
Wolfgang UngerEmmy NoetherFellow

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Emmy Noether was a German Mathematician who worked on symmetries. She lived from 1882 to 1935, studied in Erlangen and spent most of her professional life in Göttingen. Since in the early 20th century, women were not allowed to become professors, she had to give her lectures in the name of David Hilbert, with whom she worked together. The situation changed after the fist world war, and in 1922 Emmy Noether was the first woman in Germany to receive a professorship. See here for her ► Biography. To physicists she is best known because of the Noether theorem and the Noether current/charge. The Noether theorem states that if a system has a continuous symmetry, then there is a corresponding charge which is conserved in time. The "Deutsche Forschungsgesellschaft" DFG has established in 1997 the Emmy Noether Program to give young scientists the opportunity to achieve independence in research at an early stage. The group is funded for 5 years. 

The EmmyNoether junior reseearch group "Lattice QCD at Strong Coupling", which was established July 1st 2015, aims to contribute to the determination of the QCD phase diagram via strong coupling expansion: 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 nonzero baryon densities, and in particular whether there exists a chiral critical endpoint. Since QCD is nonperturbative 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 nonzero temperatures and densities can be investigated only via computer simulations from first principles. The usual simulations are based on the fermion determinant. However, due to the "sign problem", no direct simulations at nonzero baryon density can be performed. Hence, also the question about the existence of the critical point can not be addressed directly. The aim of the Emmy Noetherproject is to measure the full QCD phase diagram in the μTplane, based on a dual representation of lattice QCD in terms of color singlets. This 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 such 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 qualitative statements about the phase structure away from the strong coupling limit. For this purpose, more complicated gauge integrals have to be computed which enter the gauge corrections of higher order. Within the research group the corresponding weights for a Hamiltonian formulation of lattice QCD shall be determined which then enter a quantum Monte Carlo algorithm. With this approach, simulations on the dependence of the full μT phase diagram on the gauge coupling shall be performed. 
