[Show abstract][Hide abstract] ABSTRACT: We develop the worldline formalism for computations of composite operators
such as the fluctuation induced energy-momentum tensor. As an example, we use a
fluctuating real scalar field subject to Dirichlet boundary conditions. The
resulting worldline representation can be evaluated by worldline Monte-Carlo
methods in continuous spacetime. We benchmark this worldline numerical
algorithm with the aid of analytically accessible single-plate and
parallel-plate Casimir configurations, providing a detailed analysis of
statistical and systematic errors. The method generalizes straightforwardly to
arbitrary Casimir geometries and general background potentials.
[Show abstract][Hide abstract] ABSTRACT: We critically examine the gauge, and field-parametrization dependence of
renormalization group flows in the vicinity of non-Gau\ss{}ian fixed points in
quantum gravity. While physical observables are independent of such
calculational specifications, the construction of quantum gravity field
theories typically relies on off-shell quantities such as $\beta$ functions and
generating functionals and thus face potential stability issues with regard to
such generalized parametrizations. We analyze a two-parameter class of
covariant gauge conditions, the role of momentum-dependent field rescalings and
a class of field parametrizations. Using the product of Newton and cosmological
constant as an indicator, the principle of minimum sensitivity identifies
stationary points in this parametrization space which show a remarkable
insensitivity to the parametrization. In the most insensitive cases, the
quantized gravity system exhibits a non-Gau\ss{}ian UV stable fixed point,
lending further support to asymptotically free quantum gravity. One of the
stationary points facilitates an analytical determination of the quantum
gravity phase diagram and features ultraviolet and infrared complete RG
trajectories with a classical regime.
[Show abstract][Hide abstract] ABSTRACT: We investigate Schwinger pair production in spatially inhomogeneous electric
backgrounds. A critical point for the onset of pair production can be
approached by fields that marginally provide sufficient electrostatic energy
for an off-shell long-range electron-positron fluctuation to become a real
pair. Close to this critical point, we observe features of universality which
are analogous to continuous phase transitions in critical phenomena with the
pair-production rate serving as an order parameter: electric backgrounds can be
subdivided into universality classes and the onset of pair production exhibits
characteristic scaling laws. An appropriate design of the electric background
field can interpolate between power-law scaling, essential BKT-type scaling and
a power-law scaling with log corrections. The corresponding critical exponents
only depend on the large-scale features of the electric background, whereas the
microscopic details of the background play the role of irrelevant perturbations
not affecting criticality.
[Show abstract][Hide abstract] ABSTRACT: Birefringence is one of the fascinating properties of the vacuum of quantum
electrodynamics (QED) in strong electromagnetic fields. The scattering of
linearly polarized incident probe photons into a perpendicularly polarized mode
provides a distinct signature of the optical activity of the quantum vacuum and
thus offers an excellent opportunity for a precision test of non-linear QED.
Precision tests require accurate predictions and thus a theoretical framework
that is capable of taking the detailed experimental geometry into account. We
derive analytical solutions for vacuum birefringence which include the
spatio-temporal field structure of a strong optical pump laser field and an
x-ray probe. We show that the angular distribution of the scattered photons
depends strongly on the interaction geometry and find that scattering of the
perpendicularly polarized scattered photons out of the cone of the incident
probe x-ray beam is the key to making the phenomenon experimentally accessible
with the current generation of FEL/high-field laser facilities.
[Show abstract][Hide abstract] ABSTRACT: We investigate a class of relativistic fermion theories in 2<d<4 space-time
dimensions with continuous chiral U(Nf)xU(Nf) symmetry. This includes a number
of well-studied models, e.g., of Gross-Neveu and Thirring type, in a unified
framework. Within the limit of pointlike interactions, the RG flow of couplings
reveals a network of interacting fixed points, each of which defines a
universality class. A subset of fixed points are "critical fixed points" with
one RG relevant direction being candidates for critical points of second-order
phase transitions. Identifying invariant hyperplanes of the RG flow and
classifying their attractive/repulsive properties, we find evidence for
emergent higher chiral symmetries as a function of Nf. For the case of the
Thirring model, we discover a new critical flavor number that separates the RG
stable large-Nf regime from an intermediate-Nf regime in which
symmetry-breaking perturbations become RG relevant. This new critical flavor
number has to be distinguished from the chiral-critical flavor number, below
which the Thirring model is expected to allow spontaneous chiral symmetry
breaking, and its existence offers a resolution to the discrepancy between
previous results obtained in the continuum and the lattice Thirring models.
Moreover, we find indications for a new feature of universality: details of the
critical behavior can depend on additional "spectator symmetries" that remain
intact across the phase transition. Implications for the physics of interacting
fermions on the honeycomb lattice, for which our theory space provides a simple
model, are given.
[Show abstract][Hide abstract] ABSTRACT: We construct asymptotically free renormalization group trajectories for the
generic nonabelian Higgs model in four-dimensional spacetime. These
ultraviolet-complete trajectories become visible by generalizing the
renormalization/boundary conditions in the definition of the correlation
functions of the theory. We identify a candidate three-parameter family of
renormalization group trajectories interconnecting the asymptotically free
ultraviolet regime with a Higgs phase in the low-energy limit. We provide
estimates of their low-energy properties in the light of a possible application
to the standard model Higgs sector. Finally, we find a two-parameter subclass
of asymptotically free Coleman-Weinberg-type trajectories that do not suffer
from a naturalness problem.
Physical Review D 02/2015; 92(2). DOI:10.1103/PhysRevD.92.025016 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The spin-base invariant formalism of Dirac fermions in curved space maintains
the essential symmetries of general covariance as well as similarity
transformations of the Clifford algebra. We emphasize the advantages of the
spin-base invariant formalism both from a conceptual as well as from a
practical viewpoint. This suggests that local spin-base invariance should be
added to the list of (effective) properties of (quantum) gravity theories. We
find support for this viewpoint by the explicit construction of a global
realization of the Clifford algebra on a 2-sphere which is impossible in the
spin-base non-invariant vielbein formalism.
Physics Letters B 02/2015; 743. DOI:10.1016/j.physletb.2015.03.014 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In view of the measured Higgs mass of 125 GeV, the perturbative
renormalization group evolution of the Standard Model suggests that our Higgs
vacuum might not be stable. We connect the usual perturbative approach and the
functional renormalization group which allows for a straightforward inclusion
of higher-dimensional operators in the presence of an ultraviolet cutoff. In
the latter framework we study vacuum stability in the presence of
higher-dimensional operators. We find that their presence can have a sizable
influence on the maximum ultraviolet scale of the Standard Model and the
existence of instabilities. Finally, we discuss how such operators can be
generated in specific models and study the relation between the instability
scale of the potential and the scale of new physics required to avoid
instabilities.
Journal of High Energy Physics 01/2015; 2015(4). DOI:10.1007/JHEP04(2015)022 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We reconsider the recently proposed nonlinear QED effect of quantum
reflection of photons off an inhomogeneous strong-field region. We present new
results for strong fields varying both in space and time. While such
configurations can give rise to new effects such as frequency mixing, estimated
reflection rates based on previous one-dimensional studies are corroborated. On
a conceptual level, we critically re-examine the validity regime of the
conventional locally-constant-field approximation and identify kinematic
configurations which can be treated reliably. Our results further underline the
discovery potential of quantum reflection as a new signature of the
nonlinearity of the quantum vacuum.
New Journal of Physics 12/2014; 17(4). DOI:10.1088/1367-2630/17/4/043060 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a chiral Yukawa model mimicking the Higgs-top-bottom sector of the
standard model. We re-analyze the conventional arguments that relate a lower
bound for the Higgs mass with vacuum stability in the light of exact results
for the regularized fermion determinant as well as in the framework of the
functional renormalization group. In both cases, we find no indication for
vacuum instability nor meta-stability induced by top-fluctuations if the cutoff
is kept finite but arbitrary. A lower bound for the Higgs mass arises for the
class of standard bare potentials of \phi^4 type from the requirement of a
well-defined functional integral (i.e., stability of the bare potential). This
consistency bound can however be relaxed considerably by more general forms of
the bare potential without necessarily introducing new meta-stable minima.
European Physical Journal C 07/2014; 75(2). DOI:10.1140/epjc/s10052-015-3284-1 · 5.08 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the effect of laser photon merging, or equivalently high harmonic
generation, in the quantum vacuum subject to inhomogeneous electromagnetic
fields. Such a process is facilitated by the effective nonlinear couplings
arising from charged particle-antiparticle fluctuations in the quantum vacuum
subject to strong electromagnetic fields. We derive explicit results for
general kinematic and polarization configurations involving optical photons.
Concentrating on merged photons in reflected channels which are preferable in
experiments for reasons of noise suppression, we demonstrate that photon
merging is typically dominated by the competing nonlinear process of quantum
reflection, though appropriate polarization and signal filtering could
specifically search for the merging process. As a byproduct, we devise a novel
systematic expansion of the photon polarization tensor in plane wave fields.
Physical Review D 06/2014; 90(3). DOI:10.1103/PhysRevD.90.033007 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We analyze the many-flavor phase diagram of quantum electrodynamics (QED) in
2+1 (Euclidean) space-time dimensions. We compute the critical flavor number
above which the theory is in the quasi-conformal massless phase. For this, we
study the renormalization group fixed-point structure in the space of gauge
interactions and pointlike fermionic self-interactions, the latter of which are
induced dynamically by fermion-photon interactions. We find that a reliable
estimate of the critical flavor number crucially relies on a careful treatment
of the Fierz ambiguity in the fermionic sector. Using a Fierz-complete basis,
our results indicate that the phase transition towards a chirally-broken phase
occurring at small flavor numbers could be separated from the quasi-conformal
phase at larger flavor numbers, allowing for an intermediate phase which is
dominated by fluctuations in a vector channel. If these interactions approach
criticality, the intermediate phase could be characterized by a
Lorentz-breaking vector condensate.
Physical Review D 04/2014; 90(3). DOI:10.1103/PhysRevD.90.036002 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Electron-positron pair production in oscillating electric fields is investigated in the nonperturbative threshold regime. Accurate numerical solutions of quantum kinetic theory for corresponding observables are presented and analyzed in terms of a proposed model for an effective mass of electrons and positrons acquired within the given strong electric field. Although this effective mass cannot provide an exact description of the collective interaction of a charged particle with the strong field, physical observables are identified which carry direct and sensitive signatures of the effective mass.
[Show abstract][Hide abstract] ABSTRACT: We explore Schwinger pair production in rotating time-dependent electric
fields using the real-time DHW formalism. We determine the time evolution of
the Wigner function as well as asymptotic particle distributions neglecting
back-reactions on the electric field. Whereas qualitative features can be
understood in terms of effective Keldysh parameters, the field rotation leaves
characteristic imprints in the momentum distribution that can be interpreted in
terms of interference and multiphoton effects. These phenomena may seed
characteristic features of QED cascades created in the antinodes of a
high-intensity standing wave laser field.
Physical Review D 11/2013; 89(8):085001. DOI:10.1103/PhysRevD.89.085001 · 4.86 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study a formulation of Dirac fermions in curved spacetime that respects
general coordinate invariance as well as invariance under local spin-base
transformations. The natural variables for this formulation are
spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint.
In particular, a coframe, i.e. vierbein field is not required. The
corresponding affine spin connection consists of a canonical part that is
completely fixed in terms of the Dirac matrices and a free part that can be
interpreted as spin torsion. A general variation of the Dirac matrices
naturally induces a spinorial Lie derivative which coincides with the known
Kosmann-Lie derivative in the absence of torsion. Using this formulation for
building a field theory of quantized gravity and matter fields, we show that it
suffices to quantize the metric and the matter fields. This observation is of
particular relevance for field theory approaches to quantum gravity, as it can
serve for a purely metric-based quantization scheme for gravity even in the
presence of fermions.
Physical Review D 10/2013; 89(6). DOI:10.1103/PhysRevD.89.064040 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the functional renormalization group flow of a Higgs-Yukawa toy
model mimicking the top-Higgs sector of the standard model. This approach
allows for treating arbitrary bare couplings. For the class of standard bare
potentials of \phi^4-type at a given ultraviolet cut-off, we show that a finite
infrared Higgs mass range emerges naturally from the renormalization group flow
itself. Higgs masses outside the resulting bounds cannot be connected to any
conceivable set of bare parameters in this standard-model \phi^4 class. By
contrast, more general bare potentials allow to diminish the lower bound
considerably. We identify a simple renormalization group mechanism for this
depletion of the lower bound. If active also in the full standard model, Higgs
masses smaller than the conventional infrared window do not necessarily require
new physics at low scales or give rise to instability problems.
Physical Review D 08/2013; 89(4). DOI:10.1103/PhysRevD.89.045012 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate chiral Higgs-Yukawa models with a non-abelian gauged
left-handed sector reminiscent to a sub-sector of the standard model. We
discover a new weak-coupling fixed-point behavior that allows for ultraviolet
complete RG trajectories which can be connected with a conventional long-range
infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is
characterized by asymptotic freedom in all interaction couplings, but a quasi
conformal behavior in all mass-like parameters. The stable microscopic scalar
potential asymptotically approaches flatness in the ultraviolet, however, with
a non-vanishing minimum increasing inversely proportional to the asymptotically
free gauge coupling. This gives rise to nonperturbative -- though weak-coupling
-- threshold effects which induce ultraviolet stability along a line of fixed
points. Despite the weak-coupling properties, the system exhibits non-Gaussian
features which are distinctly different from its standard perturbative
counterpart: e.g., on a branch of the line of fixed points, we find linear
instead of quadratically running renormalization constants. Whereas the Fermi
constant and the top mass are naturally of the same order of magnitude, our
model generically allows for light Higgs boson masses. Realistic mass ratios
are related to particular RG trajectories with a "walking" mid-momentum regime.
European Physical Journal C 06/2013; 73(12). DOI:10.1140/epjc/s10052-013-2652-y · 5.08 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Standard Model extensions often predict low-mass and very weakly interacting
particles, such as the axion. A number of small-scale experiments at the
intensity/precision frontier are actively searching for these elusive
particles, complementing searches for physics beyond the Standard Model at
colliders. Whilst a next generation of experiments will give access to a huge
unexplored parameter space, a discovery would have a tremendous impact on our
understanding of fundamental physics.
Annalen der Physik 06/2013; 525(6). DOI:10.1002/andp.201300727 · 3.05 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that photons subject to a spatially inhomogeneous electromagnetic
field can experience quantum reflection. Based on this observation, we propose
quantum reflection as a novel means to probe the nonlinearity of the quantum
vacuum in the presence of strong electromagnetic fields.
New Journal of Physics 05/2013; 15(8). DOI:10.1088/1367-2630/15/8/083002 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Catalyzed symmetry breaking arises from a parametric enhancement of critical
fluctuations independently of the coupling strength. Symmetry-breaking
fermionic long-range fluctuations exhibit such an enhancement on negatively
curved spaces, as is known from mean-field studies. We study gravitational
catalysis from the viewpoint of the functional renormalization group using the
3d Gross-Neveu model as a specific example. We observe gravitational catalysis
towards a phase of broken discrete chiral symmetry both on a maximally
symmetric (AdS) and on a purely spatially curved manifold for constant negative
curvature (Lobachevsky plane). The resulting picture for gravitational
catalysis obtained from the renormalization flow is closely related to that of
magnetic catalysis. As an application, we estimate the curvature required for
subcritical systems of finite length to acquire a gravitionally catalyzed gap.