arXiv subjects
Publications and source records attributed to Michaela Oswald.
To investigate the non-perturbative, electric sector of a deconfined gauge theory at nonzero temperature, we consider a SU(2) matrix model. We compute beta-functions to one loop order for the simplest extension of the O(4) nonlinear sigma model, which involves three coupling constants. Computing in the ultraviolet limit in 2 + epsilon dimensions, we find that at least one coupling is not asymptotically free.
We integrate out fast varying quantum fluctuations around static A_4 and A_i fields for the SU(N) gauge group. By assuming that the gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4 we obtain two variants of the effective high-temperature theory for the Polyakov line. One is the effective action for the gauge-invariant eigenvalues of the Polyakov line, and it is explicitly Z(N) symmetric. The other is the effective action for the Polyakov line itself as an element of the SU(N). In this case the theory necessarily includes the spatial components A_i to ensure its gauge invariance under spatial gauge transformations. We derive the 1-loop effective action in the `electric' and `magnetic' sectors, summing up all powers of A_4.
We derive the fermionic contribution to the 1-loop effective action for A_4 and A_i fields at high temperatures, assuming that gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4.
At very high temperatures Yang--Mills theories can be described through perturbation theory. At the tree level the time components of the gluon fields decouple and yield a dimensionally reduced theory. The expectation value of the Polyakov loop then assumes values of the Z(N) center group. At intermediate temperatures, however, this is not true anymore. The time dependence shows up in loops. In a recent work we integrated out fast varying quantum fluctuations around background A_i and static A_4 fields. We assumed that these fields are slowly varying but that the amplitude of A_4 is arbitrary. As a result we obtained the kinetic energy terms for the Polyakov loop both for the electric and the magnetic sector of SU(2).
We find a relationship between the partition function mass zeros and the spectral properties of the QCD Dirac operator in the context of chiral Random Matrix Theory. Introducing the concept of normal modes we see that certain features of the QCD partition function are universal.