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Instantons and Matrix Models

By: Ricardo Schiappa
From: Dep. Matemática, Instituto Superior Técnico
At: Complexo Interdisciplinar, Anfiteatro
[2008-06-11] 11:30

Most quantum problems are solved using perturbation theory, which is known not to converge. The large order behavior of perturbation theory, and its divergence, is controlled by instantons, non-perturbative solutions to the Euclidean equations of motion. We shall study instantons and large-order behavior in the simplest possible examples, those of matrix models — 0-dimensional field theories. Interestingly enough, matrix models are also related to string theory and we shall see how to apply instanton calculus in string theory via matrix models. We will study the large order behavior both analytically, up to two loops, and numerically, in several cases of both pure matrix models and topological strings. Some of this information may also be derived via the Painleve I equation, an integrable system which describes 2-dimensional quantum gravity. If time permits, we shall also cover applications to cases involving multi-instantons, and matrix models with several cuts in the complex plane. We plan this talk to be accessible to anyone with a good knowledge of quantum mechanics.