A new pentagon identity for the tetrahedron index

Recently Kashaev, Luo and Vartanov, using the reduction from a four-dimensional superconformal index to a three-dimensional partition function, found a pentagon identity for a special combination of hyperbolic Gamma functions. Following their idea we have obtained a new pentagon identity for a certain combination of so-called tetrahedron indices arising from the equality of superconformal indices of dual three-dimensional N=2 supersymmetric theories and give a mathematical proof of it.Comment: 13 pages, v2: we added a new section with the proof of the identity, misprints correcte

Tax Evasion and Dynamic Inefficiency

I show within a two-period overlapping generations model with income tax evasion that when the penalty rate set by the government is su¢ ciently small, it is theoretically possible for the capital stock to exceed the golden-rule level on the balanced-growth path. However, such a dynamic inefficiency cannot be guaranteed when the probability of evasion detection is nil.

Comments on the multi-spin solution to the Yang-Baxter equation and basic hypergeometric sum/integral identity

We present a multi-spin solution to the Yang-Baxter equation. The solution corresponds to the integrable lattice spin model of statistical mechanics with positive Boltzmann weights and parameterized in terms of the basic hypergeometric functions. We obtain this solution from a non-trivial basic hypergeometric sum-integral identity which originates from the equality of supersymmetric indices for certain three-dimensional N=2 Seiberg dual theories.Comment: 8 pp, based on a talk given at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, Czech Republic, 06-10 June, 2017; v2: minor change

Integral pentagon relations for 3d superconformal indices

The superconformal index of a three-dimensional supersymmetric field theory can be expressed in terms of basic hypergeometric integrals. By comparing the indices of dual theories, one can find new integral identities for basic hypergeometric integrals. Some of these integral identities have the form of the pentagon identity which can be interpreted as the 2-3 Pachner move for triangulated 3-manifolds.Comment: 9 pages. Based on arXiv:1309.2195 with new results and comments. Presented at String-Math conference, Edmonton, Canada, June 9-13, 2014; v2: minor corrections and comments adde

Basic hypergeometry of supersymmetric dualities

We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.Comment: 25 pages, v2: minor corrections and comment

Integrable lattice spin models from supersymmetric dualities

Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the Yang-Baxter equation expresses the identity of partition functions for dual pairs. This correspondence is a powerful tool which enables us to generate new integrable models. The aim of the present paper is to give a short account on a progress in integrable lattice models which has been made due to the relationship with supersymmetric gauge theories.Comment: 35 pages, preliminary versio

The star-triangle relation and 3d superconformal indices

Superconformal indices of 3d N=2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the q-special functions associated with these 3d indices. For a two-dimensional monopole-spin system on the square lattice a free energy per spin is explicitly determined. Similar to the partition functions, superconformal indices of 3d theories with the chiral symmetry breaking reduce to Dirac delta functions with the support on chemical potentials of the preserved flavor groups.Comment: 20 pages, v2: minor corrections, comments and refs. adde

A Stochastic Growth Model with Income Tax Evasion: Implications for Australia

In this paper we develop a stochastic endogenous growth model augmented with income tax evasion. Our model avoids some existing discrepancies between empirical evidence and theoretical predictions of traditional tax evasion models. Further, we show that: i) productive government expenditures play an important role in affecting economy's tax evasion rate; ii) the average marginal income tax rate in Australia come close to the optimal; and iii) the phenomenon of tax evasion is not an excuse for a productive government to advocate an excessive income taxation.Tax evasion; Economic growth; Public services

CAN WE TAX THE DESIRE FOR TAX EVASION?

A static income tax evasion model ?? la Yitzhaki (1974) predicts that an increase in the tax rate causes taxpayers to increase their income declaration. In an important contribution, Lin and Yang (2001) obtained exactly the opposite result by extending the Yitzhaki (1974) model to a dynamic one with Ak(t) production technology. In this paper we show that once the Lin and Yang (2001) model becomes fully compatible with the Yitzhaki's (1974) setting, the negative relationship between taxes and evasion still prevails. We then enrich the dynamic model with a productive public sector, and obtain an ambiguous relationship between taxes and evasion incentives as in Allingham and Sandmo (1972). We also prove that the growth-maximizing share of public expenditures in total output satisfies the natural efficiency condition even in the presence of tax evasion. However, the latter result is not robust to the introduction of the costs associated with income declaration and concealment activities.Tax Evasion, Optimal Taxation, Economic Growth