Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. I

Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model.Comment: 24 pages, 1 figure, contribution to ``Conformal Field Theory and Integrable Models'', Chernogolovka, Moscow Region, Russia, on September 15--21, 2002; typos corrected, references added (v2); typos corrected, final version (v3

Inequality and risk aversion in health and income: an empirical analysis using hypothetical scenarios with losses

Four kinds of distributional preferences are explored: inequality aversion in health, inequality aversion in income, risk aversion in health, and risk aversion in income. Face to face interviews of a representative sample of the general public are undertaken using hypothetical scenarios involving losses in either health or income. Whilst in health risk aversion is stronger than inequality aversion, in the income context we cannot reject that attitudes to inequality aversion and risk aversion are the same. When we compare across contexts we find that inequality aversion and risk aversion are both stronger in income than they each are in health

Is more health always better? Exploring public preferences that violate monotonicity

Abásolo and Tsuchiya (2004a) report on an empirical study to elicit public preferences regarding the efficiency-equality trade-off in health, where the majority of respondents violated monotonicity. The procedure used has been subject to criticisms regarding potential biases in the results. The aim of this paper is to analyse whether violation of monotonicity remains when a revised questionnaire is used. We test: whether monotonicity is violated when we allow for inequality neutral preferences and also if we allow for preferences that would reject any option which gives no health gain to one group; whether those who violate monotonicity actually have non-monotonic or Rawlsian preferences; whether the titration sequence of the original questionnaire may have biased the results; whether monotonicity is violated when an alternative question is administered. Finally, we also test for symmetry of preferences. The results confirm the evidence of the previous study regarding violation of monotonicity

Abelian Conformal Field theories and Determinant Bundles

The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichm\"uller space of an oriented pointed surface gives the vectorspace the modular functor associates to the oriented pointed surface. However the connection on the sheaf of vacua is only projectively flat, so we need to find a suitable line bundle with a connection, such that the tensor product of the two has a flat connection. We shall construct a line bundle with a connection on any family of pointed curves with formal coordinates. By computing the curvature of this line bundle, we conclude that we actually need a fractional power of this line bundle so as to obtain a flat connection after tensoring. In order to functorially extract this fractional power, we need to construct a preferred section of the line bundle. We shall construct the line bundle by the use of the so-called $bc$-ghost systems (Faddeev-Popov ghosts) first introduced in covariant quantization [FP]. We follow the ideas of [KNTY], but decribe it from the point of view of [TUY].Comment: A couple of typos correcte

USp(2k) Matrix Model: Schwinger-Dyson Equations and Closed-Open String Interactions

We derive the Schwinger-Dyson/loop equations for the USp(2k) matrix model which close among the closed and open Wilson loop variables. These loop equations exhibit a complete set of the joining and splitting interactions required for the nonorientable Type I superstrings. The open loops realize the SO(2n_f) Chan-Paton factor and their linearized loop equations derive the mixed Dirichlet/Neumann boundary conditions.Comment: 22 pages, 13 figure

Quantum Gravity and Black Hole Dynamics in 1+1 Dimensions

We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum constraints are derived. It is pointed out that the constraints form the Virasoro algebra without central charge. In ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in ADM formalism come out. A singularity appears at \df^2 =\kappa (>0) , where $\kappa =(N-51/2)/12$ and $N$ is the number of matter fields. Behind the singularity the quantum mechanical region \kappa > \df^2 >0 extends, where the sign of the kinetic term in the Hamiltonian constraint changes. If $\kappa <0$, the singularity disappears. We discuss the quantum dynamics of black hole and then give a suggestion for the resolution of the information loss paradox. We also argue the quantization of the spherically symmetric gravitational system in 3+1 dimensions. In appendix the differences between the other quantum dilaton gravities and ours are clarified and our status is stressed.Comment: phyztex, UT-Komaba 92-14. A few misleading sentences are corrected and some references are adde

Exact Results in N_c=2 IIB Matrix Model

We investigate N_c=2 case of IIB matrix model, which is exactly soluble. We calculate the partition function exactly and obtain a finite result without introducing any cut-off. We also evaluate some correlation functions consisting of Wilson loops.Comment: 8 pages, Late