Raphaël Belliard

Raphaël Belliard
University of Alberta | UAlberta · Department of Mathematical and Statistical Sciences

About

7
Publications
322
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32
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Introduction
My interests lie in computing amplitudes in conformal quantum field theories on curved space-times, in 2 and 4 dimensions. Based on non-perturbative semi-classical analysis of conformal Schwinger-Dyson equations, it consists in the Borel resummation of solutions to Ward identities, a basis of which being computed by topological recursion. Currently: WKB-Borel in Verma modules, (q,t)-deformation of topological recursion, quantum periods from Yang² quantisation, 4D amplitudes from twistors.

Publications

Publications (7)
Preprint
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Kontsevich introduced certain ribbon graphs as cell decompositions for combinatorial models of moduli spaces of complex curves with boundaries in his proof of Witten's conjecture. In this work, we define four types of generalised Kontsevich graphs and find combinatorial relations among them. We call the main type ciliated maps and use the auxiliary...
Preprint
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We consider the moduli space of holomorphic principal bundles for reductive Lie groups over Riemann surfaces (possibly with boundaries) and equipped with meromorphic connections. We associate to this space a point-wise notion of quantum spectral curve whose generalized periods define a new set of moduli. We define homology cycles and differential f...
Article
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In this article which is the first of a series of two, we consider $\mathcal W(\widehat{\mathfrak{sl}_d})$-symmetric conformal field theory in topological regimes for a generic value of the background charge, where $\mathcal W(\widehat{\mathfrak{sl}_d})$ is the W-algebra associated to the affine Lie algebra $\widehat{\mathfrak{sl}_d}$. In such regi...
Article
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To any differential system $d\Psi=\Phi\Psi$ where $\Psi$ belongs to a Lie group (a fiber of a principal bundle) and $\Phi$ is a Lie algebra $\Lieg$ valued 1-form on a Riemann surface $\curve$, is associated an infinite sequence of ``correlators" $W_n$ that are symmetric $n$-forms on $\curve^n$. The goal of this article is to prove that these corre...
Thesis
This PhD thesis is about a framework in complex geometry and methods thereof for solving sets of compatible differential equations arising from integrable systems, classical or quantum, in the context of the geometry of moduli spaces of connections over complex curves, or Riemann surfaces. It is based on the idea in mathematical Physics that integr...
Article
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Let $\mathfrak{g}$ be a simply laced Lie algebra, $\widehat{\mathfrak{g}}_1$ the corresponding affine Lie algebra at level one, and $\mathcal{W}(\mathfrak{g})$ the corresponding Casimir W-algebra. We consider $\mathcal{W}(\mathfrak{g})$-symmetric conformal field theory on the Riemann sphere. To a number of $\mathcal{W}(\mathfrak{g})$-primary fields...
Article
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Starting from a $d\times d$ rational Lax pair system of the form $\hbar \partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under certain assumptions (genus $0$ spectral curve and additional conditions on $R$ and $L$), the system satisfies the "topological type property". A consequence is that the formal $\hbar$-WKB expansion o...

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