# The Beta Function of Strongly Coupled Gauge Theories near the Non-perturbative Conformal Edge

**Principal Investigator:** Chik Him Wong, University of Wuppertal (Germany)

**HPC Platform:** JUQUEEN of JSC

Strongly Coupled Gauge Theories (SCGTs) play an important role in High Energy Physics. A well-known example is Quantum Chromodynamics (QCD), which describes the strong force among subatomic particles. The properties of SCGTs depend on the number of flavours, the types of fermions (representation) and interaction (symmetry group). For certain combinations, the theory would behave nearly the same at different low probing energies, or equivalently different large size scales. This property is known as being almost conformal.

In the search of new physics, nearly conformal SCGTs are of particular interest because theories with approximate conformality are more likely to be compatible with existing experimental constraints, which is an essential criterium of being a viable candidate. Since the properties of a theory is governed by the behaviour of interaction strength, how conformal the theory is can be studied by the rate of change in the interaction strength with respect to probing energy, which is known as the beta function.

For a nearly conformal SCGT, the beta function becomes very close to zero below certain probing energy. According to perturbative calculations, it is expected that SCGTs approach conformality as the number of fermion flavours increases. However, the exact number at which the theory becomes truly conformal is not known. In order to quantitatively investigate this, a non-perturbative calculation is needed. A popular approach is to simulate the models numerically.

The computation of beta functions of nearly conformal theories is very challenging. Space-time is replaced by a four-dimensional discrete lattice. For nearly conformal theories, the correlation lengths become very long, imposing difficulties of removing the discretization effects and thus requires very large lattices. This implies that the simulations are only possible on powerful high performance computing systems (HPC) such as the GCS supercomputer JUQUEEN in Jülich.

In this project, the Lattice Higgs Collaboration (LatHC), which consists of scientists from University of Wuppertal, Eotvos University, University of the Pacific and University of California, San Diego, investigates the beta function of SCGTs which are similar to QCD. From the simulation, it is observed that the beta function decreases with increasing number of fermion flavours. This is a non-perturbative evidence of nearly conformal behaviour of many flavoured QCD-like theories. It also provides a quantitative estimate of how close to conformality these theories are, which is crucial in the search of viable models of new physics.

*Fig. 01: The beta functions in terms of decreasing probing energy (increasing interaction strength g*

^{2}). The beta function decreases as the number of fermion flavors (N_{f}) increases, hinting that the theories are approaching conformality. The Sextet model, which is also a nearly conformal theory, is plotted together for comparison. (c) University of Wuppertal**Team: Lattice Higgs Collaboration (LatHC)**

Zoltan Fodor (Eotvos U. & IAS, Julich & Wuppertal U.)

Kieran Holland (U. Pacific, Stockton & U. Bern, AEC)

Julius Kuti (UC, San Diego)

Daniel Nogradi (Eotvos U. & Eotvos Lorand U., Budapest, Inst. Theor. Phys.)

Chik Him Wong (Wuppertal U.)

**Scientific Contact:**

Dr. Chik Him (Ricky) Wong

Institut für Theoretische Teilchenphysik

Fakultät für Mathematik und Naturwissenschaften

Bergische Universität Wuppertal, D-42097 Wuppertal (Germany)

e-mail: cwong [at] uni-wuppertal.de

*July 2017*