Triangle Seminars
Wednesday, 30 Apr 2014
Resurgent Analysis in Quantum Theories: Perturbative Theory and Beyond
Ines Aniceto
(Lisbon)
Abstract:
In order to study the weakly coupled regime of some given quantum theory we often make use of perturbative expansions of the physical quantities of interest. But such expansions are often divergent, with zero radius of convergence, and defined only as asymptotic series. In fact, this divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects that cannot be simply captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data. In this talk, I will review the essential role of resurgence theory in the description of the analytic solution behind the asymptotic series. I will then relate resurgence to the so-called Stokes phenomena and phase transitions using a simple example, and will further discuss some major applications of this construction.
In order to study the weakly coupled regime of some given quantum theory we often make use of perturbative expansions of the physical quantities of interest. But such expansions are often divergent, with zero radius of convergence, and defined only as asymptotic series. In fact, this divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects that cannot be simply captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data. In this talk, I will review the essential role of resurgence theory in the description of the analytic solution behind the asymptotic series. I will then relate resurgence to the so-called Stokes phenomena and phase transitions using a simple example, and will further discuss some major applications of this construction.
Posted by: QMW
Thursday, 1 May 2014
The geometry of supersymmetric partition functions
Guido Festuccia
(Niels Bohr Inst.)
Abstract:
I will consider supersymmetric field theories on compact manifolds M and obtain constraints on the dependence of their partition functions Z_M on the geometry of M. For N=1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. I will show how to describe the theory in terms of twisted variables that make easy to analyze the dependence of Z_M on the parameters entering the Lagrangian. I will also show that Z_M is "almost" topological: Z_M is independent of the Hermitian metric and depends holomorphically on the complex structure moduli.
I will consider supersymmetric field theories on compact manifolds M and obtain constraints on the dependence of their partition functions Z_M on the geometry of M. For N=1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. I will show how to describe the theory in terms of twisted variables that make easy to analyze the dependence of Z_M on the parameters entering the Lagrangian. I will also show that Z_M is "almost" topological: Z_M is independent of the Hermitian metric and depends holomorphically on the complex structure moduli.
Posted by: IC