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The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated in the 1/N expansion by means of the Functional Renormalization Group equations. At leading order, the non-trivial Lifshitz point is observed if the number of dimensions d is taken between d=4 and d=8, and the eigenvalue spectrum of the associated eigendirections is derived. At order 1/N, the anomalous dimension eta_N is computed and it is found to vanish both in d=4 and d=8, while it turns out to be positive between these two values, although strongly dependent on the choice of infrared regulator., Published version

Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale $k$ is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of $k$. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity., 7 pages, 4 figures

The large class of inflationary models known as $\alpha$- and $\xi$-attractors gives identical cosmological predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This means that for all the models considered the inflationary parameters $(n_s,r)$ are (nearly) independent on the Renormalization Group flow. The result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation (which is a particular $\xi$-attractor) this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense., Comment: 11 pages, 1 figure; v2: final version accepted by the journal

We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein-Cartan gravity without the selfduality condition., 14 pages, 4 fgures

In this study, we investigate the Nambu--Jona-Lasinio (NJL) model at finite temperature and finite density in an external magnetic field using the functional renormalization group. We investigate the dependence of the position of the ultraviolet fixed point (UVFP) of the four-Fermi coupling constant on the temperature, density, and external magnetic field, and we obtain the chiral phase structure. The UVFP at low temperature and finite chemical potential oscillates in a small external magnetic field, which can be interpreted as the de Haas--van Alphen effect. We also obtain phase diagrams with complex structures, where the phase boundary moves back and forth as the external magnetic field increases in the low temperature and high density region., Comment: 6 pages, 6 figures, published version

Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the $\varphi^4$ theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime., Comment: 6 pages, 3 figures, and 1 table

We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium., 4 pages, 2 figures

The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero $\beta$-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence \mbox{(PMC-I)}; the other, more recent, method \mbox{(PMC-II)} uses the ${\cal R}_\delta$-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio $R_{e^+ e^-}$ and the Higgs partial width $\Gamma(H\to b\bar{b})$. Both methods lead to the same resummed (`conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group $\{\beta_i\}$-terms in the pQCD expansion are taken into account. We also show that {\it special degeneracy relations}, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory., Comment: 7 pages, 1 figure

The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter., Comment: 5 pages, 4 figures, to appear in Phys. Lett. B

Basis Light-front Quantization has been proposed as a nonperturbative framework for solving quantum field theory. We apply this approach to Quantum Electrodynamics and explicitly solve for the light-front wave function of a physical electron. Based on the resulting light-front wave function, we evaluate the electron anomalous magnetic moment. Nonperturbative mass renormalization is performed. Upon extrapolation to the infinite basis limit our numerical results agree with the Schwinger result obtained in perturbation theory to an accuracy of 0.06%., Comment: 6 pages, 4 figures

We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework., Comment: 6 pages; v2) correcting powers of g in eqs. (23), (24), (27) and (28)

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, $\mu_B$ and $\mu_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite $\mu_B=3\mu$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the ($\mu_I,\mu$)-plane of this phase diagram is strongly constrained by the "Silver Blaze problem." In particular, the onset of pion condensation must occur at $\mu_I= m_{\pi}/2$, independent of $\mu $ as long as $\mu + \mu_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way., Comment: 10 pages, 11 figures; matches published version

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case., Comment: 11 pages, 3 figures, 4 tables; minor text corrections, one figure added, appendix added, references added, matches PLB version

We investigate the chiral phase transition at finite temperature (T) in colour SU(Nc=3) Quantum Chromodynamics (QCD) with six species of fermions (Nf=6) in the fundamental representation by using lattice QCD with improved staggered fermions. By considering lattices with several temporal extensions Nt, we observe asymptotic scaling for Nt > 4. We then extract the dimensionless ratio Tc/Lambda_L (Lambda_L = Lattice Lambda-parameter) for Nf = 6 and Nf = 8, the latter relying on our earlier results. Further, we collect the critical couplings beta^c for the chiral phase transition at Nf = 0 (quenched), and Nf = 4 at a fixed Nt = 6. The results are consistent with enhanced fermionic screening at larger Nf. The Tc/Lambda_L depends very mildly on Nf in the Nf = 0 - 4 region, starts increasing at Nf = 6, and becomes significantly larger at Nf = 8, close to the edge of the conformal window. We discuss interpretations of these results as well as their possible interrelation with preconformal dynamics in the light of a functional renormalization group analysis., 8 pages, 9 figures

The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way., 5 pages, 1 figure

Renormalization of composite three-quark operators in dimensional regularization is complicated by the mixing of physical and unphysical (evanescent) operators. This mixing must be taken into account in a consistent subtraction scheme. In this work we propose a particular scheme that allows one to avoid the necessity of additional finite renormalization and is convenient in QCD applications. As an illustration, we calculate the two-loop anomalous dimensions of local three-quark operators in this scheme., 6 pages, 1 figure; published version, typos corrected

Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which contains a linearly divergent piece. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the latter are equal to one., 11 pages, 1 figure, discussion of renormalization of four-momentum modified, increased numerical precision of one-loop integrals, results and conclusions unchanged

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)

Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z 5 . New fixed points are found and classified.

We present an exact evaluation of the generalized ζ -function for a real scalar field in a δ -function potential in the spacetime S 1 × R D − 1 . The result for the ζ -function is used to obtain the effective action. As a byproduct of the calculation the heat-kernel coefficients are obtained to all orders in a closed form. The regularized zero-point energy is found and we discuss the renormalization of the effective action.

We propose a simple derivation of renormalization group equations and Callan-Symanzik equations as decoupling theorems of the structures underlying effective field theories., 7 pages, no figure, revtex4, additional typos removed, published in Phys. Lett. B

We present an update on the phase diagram of two-color QCD from a chiral effective model approach based on a quark-meson-diquark model using the Functional Renormalization Group (FRG). We discuss the impact of perturbative UV contributions, the inclusion of gauge field dynamics via a phenomenological Polyakov loop potential, and the impact of matter backcoupling on the gauge sector. The corresponding phase diagram including these effects is found to be in qualitative agreement with recent lattice investigations., Comment: 8 pages, 9 figures; published version

We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of a nth order derivative equation in respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism. Scaled running potentials for the subtracted equations keep the physics invariant for a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory is shown. q 2000 Published by Elsevier Science B.V. All rights reserved.

We apply the conical singularity method to calculate the tree-level entropy and its one-loop corrections for a black hole and study the statement that the divergence of the entropy can be completely removed by the renormalization of both the Newton constant and other coefficients by the curvature squared ( R 2 ) terms in the effective gravitational action. This statement is extended to the case where the theory includes not only nonminimally coupled massive scalar fields but also spinor and vector fields . This result confirms us that the renormalization statement works universally, irrespective of field species in nature.

I derive a Wick-ordered continuous renormalization group equation for fermions and show a determinant bound for the solution. This reduces the combinatorial factor in the recursion for fermionic theories by a factorial, as compared to bosons, and thus suggests that convergence of perturbation theory can be proven in the absence of couplings that grow under the renormalization flow.

A continuum limit of the ( λφ 4 ) 4 theory exists which is “trivial” (all scattering amplitudes vanish), but which does not correspond to the zero-renormalized-coupling limit of conventional perturbation theory. This allows Spontaneous Symmetry Breaking and a very heavy, but still weakly interacting, Higgs boson. We answer some criticisms of this work, emphasizing that results from renormalization-group-improved perturbation theory are not valid. The phase transition encountered as the bare mass-squared is made more and more negative is first order , contrary to the assumption of the conventional perturbative “RG-improvement” program.

The applicability of the background field method in spontaneously broken gauge theories is examined with new features emphasized. An explicit one loop analysis in the electroweak theory shows that the method can be consistently implemented in the on-shell renormalization scheme. Some implications and possible applications are also briefly indicated.

The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β -function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.

A general formalism for studying the one-loop and renormalization group (RG) improved potential (in linear curvature approximation) in a multiplicatively renormalizable theory of matter with quantum R 2 -gravity is presented. The phenomenon of dimensional transmutation, which leads to the definition of a scalar coupling constant in terms of gravitational couplings, is discussed in the examples of the fϕ 4 theory and scalar QED. The RG improved potential in the fϕ 4 theory is found. It is shown that the stability of this potential can be influenced by quantum gravity (QG) effects. The QG corrections to scalar-to-vector mass ratio are found in scalar electrodynamics.

The question of the renormalization scheme dependence of the $\tau$ semileptonic decay rate is revisited in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ``acceptable'' renormalization schemes. It is argued that a reasonable universal measure of the renormalization scheme dependence can be formulated, which gives encouraging results when applied to various physical quantities, including the semileptonic $\tau$ decay rate., Comment: Latex 6 pages, 2 Postscript figures appended at the end of this file

We discuss the renormalization scheme dependence of large-order estimates for perturbative series of physical quantities and obtain the renormalization scheme-invariant asymptotics of its effective β-function. As an application we consider infrared renormalons in QCD. For the first infrared renormalon of the electromagnetic current-current correlation function we find the 1 n -corrections to the leading large- n asymptotics.

We present a detailed investigation of the renormalization scheme dependence of the next-to-next-to-leading order QCD predictions for the processes e+e−→hadrons and τ→ντ+hadrons. Based on it the comparison of the results obtained in three frequently used approaches to resolving the renormalization scheme ambiguities with experimental data is carried out.

The one-loop divergences of scale-invariant two-dimensional induced quantum gravity with local action are calculated. It is shown that the theory is multiplicatively-renormalized and is equivalent to a model with non-local action. The one-loop β-function of scalar-graviton interaction coupling is found to be arbitrary.

Polyakov’s two-dimensional quantum gravity is analysed in the perturbative approach. The two-dimensional general invariance of the effective action is preserved using the background-field method. Renormalization of the gravitational coupling and redefinition of the graviton field are performed explicitly at the one-loop order. Some interesting aspects (renormalizability, gauge condition, renormalization and β-function of the gravitational coupling, redefinition of the graviton field) are found.

The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted.

We express the action of a two-dimensional field theory corresponding to a general closed bosonic string field in terms of a single vertex generating operator. This allows us to derive the analog of the exact renormalization group equation without introducing OPE coefficients. Accordingly we can look for explicit solutions of this equation; from the perturbative solution we obtain the four-tachyon scattering amplitude decomposed into three Feynman-like diagrams.

We analyze a regularization of Chern-Simons theory based on a geometrical interpretation of the functional integral in the covariant formalism. Perturbative calculations show the existence of two independent finite renormalization of the gauge field and the Chern-Simons coupling constant. Both renormalizations do not depend on the space-time volume and the gauge condition. Coupling constant renormalization, unlike gauge field renormalization, is also independent of the regulating parameters. The method opens the possibility of a non-perturbative approach in the covariant formalism.

The analytic renormalization procedure for 2D field theory is studied. The consequences for the string effective action are investigated, comparing the R -operation with the Legendre transform. To show where and why they differ, the renormalization is explicitly carried out to third order.

The crucial role of the mass renormalization condition leading to spontaneous symmetry breaking in λΦ 4 theory is discussed. By using the renormalization group equations and a variational estimate of the ground state energy, it is suggested that massless λΦ 4 theory in four dimensions is asymptotically free, not in contradiction with known rigorous results.

A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables.