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We review the construction of the $\lambda\phi^4$-model on noncommutative geometries via exact solutions of Dyson-Schwinger equations and explain how this construction relates via (blobbed) topological recursion to problems in algebraic and enumerative geometry.
Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
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Solution of all quartic matrix models
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H. Grosse and R. Wulkenhaar · 1906
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An algebraic approach to a quartic analogue of the Kontsevich model
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On the triviality of λ ϕ d 4 \lambda\phi^{4}_{d} theories and the approach to the critical point in d ≥ 4 d\geq 4 dimensions
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Intersection theory on the moduli space of curves and the matrix Airy function
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Divergencies in a field theory on quantum space
T. Filk · 1996
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Towards finite quantum field theory in noncommutative geometry
H. Grosse, C. Klimčík, and P. Prešnajder · 1996
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Noncommutative geometry and matrix theory: Compactification on tori
A. Connes, M. R. Douglas, and A. S. Schwarz · 1998
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The one loop UV divergent structure of U(1) Yang-Mills theory on noncommutative ℝ 4 \mathbb{R}^{4}
C. P. Martín and D. Sánchez-Ruiz · 1999
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Renormalization in quantum field theory and the Riemann-Hilbert problem. 1. The Hopf algebra structure of graphs and the main theorem
A. Connes and D. Kreimer · 2000
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Renormalization of quantum field theories on noncommutative ℝ d \mathbb{R}^{d} . 1. Scalars
I. Chepelev and R. Roiban · 2000
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Perturbative quantum gauge fields on the noncommutative torus
T. Krajewski and R. Wulkenhaar · 2000
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Noncommutative perturbative dynamics
S. Minwalla, M. Van Raamsdonk, and N. Seiberg · 2000
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Duality in scalar field theory on noncommutative phase spaces
E. Langmann and R. J. Szabo · 2002
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Large N expansion of the 2 matrix model
B. Eynard · 2003
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R. J. Szabo · 2003
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The β \beta -function in duality covariant noncommutative ϕ 4 \phi^{4} -theory
H. Grosse and R. Wulkenhaar · 2004
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Mixed correlation functions in the 2-matrix model, and the Bethe ansatz
B. Eynard and N. Orantin · 2005
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Progress in solving a noncommutative quantum field theory in four dimensions
H. Grosse and R. Wulkenhaar · 2009
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Blobbed topological recursion for correlation functions in tensor models
V. Bonzom and N. Dub · 2011
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Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
B. Bychkov, P. Dunin-Barkowski, M. Kazarian, and S. Shadrin · 2012
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Formal multidimensional integrals, stuffed maps, and topological recursion
G. Borot · 2014
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Abstract loop equations, topological recursion and new applications
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Lambert-W solves the noncommutative Φ 4 \Phi^{4} -model
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