# From scalar fields on quantum spaces to blobbed topological recursion

@inproceedings{Branahl2021FromSF, title={From scalar fields on quantum spaces to blobbed topological recursion}, author={Johannes Branahl and Harald Grosse and Alexander Hock and Raimar Wulkenhaar}, year={2021} }

We review the construction of the λφ-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.

## 3 Citations

From Noncommutative Geometry to Random Matrix Theory

- Mathematics
- 2022

We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers ﬁnite real spectral triples where the space of possible Dirac operators is…

Genus one free energy contribution to the quartic Kontsevich model

- Mathematics
- 2021

We prove a formula for the genus one free energy F (1) of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion. We…

Two Approaches For a Perturbative Expansion in Blobbed Topological Recursion

- Mathematics
- 2022

. In this paper we continue the perturbative analysis of the quartic Kontsevich model. We investigate meromorphic functions Ω (0) m with m = 1 , 2 , that obey blobbed topological recursion. We…

## References

SHOWING 1-10 OF 75 REFERENCES

Towards Finite Quantum Field Theory in Non-Commutative Geometry

- Mathematics
- 1995

We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect…

Intersection theory on the moduli space of curves and the matrix airy function

- Mathematics
- 1992

We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical…

PERTURBATIVE QUANTUM GAUGE FIELDS ON THE NONCOMMUTATIVE TORUS

- Physics
- 2000

Using standard field theoretical techniques, we survey pure Yang–Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared…

Non-commutative Renormalization

- Physics
- 2004

We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non-commutative field theory and suggest a related constructive program. This paper is dedicated to J.…

Noncommutative Geometry and Matrix Theory: Compactification on Tori

- Mathematics
- 1997

We study toroidal compactification of Matrix theory, using ideas and results of noncommutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification…