Probabilistic sigma models
Antti Kupiainen
Université d'Helsinski
Date(s) : 24/03/2026 iCal
15h30 - 16h30
In a probabilistic formulation of quantum field theory
a sigma model is a theory of a random field
defined on space (a manifold in general)
and taking values in a Riemannian manifold M.
On a two dimensional space
sigma models describe statistical mechanics systems,
important examples being the XY model (M=S^1)
and the Heisenberg model (M=S^2)
and the Wess-Zumino-Witten model (M= semi simple Lie group).
They also play a prominent role in string theory,
M being the space where strings move.
I will briefly discuss the problems
for a rigorous analysis of sigma models
and then explain construction of a sigma model
where M is a three dimensional hyperbolic space
giving rise to a conformal field theory.
This theory has an interesting connection to Liouville CFT
which connection in turn has applications to integrable systems
and geometry.
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