Gravity-Matter Couplings from Liouville Theory

The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations on the sphere. The precise definition of the corresponding cosmological constant is given in the operator solution of the quantum Liouville theory. It is shown that the symmetry between quantum-group spins $J$ and $-J-1$ previously put forward by the author is the explanation of the continuation in the number of screening operators discovered by Goulian and Li. Contrary to the previous discussions of this problem, the present approach clearly separates the emission operators for each leg. This clarifies the structure of the dressing by gravity. It is shown, in particular that the end points are not treated on the same footing as the mid point. Since the outcome is completely symmetric this suggests the existence of a picture-changing mechanism in two dimensional gravity.Comment: (40 pages, Latex file

Negative Screenings in Liouville Theory

We demonstrate how negative powers of screenings arise as a nonperturbative effect within the operator approach to Liouville theory. This explains the origin of the corresponding poles in the exact Liouville three point function proposed by Dorn/Otto and $(\hbox{Zamolodchikov})^2$ (DOZZ) and leads to a consistent extension of the operator approach to arbitrary integer numbers of screenings of both types. The general Liouville three point function in this setting is computed without any analytic continuation procedure, and found to support the DOZZ conjecture. We point out the importance of the concept of free field expansions with adjustable monodromies - recently advocated by Petersen, Rasmussen and Yu - in the present context, and show that it provides a unifying interpretation for two types of previously constructed local observables.Comment: 41 pages, LaTe

A Note on Quantum Liouville Theory via Quantum Group; an Approach to Strong Coupling Liouville Theory

Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this Liouville theory are factorized into `classical' vertex operators and those which are constructed from the finite dimensional representations of $U_qsl(2,C)$. We further show explicitly that fusion rules in this model also enjoys such a factorization. Upon the conjecture that the Liouville action effectively decouples into the classical Liouville action and that of a quantum theory, correlation functions and transition amplitudes are discussed, especially an intimate relation between our model and geometric quantization of the moduli space of Riemann surfaces is suggested. The most important result is that our Liouville theory is in the strong coupling region, i.e., the central charge c_L satisfies $1<c_L<25$. An interpretation of quantum space-time is also given within this formulation.Comment: 25 pages, Latex file, no figure

Human Capital Investment and Debt Constraints

When young individuals face binding debt constraints, their human capital investments will be insufficiently financed by private creditors. If generations overlap, then a well-designed fiscal policy may be able to improve human capital investments by replacing missing capital markets with an intergenerational transfer scheme. Boldrin and Monte (2002) demonstrate that the optimal (balanced budget) fiscal policy in this context entails the joint provision of an education subsidy for the young and a pension program for the old, financed with a tax on those in their peak earning years. We demonstrate, however, that the desirability of such a policy depends crucially on the assumption of an exogenous debt constraint. If debt constraints arise endogenously for reasons of limited commitment, then the optimal (balanced budget) fiscal policy looks radically different. Furthermore, we find that arbitrary (non-optimal) policy interventions may actually lead to lower levels of human capital investment as altered default incentives induce private creditors to contract the supply of student loans by an amount greater than the subsidy. In some cases, the constrained-optimal policy entails zero intervention. These results highlight the importance of taking seriously the reasons for why debt constraints exist, before recommending any specific policy intervention.

Quantum Liouville Theory On The Riemann Sphere With n>3n>3 Punctures

We have studied the quantum Liouville theory on the Riemann sphere with n>3 punctures. While considering the theory on the Riemann surfaces with n=4 punctures, the quantum theory near an arbitrary but fixed puncture can be obtained via canonical quantization and an extra symmetry is explored. While considering more than four distinguished punctures, we have found the exchange relations of the monodromy parameters from which we can get a reasonable quantum theory.Comment: 13 page

Two and three-point functions in Liouville theory

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself.Comment: 15 pages, Latex, Revised version: A sign error in formula (50) is correcte

Investigating Canadian Chicken Importers' Preferences Towards TRQ Import Licensing Mechanisms

The Agreement on Agriculture ratified at the end of the Uruguay Round of WTO negotiations called for the conversion of non-tariff barriers to trade into bound tariffs. This tariffication would have resulted in excessively high tariffs, which would have threatened historic market access levels if not for WTO member countries agreeing to introduce tariff-rate quotas (TRQs). TRQs are two-tier tariffs. Imports below an agreed quota are taxed at a usually low (or zero) in-quota tariff rate while imported commodities in excess of the quota level are taxed at the higher (often prohibitive) over-quota tariff rate. In the process of implementing TRQs, WTO members failed to explicitly regulate TRQ administration procedures. As a result, numerous administration procedures for allocating import licenses were developed in many countries. Importing activities in the Canadian chicken industry have been regulated with a TRQ since 1995. Firms holding the right to import chicken products at the in-quota tariff can potentially enjoy significant rents due to the spread between domestic and world prices. The magnitude of these rents depends upon a number of domestic factors such as market concentration in the processing and retail sectors, production technology, farm output regulation, and so on. This analysis evaluates the preferences of Canadian chicken importers towards TRQ import licensing mechanisms and provides insights about importers’ attitudes towards Canadian trade policy in the chicken sector.Agricultural and Food Policy, International Relations/Trade,

2D Quantum Gravity in the Proper-Time Gauge

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.Comment: 12 pages, late

Classical Liouville action on the sphere with three hyperbolic singularities

The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three point function in the DOZZ solution of the quantum Liouville theory.Comment: 14 pages, 2 eps figure

Quantum Analysis of Jackiw and Teitelboim's Model for 1+1 D Gravity and Topological Gauge Theory

We study the BRST quantization of the 1+1 dimensional gravity model proposed by Jackiw and Teitelboim and also the topological gauge model which is equivalent to the gravity model at least classically. The gravity model quantized in the light-cone gauge is found to be a free theory with a nilpotent BRST charge. We show also that there exist twisted N=2 superconformal algebras in the Jackiw-Teitelboim's model as well as in the topological gauge model. We discuss the quantum equivalence between the gravity theory and the topological gauge theory. It is shown that these theories are indeed equivalent to each other in the light-cone gauge.Comment: 31 page