Raimar Wulkenhaar
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View article: Solution of all quartic matrix models
Solution of all quartic matrix models Open
View article: Relationship between a $Φ^4$ matrix model and harmonic oscillator systems
Relationship between a $Φ^4$ matrix model and harmonic oscillator systems Open
A Hermitian $Φ^4$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schrödinger equation of the $N$-body harmonic oscillator, and that eig…
View article: Characterization of the $W_{1+\infty}$-n-algebra and applications
Characterization of the $W_{1+\infty}$-n-algebra and applications Open
In this paper, we construct the $W_{1+\infty}$-n-algebras in the framework of the generalized quantum algebra. We characterize the $\mathcal{R}(p,q)$-multi-variable $W_{1+\infty}$-algebra and derive its $n$-algebra which is the generalized…
View article: Blobbed topological recursion from extended loop equations
Blobbed topological recursion from extended loop equations Open
View article: Stochastic quantization of $λϕ_2^4$- theory in 2-d Moyal space
Stochastic quantization of $λϕ_2^4$- theory in 2-d Moyal space Open
There is strong evidence for the conjecture that the $λϕ^4$ QFT- model on 4-dimensional non-commutative Moyal space can be non-perturbatively constructed. As preparation, in this paper we construct the 2-dimensional case with the method of…
View article: Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions
Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions Open
We prove that meromorphic differentials $ω^{(0)}_n(z_1,...,z_n)$ which are recursively generated by an involution identity are symmetric in all their arguments $z_1,...,z_n$. The proof involves an intriguing combinatorial identity between …
View article: Relationship between Φ<sup>4</sup>-matrix model and N-body harmonic oscillator or Calogero-Moser model
Relationship between Φ<sup>4</sup>-matrix model and N-body harmonic oscillator or Calogero-Moser model Open
We study some Hermitian Φ 4 -matrix model and some real symmetric Φ 4 -matrix model whose kinetic terms are given by Tr( E Φ 2 ), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition functions of…
View article: Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 (with an appendix by Maciej Dołęga)
Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 (with an appendix by Maciej Dołęga) Open
We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential \omega_{0,n} at a reflected point \iota z in terms of all \omega…
View article: A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential Open
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan-Plücker relations of certain avera…
View article: Real symmetric $$ \Phi ^4$$-matrix model as Calogero–Moser model
Real symmetric $$ \Phi ^4$$-matrix model as Calogero–Moser model Open
We study a real symmetric $$\Phi ^4$$ -matrix model whose kinetic term is given by $$\textrm{Tr}( E \Phi ^2)$$ , where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this…
View article: Real symmetric $Φ^4$-matrix model as Calogero-Moser model
Real symmetric $Φ^4$-matrix model as Calogero-Moser model Open
We study a real symmetric $Φ^4$-matrix model whose kinetic term is given by $\mathrm{Tr}( E Φ^2)$, where $E$ is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds…
View article: Generalized Heisenberg–Virasoro algebra and matrix models from quantum algebra
Generalized Heisenberg–Virasoro algebra and matrix models from quantum algebra Open
In this paper, we construct the Heisenberg–Virasoro algebra in the framework of the R(p,q)-deformed quantum algebras. Moreover, the R(p,q)-Heisenberg–Witt n-algebras is also investigated. Furthermore, we generalize the notion of the ellipt…
View article: A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential
A Note on BKP for the Kontsevich Matrix Model with Arbitrary Potential Open
We exhibit the Kontsevich matrix model with arbitrary potential as a BKP tau-function with respect to polynomial deformations of the potential. The result can be equivalently formulated in terms of Cartan-Plücker relations of certain avera…
View article: Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra
Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra Open
In this paper, we construct the Heisenberg-Virasoro algebra in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Moreover, the $\mathcal{R}(p,q)$-Heisenberg-Witt $n$-algebras is also investigated. Furthermore, we generaliz…
View article: Blobbed topological recursion from extended loop equations
Blobbed topological recursion from extended loop equations Open
We consider the $N\times N$ Hermitian matrix model with measure $dμ_{E,λ}(M)=\frac{1}{Z} \exp(-\frac{λN}{4} \mathrm{tr}(M^4)) dμ_{E,0}(M)$, where $dμ_{E,0}$ is the Gaussian measure with covariance $\langle M_{kl}M_{mn}\rangle=\frac{δ_{kn}δ…
View article: A Laplacian to Compute Intersection Numbers on $$\overline{{{\mathcal {M}}}}_{g,n}$$ and Correlation Functions in NCQFT
A Laplacian to Compute Intersection Numbers on $$\overline{{{\mathcal {M}}}}_{g,n}$$ and Correlation Functions in NCQFT Open
Let $$F_g(t)$$ be the generating function of intersection numbers of $$\psi $$ -classes on the moduli spaces $$\overline{{{\mathcal {M}}}}_{g,n}$$ of stable complex curves of genus g . As by-product of a complete solution of all non-pla…
View article: Intersection theory of the complex quartic Kontsevich model
Intersection theory of the complex quartic Kontsevich model Open
We expand correlation functions of the Langmann-Szabo-Zarembo (LSZ) model in terms of intersection numbers on the moduli space of complex curves. This provides an explicit, physically motivated example for the expansion of correlation func…
View article: An algebraic approach to a quartic analogue of the Kontsevich model
An algebraic approach to a quartic analogue of the Kontsevich model Open
We consider an analogue of Kontsevich’s matrix Airy function where the cubic potential $\textrm{Tr}(\Phi^3)$ is replaced by a quartic term $\textrm{Tr}\!\left(\Phi^4\right)$ . Cumulants of the resulting measure are known to decompose into …
View article: From scalar fields on quantum spaces to blobbed topological recursion
From scalar fields on quantum spaces to blobbed topological recursion Open
We review the construction of the λϕ 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 enumerat…
View article: Blobbed Topological Recursion of the Quartic Kontsevich Model I: Loop Equations and Conjectures
Blobbed Topological Recursion of the Quartic Kontsevich Model I: Loop Equations and Conjectures Open
View article: Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Nested Catalan tables and a recurrence relation in noncommutative quantum field theory Open
Correlation functions in a dynamic quartic matrix model are obtained from the twopoint function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinat…
View article: From scalar fields on quantum spaces to blobbed topological recursion
From scalar fields on quantum spaces to blobbed topological recursion Open
We review the construction of the $λϕ^4$-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 enumera…
View article: Perturbative and Geometric Analysis of the Quartic Kontsevich Model
Perturbative and Geometric Analysis of the Quartic Kontsevich Model Open
The analogue of Kontsevich's matrix Airy function, with the cubic potential\n$\\operatorname{Tr}\\big(\\Phi^3\\big)$ replaced by a quartic term\n$\\operatorname{Tr}\\big(\\Phi^4\\big)$ with the same covariance, provides a toy\nmodel for qu…
View article: Blobbed topological recursion of the quartic Kontsevich model II: Genus=0
Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 Open
We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential $ω_{0,n}$ at a reflected point $ιz$ in terms of all $ω_{0,m}$ wi…
View article: Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures Open
We provide strong evidence for the conjecture that the analogue of Kontsevich's matrix Airy function, with the cubic potential $\mathrm{Tr}(Φ^3)$ replaced by a quartic term $\mathrm{Tr}(Φ^4)$, obeys the blobbed topological recursion of Bor…
View article: Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space
Solution of the self-dual Φ4 QFT-model on four-dimensional Moyal space Open
View article: Towards integrability of a quartic analogue of the Kontsevich model
Towards integrability of a quartic analogue of the Kontsevich model Open
We consider an analogue of Kontsevich's matrix Airy function where the cubic potential $\mathrm{Tr}(\Phi^3)$ is replaced by a quartic term $\mathrm{Tr}(\Phi^4)$. Cumulants of the resulting measure are known to decompose into cycle types fo…
View article: An algebraic approach to a quartic analogue of the Kontsevich model
An algebraic approach to a quartic analogue of the Kontsevich model Open
We consider an analogue of Kontsevich's matrix Airy function where the cubic potential $\mathrm{Tr}(Φ^3)$ is replaced by a quartic term $\mathrm{Tr}(Φ^4)$. Cumulants of the resulting measure are known to decompose into cycle types for whic…
View article: The Leutwyler–Smilga relation on the lattice
The Leutwyler–Smilga relation on the lattice Open
According to the Leutwyler–Smilga relation, in Quantum Chromodynamics (QCD), the topological susceptibility vanishes linearly with the quark masses. Calculations of the topological susceptibility in the context of lattice QCD, extrapolated…
View article: Catalan tables and a recursion relation in noncommutative quantum field theory
Catalan tables and a recursion relation in noncommutative quantum field theory Open
Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recursion relation. This paper gives the explicit solution of the recursion by mapping it bijectively to a combinatorial structure n…