50 research outputs found
Universality and the Renormalisation Group
Several functional renormalisation group (RG) equations including Polchinski
flows and Exact RG flows are compared from a conceptual point of view and in
given truncations. Similarities and differences are highlighted with special
emphasis on stability properties. The main observations are worked out at the
example of O(N) symmetric scalar field theories where the flows, universal
critical exponents and scaling potentials are compared within a derivative
expansion. To leading order, it is established that Polchinski flows and ERG
flows - despite their inequivalent derivative expansions - have identical
universal content, if the ERG flow is amended by an adequate optimisation. The
results are also evaluated in the light of stability and minimum sensitivity
considerations. Extensions to higher order and further implications are
emphasized.Comment: 15 pages, 2 figures; paragraph after (19), figure 2, and references
adde
Non-perturbative thermal flows and resummations
We construct a functional renormalisation group for thermal fluctuations.
Thermal resummations are naturally built in, and the infrared problem of
thermal fluctuations is well under control. The viability of the approach is
exemplified for thermal scalar field theories. In gauge theories the present
setting allows for the construction of a gauge-invariant thermal
renormalisation group.Comment: 16 pages, eq (38) added to match published versio
Renormalization group flows for gauge theories in axial gauges
Gauge theories in axial gauges are studied using Exact Renormalisation Group flows. We introduce a background field in the infrared regulator, but not in the gauge fixing, in contrast to the usual background field gauge. It is shown how heat-kernel methods can be used to obtain approximate solutions to the flow and the corresponding Ward identities. Expansion schemes are discussed, which are not applicable in covariant gauges. As an application, we derive the one-loop effective action for covariantly constant field strength, and the one-loop beta-function for arbitrary regulator
Fixed points and infrared completion of quantum gravity
The phase diagram of four-dimensional Einstein–Hilbert gravity is studied using Wilsonʼs renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed
Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization
We compute the scale-dependence of the Planck mass and of the vacuum
expectation value of the Higgs field using two very different renormalization
group methods: a "holographic" procedure based on Einstein's equations in five
dimensions with matter confined to a 3-brane, and a "functional" procedure in
four dimensions based on a Wilsonian momentum cutoff. Both calculations lead to
very similar results, suggesting that the coupled theory approaches a
non-trivial fixed point in the ultraviolet.Comment: 11 pages, 1 figur
On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
We study the nature of the confinement phase transition in d=3+1 dimensions
in various non-abelian gauge theories with the approach put forward in [1]. We
compute an order-parameter potential associated with the Polyakov loop from the
knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and
Sp(2) we find a first-order phase transition in agreement with general
expectations. Moreover our study suggests that the phase transition in E(7)
Yang-Mills theory also is of first order. We find that it is weaker than for
SU(N). We show that this can be understood in terms of the eigenvalue
distribution of the order parameter potential close to the phase transition.Comment: 15 page
Perturbative and non-perturbative aspects of the proper time renormalization group
The renormalization group flow equation obtained by means of a proper time
regulator is used to calculate the two loop beta function and anomalous
dimension eta of the field for the O(N) symmetric scalar theory. The standard
perturbative analysis of the flow equation does not yield the correct results
for both beta and eta. We also show that it is still possible to extract the
correct beta and eta from the flow equation in a particular limit of the
infrared scale. A modification of the derivation of the Exact Renormalization
Group flow, which involves a more general class of regulators, to recover the
proper time renormalization group flow is analyzed.Comment: 26 pages.Latex.Version accepted for publicatio
Towards a renormalizable standard model without fundamental Higgs scalar
We investigate the possibility of constructing a renormalizable standard
model with purely fermionic matter content. The Higgs scalar is replaced by
point-like fermionic self-interactions with couplings growing large at the
Fermi scale. An analysis of the UV behavior in the point-like approximation
reveals a variety of non-Gaussian fixed points for the fermion couplings. If
real, such fixed points would imply nonperturbative renormalizability and evade
triviality of the Higgs sector. For point-like fermionic self-interactions and
weak gauge couplings, one encounters a hierarchy problem similar to the one for
a fundamental Higgs scalar.Comment: 18 pages, 4 figure
The Functional Renormalization Group and O(4) scaling
The critical behavior of the chiral quark-meson model is studied within the
Functional Renormalization Group (FRG). We derive the flow equation for the
scale dependent thermodynamic potential at finite temperature and density in
the presence of a symmetry-breaking external field. Within this scheme, the
critical scaling behavior of the order parameter, its transverse and
longitudinal susceptibilities as well as the correlation lengths near the
chiral phase transition are computed. We focus on the scaling properties of
these observables at non-vanishing external field when approaching the critical
point from the symmetric as well as from the broken phase. We confront our
numerical results with the Widom-Griffiths form of the magnetic equation of
state, obtained by a systematic epsilon-expansion of the scaling function. Our
results for the critical exponents are consistent with those recently computed
within Lattice Monte-Carlo studies of the O(4) spin system.Comment: 14 pages, 11 figure
Flow Equation for Supersymmetric Quantum Mechanics
We study supersymmetric quantum mechanics with the functional RG formulated
in terms of an exact and manifestly off-shell supersymmetric flow equation for
the effective action. We solve the flow equation nonperturbatively in a
systematic super-covariant derivative expansion and concentrate on systems with
unbroken supersymmetry. Already at next-to-leading order, the energy of the
first excited state for convex potentials is accurately determined within a 1%
error for a wide range of couplings including deeply nonperturbative regimes.Comment: 24 pages, 8 figures, references added, typos correcte