## Theories of the fundamental interactions

On the one hand, for well accepted or even established theories a solid understanding of their non-perturbative dynamics remains largely wanting. Undoubtedly, topological and geometrical properties in field space in relation to large gauge symmetries play crucial roles in this regard, to which perturbative gauge fixing procedures remain totally oblivious. A significant component of our research efforts addresses such issues within lower dimensional gauge theories from complementary non-perturbative points of view, also unraveling dualities between apparently disconnected theories.

Parallel to such studies is the pursuit of novel computational techniques and approaches towards multi-loop scattering amplitudes, on a par with studies of the mathematical structures of Feynman integrals and scattering amplitudes, relying on as many new mathematical frameworks as may be garnered and call on, with the aim to design new mathematical tools for precision computations in QFT, especially for LHC motivated precision processes. In particular, as soon as supersymmetries are involved, especially with N=4 supersymmetry in four dimensional space-time, much progress has been made over recent years and much scope for further understanding remains within reach.

On the other hand, present day gauge theories of the fundamental quantum interactions present their own challenges pointing towards new fundamental conceptual paradigms beyond quantum physics and gravity. Some of the exploratory paths being trodden are deformations of quantum mechanics, non-commutative or fuzzy space-time geometries, and topological theories for pure quantum gravity, being applied in a variety of physical circumstances. Approached from other perspectives, attempts are being pursued as well that aim to relate gauge coupling constant sectors and electroweak flavor coupling constant sectors within new unification schemes for all interactions.

Finally, progress in non-perturbative dynamics of gauge theories has often exploited advances made in condensed matter physics. Collective phenomena in lower dimensional fermionic systems display a variety of behaviors, in particular quantum Hall systems and their recently identified generalizations with a topological understanding having been achieved over the recent years of their distinctive physical properties reminding one of holographic-like properties in theories of gravity, which may well prove relevant to non-perturbative gauge dynamics alike. Thus some part of our research activities addresses such issues as well.

### Members

#### Professors

##### Claude Duhr

Jean-Marc Gérard

Jan Govaerts

#### PhD students

##### Robin Marzucca

Bram Verbeek

### Projects

#### Integrable quantum dynamics, Klauder-Daubechies deformations and noncommutative geometric structures.

Combining complementary approaches to quantisation, exploration of integrability issues in quantum dynamics and noncommutative geometric structures

External collaborators: M. Norbert Hounkonnou (ICMPA-UNESCO Chair, UAC, Benin) Calvin Matondo Bwayi (UNIKIN, DRC).

#### Mathematical Structure of Feynman Integrals and Scattering Amplitudes

Analytic and algebraic properties of multi-loop integrals are analysed in the view of devising new mathematical tools for precision computations in QFT.

External collaborators: Samuel Abreu (Universität Freiburg) Ruth Britto (Trinity College Dublin) Einan Gardi (University of Edinburgh).

#### Multi-loop scattering amplitudes in N=4 Super Yang-Mills

Multi-loops scattering amplitudes in N=4 Super Yang-Mills are analysed in the light of the integrability of the theory in the planar limit.

External collaborators: Vittorio Del Duca (ETH Zurich & INFN Frascati) Lance Dixon (SLAC) James Drummond (University of Southampton) Falko Dulat (SLAC) Georgios Papathanasiou (SLAC).

#### Non-commutative quantum dynamics and supersymmetry

Extensions to the supersymmetric context of the Moyal non-commutative plane are being considered from different perspectives.

#### Non-perturbative dynamics of QED in low dimensions

By emphasizing the relevance of topology in nonperturbative gauge dynamics in the presence of nontrivial space(time) topology, develop gauge invariant physical tools to approach the nonperturbative dynamics of such systems in approximation schemes. In an initial study, QED in lower dimensions is considered in detail.

#### Nonperturbative quantisation of gauge theories, noncommutative geometry and unification of the fundamental interactions

Development of nonperturbative quantisation techniques of gauge theories (Yang-Mills, topological, gravity) and their application to particle physics and quantum field theory at finite temperature (in particular, within the context of superconductivity).

Exploration of the consequences of noncommutative geometry in the search for the unification of the fundamental interactions (M-theory and superstrings, quantum gravity).

External collaborators: Frederik Scholtz (National Institute for Theoretical Physics, NITheP, South Africa); Hendrik Geyer (Stellenbosch Institute for Advanced Study, STIAS; University of Stellenbosch, South Africa); M. Norbert Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Benin); Calvin Matondo Bwayi (University of Kinshasa, Kinshasa, Democratic Republic of Congo); Habatwa Mweene (University of Zambia, Lusaka, Zambia); John R. Klauder (University of Florida, Gainesville, USA); Peter Jarvis (University of Tasmania, Hobart, Australia).

#### On the unification of gauge coupling constants

In the standard model version of the grand unified theory different gauge couplings intend to, but do not, meet at some higher scale. Here we will look for some better ways for the unification of the gauge coupling constants.

#### Quantum Gravity and the Cosmological Constant

Quantum diffeomorphic gauge invariance and the total cosmological constant, inclusive of the quantum fluctuations of the gravitational field

#### Topology and Non-Perturbative Gauge Dynamics

The connections between topology in space(time) and in field configuration space and the non-perturbative dynamics of general gauge theories, inclusive of mass generating mechanims, are being studied.

Show past projects.

### Publications

#### 2018

*Zhengwen Liu and Xiaoran Zhao*

Refereed paper. 19th September.

*Del Duca, Vittorio and Druc, Stefan and Drummond, James and Duhr, Claude and Dulat, Falko and Marzucca, Robin and Papathanasiou, Georgios and Verbeek, Bram*

[Abstract] [PDF]

Contribution to proceedings. 13th July.

*Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew*

Contribution to proceedings. 12th July.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

Contribution to proceedings. 12th July.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

To appear in "Elliptic integrals, elliptic functions and modular forms in quantum field theory"

Contribution to proceedings. 2nd July.