Speaker: Saveliy Timchenko (National Research University Higher School of Economics)
Time: 2026-03-10 14:00-16:00
Location: 610, SIMIS
Zoom meeting ID: 851 4030 3334 Password: SIMIS
Abstract:
I will talk about the simplest example of the landscape of conformal field theories: one-dimensional CFTs with finite-dimensional state space. Following the definition of quantum field theory given by G. Segal, I’ll formulate the condition under which a one-dimensional QFT (quantum mechanics) possesses conformal symmetry, and I’ll give a complete classification of conformal Hamiltonians with finite rank. It turns out that correlation functions in such theories are polynomial functions of the underlying geometric data. Moreover, the one-dimensional conformal Ward identities determine their scaling behavior, so that the correlators of the conformal observables are, in fact, homogeneous polynomials. This talk is based on a joint project with M. Gritskov 2512.06501.
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