Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator

The algebraic structures related with integrable structure of superconformal field theory (SCFT) are introduced. The SCFT counterparts of Baxter's Q-operator are constructed. The fusion-like relations for the transfer-matrices in different representations and their truncations are obtained.Comment: LaTeX2e, elsart.cls, 17 pages, Nuclear Physics B, 2005, in pres

Integrability of qq-oscillator lattice model

A simple formulation of an exactly integrable $q$-oscillator model on two dimensional lattice (in 2+1 dimensional space-time) is given. Its interpretation in the terms of 2d quantum inverse scattering method and nested Bethe Ansatz equations is discussed.Comment: Talk given at the conference ``New frontiers in exactly solved models'', ANU, July 21-22, 200

Excited State TBA for the ϕ2,1\phi_{2,1} perturbed M3,5M_{3,5} model

We examine some excited state energies in the non-unitary integrable quantum field theory obtained from the perturbation of the minimal conformal field theory model $M_{3,5}$ by its operator $\phi_{2,1}$. Using the correspondence of this IQFT to the scaling limit of the dilute $A_2$ lattice model (in a particular regime) we derive the functional equations for the QFT commuting transfer matrices. These functional equations can be transformed to a closed set of TBA-like integral equations which determine the excited state energies in the finite-size system. In particular, we explicitly construct these equations for the ground state and two lowest excited states. Numerical results for the associated energy gaps are compared with those obtained by the truncated conformal space approach (TCSA).Comment: LaTeX, 32 pages, 6 figure

A closed form solution to Stollery's global warming problem with temperature in utility

Stollery (1998) studied a polluting oil extracting economy governed by the constant utility criterion. The pollution caused the growth of temperature, negatively affecting production and utility. Stollery provided a closed form solution for the case with the Cobb-Douglas production function and temperature affecting only production. This paper offers a closed form solution to a non-trivial example of this economy with utility affected by temperature.essential nonrenewable resource; polluting economy; sustainable development; special function representation

Integrals of motion from TBA and lattice-conformal dictionary

The integrals of motion of the tricritical Ising model are obtained by Thermodynamic Bethe Ansatz (TBA) equations derived from the A_4 integrable lattice model. They are compared with those given by the conformal field theory leading to a unique one-to-one lattice-conformal correspondence. They can also be followed along the renormalization group flows generated by the action of the boundary field \phi_{1,3} on conformal boundary conditions in close analogy to the usual TBA description of energies.Comment: 20 pages, 1 figure, LaTeX; v2: added references, improved conventions introduced in sections 4, 5 and related tables; v3: added reference

Differential equations and duality in massless integrable field theories at zero temperature

Functional relations play a key role in the study of integrable models. We argue in this paper that for massless field theories at zero temperature, these relations can in fact be interpreted as monodromy relations. Combined with a recently discovered duality, this gives a way to bypass the Bethe ansatz, and compute directly physical quantities as solutions of a linear differential equation, or as integrals over a hyperelliptic curve. We illustrate these ideas in details in the case of the $c=1$ theory, and the associated boundary sine-Gordon model.Comment: 18 pages, harvma

The dependence of the potential sustainability of a resource economy on the initial state: a comparison of models using the example of Russian oil extraction

The studies of the International Monetary Fund offer a model for recommending sustainable budget policy to oil-exporting countries including Russia. The model does not contain any resource as a factor of production and assumes that Russian oil reserves will be exhausted by the middle of the 21st century. The current paper examines the sustainability of open and closed models, which are calibrated on Russia's data and include a resource as a factor of production. The open-model case shows that monotonic economic growth is impossible given the current state of the Russian economy. This paper offers an approach for estimating changes that improve long-term sustainability.nonrenewable resource; weak sustainability; open imperfect economy; Russian oil extraction

Investment and current utility change in dynamically inefficient economies

An extensive literature shows the importance of investment policy for sustainability of resource-based economies by examining the role of investment in current utility change (CUC) for a competitive optimizing economy. This paper extends some of these results by analysing the dependence of CUC on genuine investment (GI), expressed in marginal resource productivity, under dynamic inefficiency. The inefficiency arises when a social planner, due to imperfection in knowledge or in institutions, does not take into account deviations of real economy from a theoretical model. These deviations or distortions, connected with the resource extraction, can influence utility, production, the balance equation, and the dynamics of the reserve. The analysis of this natural discrepancy between theory and real life implies that: first, institutional and resource policies in inefficient economies may be more important for CUC than investment policy; and secondly, under uncertainties in production possibilities and in damages from economic activities, sustainability requires a more cautious resource policy than is advised by a theory. The paper also suggests that the indicators GI, expressed in accounting prices and in marginal resource productivity, can complement each other in sustainability evaluation.nonrenewable resource; dynamic inefficiency; genuine investment; resource policy; sustainable development

Baxter Q-Operators and Representations of Yangians

We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang-Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang-Baxter equation serve as elementary, "partonic" building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider sl(n) compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe ansatz techniques.Comment: 27 pages, 5 figures; v2: typos fixed, references updated and adde