Segnalo il seguente seminario, che si terrà Martedì prossimo in Sapienza.
*Martedì 11 Febbraio, ore 14:00,* Sala di Consiglio, Dipartimento di
Matematica, Sapienza Università di Roma
*Speaker:* Jacopo Borga (MIT)
*Title: *Lattice Yang-Mills theory in the large N limit via sums over
surfaces
*Abstract:* Lattice Yang-Mills theories are important models in particle
physics. They are defined on the d-dimensional lattice Z^d using a group of
matrices of dimension N, and Wilson loop expectations are the fundamental
observables of these theories. Recently, Cao, Park, and Sheffield showed
that Wilson loop expectations can be expressed as sums over certain
embedded bipartite maps of any genus. Building on this novel approach, we
prove in the so-called strongly coupled regime:
- A rigorous formula in terms of embedded bipartite planar maps of
Wilson loop expectations in the large N limit, in any dimension d.
- An exact computation of Wilson loop expectations in the large N limit,
in dimension d=2, for a large family of (simple and non-simple) loops.
Previous results to the two aforementioned points were previously
established by Chatterjee (2019) and Basu & Ganguly (2016), respectively.
Our results extend these previous results, offer simpler proofs and provide
a new perspective on these significant quantities.
This work is a collaboration with Sky Cao and Jasper Shogren-Knaak.
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Vittoria Silvestri
Assistant Professor
Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome
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