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We combine a recent construction of a BRST-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background-field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the corresponding beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one-loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter., 24 pages, 3 figures

The fundamental theory of quantum electrodynamics predicts the vacuum to resemble a polarizable medium. This gives rise to effective nonlinear interactions between electromagnetic fields and light-by-light scattering phenomena. We study the collision of two optical laser pulses in a pump-probe setup using beams with circular and elliptic cross section and estimate the number of discernible signal photons induced by quantum vacuum nonlinearities. In this analysis we study strategies to optimize the quantum vacuum signal discernible from the background of the driving lasers. One of the main results is that the collision of two maximally focused lasers does not lead to the best discernible signal. Instead, widening the focus typically improves the signal to background separation in the far field., Comment: 18 pages, 14 figures

We investigate the phenomenon of gravitational catalysis, i.e., curvature-induced chiral symmetry breaking and fermion mass generation, at finite temperature. Using a scale-dependent analysis, we derive a thermal bound on the curvature of local patches of spacetime. This bound quantifies regions in parameter space that remain unaffected by gravitational catalysis and thus are compatible with the existence of light fermions as observed in Nature. While finite temperature generically relaxes the curvature bound, we observe a comparatively strong dependence of the phenomenon on the details of the curvature. Our bound can be applied to scenarios of quantum gravity, as any realistic candidate has to accommodate a sufficient number of light fermions. We argue that our bound therefore represents a test for quantum gravity scenarios: a suitably averaged spacetime in the (trans-)Planckian regime that satisfies our curvature bound does not induce correspondingly large Planckian fermion masses by gravitational catalysis. The temperature dependence derived in this work facilitates to follow the fate of gravitational catalysis during the thermal history of the (quantum) universe. In an application to the Asymptotic Safety scenario of quantum gravity, our bound translates into a temperature-dependent upper bound on the number of fermion flavors., 12 pages, 5 figures

Quantum vacuum fluctuations give rise to effective non-linear interactions between electromagnetic fields. A prominent signature of quantum vacuum nonlinearities driven by macroscopic fields are signal photons differing in characteristic properties such as frequency, propagation direction and polarization from the driving fields. We devise a strategy for the efficient tracing of the various vacuum-fluctuation-mediated interaction processes in order to identify the most prospective signal photon channels. As an example, we study the collision of up to four optical laser pulses and pay attention to sum and difference frequency generation. We demonstrate how this information can be used to enhance the signal photon yield in laser pulse collisions for a given total laser energy., 15 pages, 9 figures

We study the perspectives of measuring the phenomenon of vacuum birefringence predicted by quantum electrodynamics using an x-ray free-electron laser (XFEL) alone. We devise an experimental scheme allowing the XFEL beam to collide with itself under a finite angle, and thus act as both pump and probe field for the effect. The signature of vacuum birefringence is encoded in polarization-flipped signal photons to be detected with high-purity x-ray polarimetry. Our findings for idealized scenarios underline that the discovery potential of solely XFEL-based setups can be comparable to those involving optical high-intensity lasers. For currently achievable scenarios, we identify several key details of the x-ray optical ingredients that exert a strong influence on the magnitude of the desired signatures., Comment: 26 pages, 2 figures; matches journal version

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take the opportunity to clarify some common misunderstandings regarding the program., Comment: 23 pages plus references

High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the gauge coupling, the electron mass and the Pauli spin-field coupling. Renormalization group trajectories emanating from these fixed points correspond to asymptotically safe theories that are free from the Landau pole problem. We analyze the resulting universality classes defined by the fixed points, determine the corresponding critical exponents, study the resulting phase diagram, and quantify the stability of our results with respect to a systematic expansion scheme. We also compute high-energy complete flows towards the long-range physics. We observe the existence of a renormalization group trajectory that interconnects one of the interacting fixed points with the physical low-energy behavior of QED as measured in experiment. Within pure QED, we estimate the crossover from perturbative QED to the asymptotically safe fixed point regime to occur somewhat above the Planck scale but far below the scale of the Landau pole., 14 pages, 4 figures; v3: minor corrections to Eq. (7), Tab. III and the figures; quantitative changes to Eqs. (19) and (20) correcting previous and published versions

Physical review letters 123(9), 091802 (2019). doi:10.1103/PhysRevLett.123.091802, We show that coherent harmonic focusing provides an efficient mechanism to boost all-optical signatures of quantum vacuum nonlinearity in the collision of high-intensity laser fields, thereby offering a promising route to their first experimental detection. Assuming two laser pulses of given parameters at our disposal, we demonstrate a substantial increase of the number of signal photons measurable in experiments where one of the pulses undergoes coherent harmonic focusing before it collides with the fundamental-frequency pulse. Imposing a quantitative criterion to discern the signal photons from the background of the driving laser photons and accounting for the finite purity of polarization filtering, we find that signal photons arising from inelastic scattering processes constitute a promising signature. By contrast, quasielastic contributions which are conventionally assumed to form the most prospective signal remain background dominated. Our findings may result in a paradigm shift concerning which photonic signatures of quantum vacuum nonlinearity are accessible in experiment., Published by APS, College Park, Md.

Recent studies have provided evidence for the existence of new asymptotically free trajectories in non-Abelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general ${\rm SU}(N_{\rm L})\times {\rm SU}(N_{\rm c})$ Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies. We construct these asymptotically free trajectories within conventional $\overline{\text{MS}}$ schemes and systematic weak coupling expansions. The existence of these solutions is argued to be a scheme-independent phenomenon, as demonstrated for mass-dependent schemes based on general momentum-space infrared regularizations. A change of scheme induces a map of the theory's coupling space onto itself, which in the present case also translates into a reparametrization of the space of asymptotically free solutions., 30 pages, 4 figures

$$\mathbb {Z}_2$$ Z2 -Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.

$$\mathbb {Z}_2$$ -Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.

Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent electromagnetic fields. Recent studies have adopted this approach to study collisions of Gaussian laser pulses in paraxial approximation. The present study extends these investigations beyond the paraxial approximation by using an efficient numerical solver for the classical input fields. This new numerical code allows for a consistent theoretical description of optical signatures of QED vacuum nonlinearities in generic electromagnetic fields governed by Maxwell's equations in the vacuum, such as manifestly non-paraxial laser pulses. Our code is based on a locally constant field approximation of the Heisenberg-Euler effective Lagrangian. As this approximation is applicable for essentially all optical high-intensity laser experiments, our code is capable of calculating signal photon emission amplitudes in completely generic input field configurations, limited only by numerical cost., Comment: 8 pages, 3 figures; talk given at LPHYS'18, Nottingham, United Kingdom

Physical review / D D 99(12), 125019 (2019). doi:10.1103/PhysRevD.99.125019, We analyze fermionic criticality in relativistic 2+1 dimensional fermion systems using the functional renormalization group (FRG), concentrating on the Gross-Neveu (chiral Ising) and the Thirring model. While a variety of methods, including the FRG, appear to reach quantitative consensus for the critical regime of the Gross-Neveu model, the situation seems more diverse for the Thirring model with different methods yielding vastly different results. We present a first exploratory FRG study of such fermion systems including momentum-dependent couplings using pseudo-spectral methods. Our results corroborate the stability of results in Gross-Neveu-type universality classes, but indicate that momentum dependencies become more important in Thirring-type models for small flavor numbers. For larger flavor numbers, we confirm the existence of a non-Gaussian fixed point and thus a physical continuum limit. In the large-N limit, we obtain an analytic solution for the momentum dependence of the fixed-point vertex., Published by Inst.189733, Melville, NY

Our goal is to study optical signatures of quantum vacuum nonlinearities in strong macroscopic electromagnetic fields provided by high-intensity laser beams. The vacuum emission scheme is perfectly suited for this task as it naturally distinguishes between incident laser beams, described as classical electromagnetic fields driving the effect, and emitted signal photons encoding the signature of quantum vacuum nonlinearity. Using the Heisenberg-Euler effective action, our approach allows for a reliable study of photonic signatures of QED vacuum nonlinearity in the parameter regimes accessible by all-optical high-intensity laser experiments. To this end, we employ an efficient, flexible numerical algorithm, which allows for a detailed study of the signal photons emerging in the collision of focused paraxial high-intensity laser pulses. Due to the high accuracy of our numerical solutions we predict the total number of signal photons, but also have full access to the signal photons' characteristics, including their spectrum, propagation directions and polarizations. We discuss setups offering an excellent background-to-noise ratio, thus providing an important step towards the experimental verification of quantum vacuum nonlinearities., 7 pages, 2 figures; talk given at LPHYS'18, Nottingham, United Kingdom

The tremendous progress in high-intensity laser technology and the establishment of dedicated high-field laboratories in recent years have paved the way towards a first observation of quantum vacuum nonlinearities at the high-intensity frontier. We advocate a particularly prospective scenario, where three synchronized high-intensity laser pulses are brought into collision, giving rise to signal photons, whose frequency and propagation direction differ from the driving laser pulses, thus providing various means to achieve an excellent signal to background separation. Based on the theoretical concept of vacuum emission, we employ an efficient numerical algorithm which allows us to model the collision of focused high-intensity laser pulses in unprecedented detail. We provide accurate predictions for the numbers of signal photons accessible in experiment. Our study paves the way for a first verification of quantum vacuum nonlinearity in a well-controlled laboratory experiment at one of the many high-intensity laser facilities currently coming online., 7 pages, 2 figures; matches journal version

We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective potential for the chiral order parameter, as induced by fermionic fluctuations on a curved spacetime with local hyperbolic properties. The bound is expressed in terms of the local curvature scalar measured in units of a gauge-invariant coarse-graining scale. We argue that any effective field theory of quantum gravity obeying this curvature bound is safe from chiral symmetry breaking through gravitational catalysis and thus compatible with the simultaneous existence of chiral fermions in the low-energy spectrum. With increasing number of dimensions, the curvature bound in terms of the hyperbolic scale parameter becomes stronger. Applying the curvature bound to the asymptotic safety scenario for quantum gravity in four spacetime dimensions translates into bounds on the matter content of particle physics models., 17 pages, 5 figures

All-optical experiments at the high-intensity frontier offer a promising route to unprecedented precision tests of quantum electrodynamics in strong macroscopic electromagnetic fields. So far, most theoretical studies of all-optical signatures of quantum vacuum nonlinearity are based on simplifying approximations of the beam profiles and pulse shapes of the driving laser fields. Since precision tests require accurate quantitative theoretical predictions, we introduce an efficient numerical tool facilitating the quantitative theoretical study of all-optical signatures of quantum vacuum nonlinearity in generic laser fields. Our approach is based on the vacuum emission picture, and makes use of the fact that the dynamics of the driving laser fields are to an excellent approximation governed by classical Maxwell theory in vacuum. In combination with a Maxwell solver, which self-consistently propagates any given laser field configuration, this allows for accurate theoretical predictions of photonic signatures of vacuum nonlinearity in high-intensity laser experiments from first principles. We employ our method to simulate photonic signatures of quantum vacuum nonlinearity in laser pulse collisions involving a few-cycle pulse, and show that the angular and spectral distributions of the emitted signal photons deviate from those of the driving laser beams., Comment: 17 pages,9 figures

The link between a modified Higgs self-coupling and the strong first-order phase transition necessary for baryogenesis is well explored for polynomial extensions of the Higgs potential. We broaden this argument beyond leading polynomial expansions of the Higgs potential to higher polynomial terms and to nonpolynomial Higgs potentials. For our quantitative analysis we resort to the functional renormalization group, which allows us to evolve the full Higgs potential to higher scales and finite temperature. In all cases we find that a strong first-order phase transition manifests itself in an enhancement of the Higgs self-coupling by at least 50%, implying that such modified Higgs potentials should be accessible at the LHC.

Physical review / D D 99(8), 085009 (2019). doi:10.1103/PhysRevD.99.085009, A mass parameter for the gauge bosons in gauge-fixed four-dimensional Yang-Mills theory can be accommodated in a local and manifestly Becchi-Rouet-Stora-Tyutin invariant action. The construction is based on the Faddeev-Popov method involving a nonlinear gauge-fixing and a background Nakanishi-Lautrup field. When applied to momentum-dependent masslike deformations, this formalism leads to a full regularization of the theory which explicitly preserves Becchi-Rouet-Stora-Tyutin symmetry. We deduce a functional renormalization group equation for the one-particle-irreducible effective action, which has a one-loop form. The master equation is compatible with it—i.e., Becchi-Rouet-Stora-Tyutin symmetry is preserved along the flow—and it has a standard regulator-independent Zinn-Justin form. As a first application, we compute the leading-order gluon wave-function renormalization., Published by Inst.189733, Melville, NY

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., 6 pages

We investigate the emergence of ${\cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the $\epsilon$-expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group., Comment: 28 pages, 2 figures; v2: published version, includes a new appendix

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows to describe the effective potential as a function of both scalar field amplitude and RG scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability., Comment: 13 pages, 3 figures, Proceedings for the meeting 'Higgs Cosmology', Kavli Royal Society Centre, Chichley Hall, UK (27-28.3.2017), invited review for Phil.Trans.R.S. A

We study electron-positron pair production by spatially inhomogeneous electric fields. Depending on the localization of the field, a critical point (critical surface) exists in the space of field configurations where the pair production probability vanishes. Near criticality, pair production exhibits universal properties similar to those of continuous phase transitions. We extend results previously obtained in the semiclassical (weak-field) critical regime to the deeply critical regime for arbitrary peak field strength. In this regime, we find an enhanced universality, featuring a unique critical exponent $\ensuremath{\beta}=3$ for all sufficiently localized fields. For a large class of field profiles, we also compute the nonuniversal amplitudes.

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.

Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase., 39 pages, 32 figures

We study the renormalization flow of the Higgs potential as a function of both field amplitude and energy scale. This overcomes limitations of conventional techniques that rely, e.g., on an identification of field amplitude and RG scale, or on local field expansions. Using a Higgs-Yukawa model with discrete chiral symmetry as an example, our global flows in field space clarify the origin of possible meta-stabilities, the fate of the pseudo-stable phase, and provide new information about the renormalization of the tunnel barrier. Our results confirm the relaxation of the lower bound for the Higgs mass in the presence of more general microscopic interactions (higher-dimensional operators) to a high quantitative accuracy., 17 pages, 13 figures

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gau{\ss}ian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space., Comment: 7 pages, 1 figure

We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields., Comment: 37 pages, 6 figures; v5: typos removed

We investigate photon merging and splitting processes in inhomogeneous, slowly varying electromagnetic fields. Our study is based on the three-photon polarization tensor following from the Heisenberg-Euler effective action. We put special emphasis on deviations from the well-known constant field results, also revisiting the selection rules for these processes. In the context of high-intensity laser facilities, we analytically determine compact expressions for the number of merged/split photons as obtained in the focal spots of intense laser beams. For the parameter range of a typical petawatt class laser system as pump and a terawatt class laser as probe, we provide estimates for the numbers of signal photons attainable in an actual experiment. The combination of frequency upshifting, polarization dependence and scattering off the inhomogeneities renders photon merging an ideal signature for the experimental exploration of nonlinear quantum vacuum properties., Comment: 14 pages, 4 figures

We report on the measurement of the highest purity of polarization of X-rays to date. The measurements are performed by combining a brilliant undulator source with an X-ray polarimeter. The polarimeter is composed of a polarizer and an analyzer, each based on four reflections at channel-cut crystals with a Bragg angle very close to 45°. Experiments were performed at three different X-ray energies, using different Bragg reflections: Si(400) at 6457.0 eV, Si(444) at 11,183.8 eV, and Si(800) at 12,914.0 eV. At 6 keV a polarization purity of 1.5 × 10− 9 is achieved. This is an improvement by more than two orders of magnitude as compared to previously reported values. The polarization purity decreases slightly for shorter X-ray wavelengths. The sensitivity of the polarimeter is discussed with respect to a proposed experiment that aims at the detection of the birefringence of vacuum induced by super-strong laser fields.

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., 15 pages

We relate quark confinement, as measured by the Polyakov-loop order parameter, to color confinement, as described by the Kugo-Ojima/Gribov-Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) -- in agreement with general expectations. As an estimate for the critical temperature, we obtain T_c=284MeV for SU(3)., Comment: 5 pages, 1 figure

We analyze the running gauge coupling at finite temperature for QCD, using the functional renormalization group. The running of the coupling is calculated for all scales and temperatures. At finite temperature, the coupling is governed by a fixed point of the 3-dimensional theory for scales smaller than the corresponding temperature. The running coupling can drive the quark sector to criticality, resulting in chiral symmetry breaking. Our results provide for a quantitative determination of the phase boundary in the plane of temperature and number of massless flavors. Using the experimental value of the coupling at the tau mass scale as the only input parameter, we obtain, e.g., for N_f=3 massless flavors a critical temperature of T_cr ~ 148 MeV in good agreement with lattice simulations., Comment: 6 pages, 3 figures; references added, results updated and discussion expanded (matches PLB version)

We investigate a class of relativistic fermion theories in 2, Comment: 18 pages, 3 figures, 2 tables; v2: references added, published version

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., Comment: 20 pages, 6 figures