# Cluster Structures, Orientifolds of Brane Tilings and Higher Laminations

Abstract : Cluster algebras and varieties naturally appear in various fields of mathematical physics, such as higher Teichmüller theory and dimer models -- known as brane tilings in the context of string theory. On the first hand, we study the generalisation of Thurston's laminations to higher Teichmüller spaces in the real split case. This guides us towards introducing topological quantum field theories associated with the Iwahori--Hecke algebras of finite Coxeter groups. Those assign a Laurent polynomial with integer coefficients to each punctured surface of finite type. On the other hand, we use dimer models to prove the existence of a stable ultraviolet completion of the dynamical supersymmetry breaking $\mathrm{SU}(5)$ model. Moreover, we derive general results on the existence of gauge anomalies in the worldvolume of D-branes at orientifolds of affine toric Calabi--Yau singularities. Lastly, we provide a physical interpretation of brane tilings on the Klein bottle. Besides, the two preliminary parts of this dissertation are pedogogical invitations first to Fock and Goncharov's higher Teichmüller theory and then to the use of dimer models in string theory and in holography.
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https://tel.archives-ouvertes.fr/tel-03766040
Contributor : Valdo Tatitscheff Connect in order to contact the contributor
Submitted on : Thursday, September 22, 2022 - 2:31:03 PM
Last modification on : Sunday, October 2, 2022 - 6:54:10 PM

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• HAL Id : tel-03766040, version 1

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Valdo Tatitscheff. Cluster Structures, Orientifolds of Brane Tilings and Higher Laminations. Mathematical Physics [math-ph]. Université de Strasbourg, 2022. English. ⟨tel-03766040⟩

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