25 citations · 158 across the 23 of their papers we have counts for
24 papers
Augmentation curve for torus knots
Alexander Hock, Sergey Shadrin
We prove a version of topological recursion for the correlation differentials of colored HOMFLY-PT polynomials of torus knots on the corresponding augmentation curves, following th…
Universal Correlators on Exponentially Ramified Spectral Curves
Mohamad Alameddine, Alexander Hock
We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting th…
Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas
Alexander Hock, Olivier Marchal, Nicolas Orantin
One of the most important applications of topological recursion concerns spectral curves for which the functions defining the spectral curve are allowed to have logarithmic…
Symplectic (Non-)Invariance of the Free Energy in Topological Recursion
Alexander Hock
Let be the free energy derived from Topological Recursion for a given spectral curve on a compact Riemann surface, and let be its - dual, that is, the free e…
Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions
Alexander Hock, Sergey Shadrin, Raimar Wulkenhaar
We prove that meromorphic differentials which are recursively generated by an involution identity are symmetric in all their arguments . The p…
duality in Topological Recursion for exponential variables via Quantum Dilogarithm
Alexander Hock
For a given spectral curve, the theory of topological recursion generates two different families and of multi-differentials, which are for algebraic spectr…
Genus Permutations and Genus Partitions
Alexander Hock
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block size…
Laplace transform of the symplectic transformation formula in Topological Recursion
Alexander Hock
The functional relation coming from the symplectic transformation of Topological Recursion has a lot of applications, for instance it is the higher order moment-cumulant rela…
Blobbed topological recursion from extended loop equations
Alexander Hock, Raimar Wulkenhaar
We consider the Hermitian matrix model with measure , where is the Gaussian measure…
A simple formula for the - symplectic transformation in topological recursion
Alexander Hock
Let be the correlators computed by Topological Recursion for some given spectral curve and for , where the role of is inverted. These…
Complete solution of the LSZ Model via Topological Recursion
Johannes Branahl, Alexander Hock
We prove that the Langmann-Szabo-Zarembo (LSZ) model with quartic potential, a toy model for a quantum field theory on noncommutative spaces grasped as a complex matrix model, obey…
An irregular spectral curve for the generation of bipartite maps in topological recursion
Johannes Branahl, Alexander Hock
We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and boundary length using a spectral curve as initial data for the framework of topol…
On the - Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
Alexander Hock
Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data . We give a functional relation between the correlators of…
Genus one free energy contribution to the quartic Kontsevich model
Johannes Branahl, Alexander Hock
We prove a formula for the genus one free energy of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blob…
From scalar fields on quantum spaces to blobbed topological recursion
Johannes Branahl, Harald Grosse, Alexander Hock +1
We review the construction of the -model on noncommutative geometries via exact solutions of Dyson-Schwinger equations and explain how this construction relates via (blobbed)…
Blobbed topological recursion of the quartic Kontsevich model II: Genus=0
Alexander Hock, Raimar Wulkenhaar
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…
Perturbative and Geometric Analysis of the Quartic Kontsevich Model
Johannes Branahl, Alexander Hock, Raimar Wulkenhaar
The analogue of Kontsevich's matrix Airy function, with the cubic potential replaced by a quartic term with the sa…
Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
Johannes Branahl, Alexander Hock, Raimar Wulkenhaar
We provide strong evidence for the conjecture that the analogue of Kontsevich's matrix Airy function, with the cubic potential replaced by a quartic term $\mathr…
Matrix Field Theory
Alexander Hock
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum fiel…
Solution of the self-dual QFT-model on four-dimensional Moyal space
Harald Grosse, Alexander Hock, Raimar Wulkenhaar
Previously the exact solution of the planar sector of the self-dual -model on 4-dimensional Moyal space was established up to the solution of a Fredholm integral equation. Thi…
Solution of all quartic matrix models
Harald Grosse, Alexander Hock, Raimar Wulkenhaar
We consider the quartic analogue of the Kontsevich model, which is defined by a measure on Hermitian -matrices, where …
Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Jins de Jong, Alexander Hock, Raimar Wulkenhaar
Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recurrence relation. This paper gives the explicit solution of the recurr…
A Laplacian to compute intersection numbers on and correlation functions in NCQFT
Harald Grosse, Alexander Hock, Raimar Wulkenhaar
Let be the generating function of intersection numbers on the moduli spaces of complex curves of genus . As by-product of a complete solution…
Noncommutative 3-colour scalar quantum field theory model in 2D
Alexander Hock, Raimar Wulkenhaar
We introduce the 3-colour noncommutative quantum field theory model in two dimensions. For this model we prove a generalised Ward-Takahashi identity, which is special to coloured n…