results show that the three-point correlation functions are determined by the scaling dimensions of the fields, as in the bosonic case.

Nonperturbative evidence for nondecoupling of heavy fermions

We investigate, using a 1/[ital N] expansion, the behavior of a parameter in the scalar-fermion sector of the standard model that shows perturbative nondecoupling as the fermion becomes heavy. This low-energy parameter is related to the [ital S] parameter defined through [ital W][sub 3][minus][ital B] mixing. We obtain the leading 1/[ital N] contribution to this parameter that, if expanded perturbatively, collapses to its constant one-loop result. Nonperturbatively, we find that as the mass of the fermion approaches the triviality scale the behavior of the parameter is nonuniversal and shows nondecoupling.

(1+1)-dimensional QCD with fundamental bosons and fermions

We analyze the properties of mesons in (1+1)-dimensional QCD with bosonic and fermionic ``quarks`` in the large {ital N}{sub {ital c}} limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two-dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of ``mesons`` formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.

W-gravity and generalized Lax equations for (super) Toda theory

Abstract We generalize the Lax pair and Backlund transformations for Toda and N = 1 super Toda equations to the case of arbitrary world-sheet background geometry. We use the fact that the Toda equations express constant curvature conditions, which arise naturally from flatness conditions equivalent to the W-gravity equation of motion.

Large order behavior of nondecoupling effects and triviality

We compute some non–decoupling effects in the standard model, such as the ρ parameter, to all orders in the coupling constant expansion. We analyze their large order behavior and explicitly show how it is related to the non–perturbative cutoff dependence of these non–decoupling effects due to the triviality of the theory. 9/93 † email: ken@phys.titech.ac.jp

Nondecoupling, triviality and the rho parameter

The dependence of the ϱ parameter on the mass of the Higgs scalar and the top quark is computed non-perturbatively using the 1/NF expansion in the standard model. We find an explicit expression for the ϱ parameter thatrequires the presence of a physical cutoff. This should come as no surprise since the theory is presumably trivial. By taking this cutoff into account, we find that the ϱ parameter can take values only within a limited range and has finite ambiguities that are suppressed by inverse powers of the cutoff scale, the so called “scaling-violations”. We find that large deviations from the perturbative results are possible, but only when the cutoff effects are also large.

Effects of fermion back reaction on instantons

Abstract We show how systematically incorporate back reaction into fermion number violating amplitudes in Yang-Mills theories. We discuss the possible recovery of unittarity at high energies for these processes.