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Gæsteforelæsning Seminar

30.11.2026   at 15:00 - 16:00

QM Research Seminar: Tropical QFT and the sine-Gordon model

<strong>Speaker: Jury Ivan Radkovski&nbsp;</strong>(​University of Copenhagen).<br><br><strong>Abstract:&nbsp;</strong><br>A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in<em> D = 2</em>&nbsp;and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the&nbsp;β-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.

Speaker: Jury Ivan Radkovski (​University of Copenhagen).

Abstract: 
A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in D = 2 and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the β-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.
30 Nov