Lattice QCD at Strong Coupling

• Applicant: Dr. Wolfgang Unger
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 272537535

Quantum Chromodynamics (QCD) is the fundamental theory of the strong interactions, which confine the quarks and gluons into baryons (e.g. protons and neutrons) and mesons. At high temperatures similar to those in the early universe, a new state of QCD matter - the quark gluon plasma - exists. This plasma has been observed in heavy ion collision experiments at RHIC and LHC. However, it is an open question what the phase diagram looks like at non-zero baryon densities, and in particular whether there exists a chiral critical endpoint. Since QCD is non-perturbative in this regime, lattice gauge theory is the method of choice. The phenomena such as quark confinement and spontaneous chiral symmetry breaking, as well as the phase structure at non-zero temperatures and densities can be investigated only via computer simulations from first principles. The usual simulations are based on sampling the fermion determinant. However, due to the "sign problem'', no direct simulations at non-zero baryon density can be performed. In particular, also the question about the existence of the critical point can not be addressed directly. The aim of this research proposal is to determine the full QCD phase diagram in the µ-T-plane, based on a dual representation of lattice QCD in terms of color singlets. This representation is obtained by integrating out all gauge degrees of freedom in a systematic "strong coupling expansion''. In the limit of infinite coupling, the pure gauge sector can be neglected so that the gauge links entering in the Dirac operator factorize and can be integrated out analytically. The resulting partition function has a very mild sign problem, thus the full phase diagram can be obtained. Now, it is important to go beyond the strong coupling limit to make statements about the phase structure in the continuum, weak coupling limit. For this purpose, more complicated gauge integrals have to be computed which enter the gauge corrections of higher order. I propose to determine the corresponding weights for a Hamiltonian formulation of lattice QCD, which then enter a quantum Monte Carlo algorithm. With this approach, simulations on the dependence of the full µ-T phase diagram on the gauge coupling shall be performed. So far, this kind of simulation has been applied to so-called staggered fermions including the first order gauge corrections, but as a matter of principle the same formalism can be applied to Wilson fermions as well, and quantum Monte Carlo simulations could be performed. Both discretizations (staggered and Wilson) are very different in the limit of strong coupling, in particular concerning the realization of spin. The aim is to compare both discretizations order by order in the strong coupling expansion such that the physical content can be isolated from the lattice artifacts.

• DFG Programme: Independent Junior Research Groups