20 research outputs found
Crystalline Ground States in Polyakov-loop extended Nambu--Jona-Lasinio Models
Nambu--Jona-Lasinio-type models have been used extensively to study the
dynamics of the theory of the strong interaction at finite temperature and
quark chemical potential on a phenomenological level. In addition to these
studies, which are often performed under the assumption that the ground state
of the theory is homogeneous, searches for the existence of crystalline phases
associated with inhomogeneous ground states have attracted a lot of interest in
recent years. In this work, we study the Polyakov-loop extended
Nambu--Jona-Lasinio model and find that the existence of a crystalline phase is
stable against a variation of the parametrization of the underlying Polyakov
loop potential. To this end, we adopt two prominent parametrizations. Moreover,
we observe that the existence of a quarkyonic phase depends crucially on the
parametrization, in particular in the regime of the phase diagram where
inhomogeneous chiral condensation is favored.Comment: 7 pages, 3 figure
Asymptotische Sicherheit von Yukawa Systemen
Different Yukawa systems in three and four dimensions are investigated. The four-dimensional systems are toy models and are plagued with the still unresolved triviality and hierarchy problem of the Standard Model Higgs sector. We use the functional renormalisation group equations and construct asymptotic safety scenarios for the four-dimensional models. This was recently done in a simple Yukawa system. In this thesis we expand this model and include a left-right asymmetry. For the three-dimensional model we investigate the critical behaviour of a second-order phase transition to a chiral-symmetry broken phase. The critical behaviour is investigated in terms of critical exponents
Asymptotically Safe Lorentzian Gravity
The gravitational asymptotic safety program strives for a consistent and
predictive quantum theory of gravity based on a non-trivial ultraviolet fixed
point of the renormalization group (RG) flow. We investigate this scenario by
employing a novel functional renormalization group equation which takes the
causal structure of space-time into account and connects the RG flows for
Euclidean and Lorentzian signature by a Wick-rotation. Within the
Einstein-Hilbert approximation, the -functions of both signatures
exhibit ultraviolet fixed points in agreement with asymptotic safety.
Surprisingly, the two fixed points have strikingly similar characteristics,
suggesting that Euclidean and Lorentzian quantum gravity belong to the same
universality class at high energies.Comment: 4 pages, 2 figure
Detecting inhomogeneous chiral condensation from the bosonic two-point function in the -dimensional Gross-Neveu model in the mean-field approximation
The phase diagram of the -dimensional Gross-Neveu model is
reanalyzed for (non-)zero chemical potential and (non-)zero temperature within
the mean-field approximation. By investigating the momentum dependence of the
bosonic two-point function, the well-known second-order phase transition from
the symmetric phase to the so-called inhomogeneous phase is
detected. In the latter phase the chiral condensate is periodically varying in
space and translational invariance is broken. This work is a proof of concept
study that confirms that it is possible to correctly localize second-order
phase transition lines between phases without condensation and phases of
spatially inhomogeneous condensation via a stability analysis of the
homogeneous phase. To complement other works relying on this technique, the
stability analysis is explained in detail and its limitations and successes are
discussed in context of the Gross-Neveu model. Additionally, we present
explicit results for the bosonic wave-function renormalization in the
mean-field approximation, which is extracted analytically from the bosonic
two-point function. We find regions -- a so-called moat regime -- where the
wave function renormalization is negative accompanying the inhomogeneous phase
as expected.Comment: 27 pages (main text 20, appendix 7), 2 tables, 13 figures (plot data
included in arXiv source file); Updated, published versio
Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems
We search for asymptotic safety in a Yukawa system with a chiral
symmetry, serving as a toy model for the
standard-model Higgs sector. Using the functional RG as a nonperturbative tool,
the leading-order derivative expansion exhibits admissible non-Ga\ssian
fixed-points for which arise from a conformal threshold
behavior induced by self-balanced boson-fermion fluctuations. If present in the
full theory, the fixed-point would solve the triviality problem. Moreover, as
one fixed point has only one relevant direction even with a reduced hierarchy
problem, the Higgs mass as well as the top mass are a prediction of the theory
in terms of the Higgs vacuum expectation value. In our toy model, the fixed
point is destabilized at higher order due to massless Goldstone and fermion
fluctuations, which are particular to our model and have no analogue in the
standard model.Comment: 16 pages, 8 figure