# (Quantum) Gauge Theories

**Members of the team**

prof. David Dudal, dr. Subhash Mahapatra (until 31/08/2017), dr. Ana Mizher, dr. Pablo Pais (from 15/10/2017 onwards), drs. Tim De Meerleer, drs. Caroline Felix, drs. Benjamin Maveau and drs. Martin Roelfs.

**Setting of the research:**

**QCD**

Quantum Chromodynamics (QCD) is the quantum field theory, using the language of locally symmetric Yang-Mills gauge theories, behind the strong colour-charge interaction between the constituents of our nucleonic matter (protons and neutrons).

It is one of the four fundamental forces in Nature, next to the electromagnetic, weak and gravitational (general relativity) interaction. Combined the latter 3 forces reside at the heart of the Standard Model, which is capable of explaining an overwhelming abundance of elementary physics processes. Till today, no physics beyond the Standard model was ever observed.

The elementary particles associated with QCD are the 6 quark flavours: 2 very light (up and down), 2 heavier (strange and charm) and 2 very heavy (bottom and top), and each flavour comes in 3 colors. The force between the quarks is mediated by 8 types of gluons.

Two characteristic features of QCD in particular are

- confinement: the colour-charged quarks and gluons are not observed as free particles in Nature in daily life. They always appear in colour-neutral composite states as protons, neutrons, etc.
- chiral symmetry breaking: the up and down quarks are (almost) massless particles, related to a (almost) chiral symmetry between left and right handed quark orientation. Nevertheless the constituent quark mass in the hadrons is significantly large, since e.g. a proton or neutron is about 200 times heavier than the (almost) massless quarks. This can be explained by an effective dynamical mass generation, made possible by chiral symmetry breaking. Essentially, chiral symmetry breaking is what provides the quantum origin of most of our body mass.

The onset of these two phenomena is intimately intertwined with the strong QCD interaction (coupling constant), which becomes too large in the infrared (low energy or long distance) region to allow for “simple” perturbative series expansions, taking us beyond the realm of standard perturbative (Feynman diagrammatic) tools that were so successful in describing the physics of e.g. quantum electrodynamics (QED).

A new dawn of interest in strong QCD emerged with the Large Hadron Collider (LHC), where the ALICE facility is devoted to the study of the quark-gluon plasma (QGP). There, heavy ions are smacked onto each other at ultrarelativistic speeds, thereby creating, during a very small time window, an enormous heat bath of about 10^{12} Kelvin, a temperature about 100000x larger than the interior of the Sun, itself a fusion reactor. A similar experiment has been and still is being conducted at RHIC (Brookhaven, USA). The resulting extremely high temperature causes the quarks and gluons to free themselves from their composite states (hadrons and glueballs), and we speak about a confinement-deconfinement phase transition.

Next to this, also a chiral restoration transition occurs. The eventual state of QCD matter is the QGP, but this plasma is nothing like a normal electromagnetic plasma. The plasma is rather a quasi-ideal fluid than a free gas, exactly because of the still strong interactions. Directly studying finite temperature QCD is an intrinsically hard problem attracting worldwide attention, especially if one desires to study the strongly coupled physics around the phase transitions.

Two major tools to study strongly coupled QCD, even under the extreme conditions as sketched before, are on the market.

- (Monte Carlo) simulations on massive High Performance Computing facilities or parallelized GPU (graphics card) clusters of a discrete version of the QCD theory.
- Another fruitful way to study extreme QCD is gauge/gravity duality: quantum gauge theories are conjectured to be dual to classical gravity theories in higher dimensions where the gauge theory side is the hologram (boundary) of a gravity theory.

**Classical Electrodynamics**

Next to QCD, we also investigate certain daily life practical applications of Maxwell's classical theory of electromagnetism. In particular are we interested in Faraday’s law of induction: an applied (variable) magnetic field creates a response magnetic field in conductive structures due to eddy currents, and by measuring that response field one can probe certain characteristics of the structure. We are interested in developing analytical and numerical models for probing layered media.

**Concrete research topics:**

- Quantization of Non-Abelian gauge theories as QCD, thereby analyzing gauge copies, BRST symmetry, renormalization theory, nonperturbative effects, nontrivial vacuum structure, phase transitions, etc.
- Inverse lattice QCD spectroscopy.
- Gauge-gravity duality applied to QCD to probe phase transitions in extreme conditions and to study transport properties of the quark-gluon plasma.
- Noninvasive electromagnetic induction-based (EMI) scanning of layered soil/seabed geometries.