Finite Yang-Mills Integrals

We use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D=3, N>3 and D=4, N>2 and, lastly, D >= 5, N >= 2. We conclude that the D=3 and D=4 integrals exist in the large N limit, and therefore lead to a well-defined, new type of Eguchi-Kawai reduced gauge theory. For the supersymmetric case, we check, up to SU(5), recently proposed exact formulas for the D=4 and D=6 D-instanton integrals, including the explicit form of the normalization factor needed to interpret the integrals as the bulk contribution to the Witten index.Comment: 7 pages, LaTeX, REVTE

Statistical Physics Approach to M-theory Integrals

We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo computability of near-singular integrals, singularity detection by Markov-chain methods, applications to asymptotic eigenvalue distributions and to numerical evaluations of multiple bosonic and supersymmetric integrals. In many cases already, it has been possible to resolve controversies between conflicting analytical results using the methods presented here.Comment: 6 pages, talk presented by WK at conference 'Non- perturbative Quantum Effects 2000', Paris, Sept 200

Cluster Monte Carlo Algorithms for Dissipative Quantum Systems

We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered.Comment: to be publushed in Proceedings of the Yukawa Symposium 200

Yang-Mills Integrals

SU(N) Yang-Mills integrals form a new class of matrix models which, in their maximally supersymmetric version, are relevant to recent non-perturbative definitions of 10-dimensional IIB superstring theory and 11-dimensional M-theory. We demonstrate how Monte Carlo methods may be used to establish important properties of these models. In particular we consider the partition functions as well as the matrix eigenvalue distributions. For the latter we derive a number of new exact results for SU(2). We also report preliminary computations of Wilson loops. (Based on talk presented by M. Staudacher at Strings '99, Potsdam, July 19-24 1999)Comment: 10 pages, 8 figures, uses iopart.cls; acknowledgements adde

Agent-based financial markets and New Keynesian macroeconomics: A synthesis

We combine a simple agent-based model of financial markets and a New Keynesian macroeconomic model with bounded rationality via two straightforward channels. The result is a macroeconomic model that allows for the endogenous development of business cycles and stock price bubbles. We show that market sentiments exert important influence on the macroeconomy. They introduce high volatility into impulse-response functions of macroeconomic variables and thus make the effect of a given shock hard to predict. We also analyze the impact of different financial transaction taxes (FTT, FAT, progressive FAT) and find that such taxes can be used to stabilize the economy and raise funds from the financial sector as a contribution to the costs produced by the recent crisis. Our results suggest that the FTT leads to higher tax revenues and better stabilization results then the FAT. However, the FTT might also create huge distortion if set too high, a threat which the FAT does not imply. --Agent-based modeling,stock market,New Keynesian macroeconomics,financial transaction tax,financial activities tax

Agent-based financial markets and New Keynesian macroeconomics: A synthesis

We combine a simple agent-based model of financial markets with a standard New Keynesian macroeconomic model via two straightforward channels. The result is a macroeconomic model that allows for the endogenous development of stock price bubbles. Even with such a simplistic comprehensive model, we can show that the behavioral foundations of the stock market exert important influence on the macroeconomy, e.g. they change the impulse-response functions of macroeconomic variables significantly. We also analyze financial market transaction taxes as well as asset price bubble deflating monetary policy, and find that both can be used to reduce volatility and distortion of the macroeconomic aggregates. --agent-based financial markets,New Keynesian macroeconomics,stock market,transaction tax,Taylor rule