arXiv subjects

Masatoshi Yamada

Publications and source records attributed to Masatoshi Yamada.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scaling solutions for asymptotically free quantum gravity

We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity.

hep-th↗

arXiv2022

Coleman-Weinberg Abrikosov-Nielsen-Olesen strings

We study properties of Abrikosov-Nielsen-Olesen (ANO) strings with the Coleman-Weinberg (CW) potential, which we call CW-ANO strings. While the scale-invariant scalar potential has a topologically trivial vacuum admitting no strings at the classical level, quantum correction allows topologically nontrivial vacua and stable string solutions. We find that the system of the CW potential exhibits significant difference from that of the conventional Abelian-Higgs model with the quadratic-quartic potential. While a single-winding string is qualitatively similar in both systems, and the static intervortex force between two strings at large distance is attractive/repulsive in the type-I/II regime for both, that between two CW-ANO strings exhibits a nontrivial structure. It develops an energy barrier between them at intermediate distance, implying that the string with winding number $n > 1$ can constitute a metastable bound state even in the type-II regime. We name such a superconductor type-$\overline{1.5}$. We also discuss implications to high-energy physics and cosmology.

hep-ph↗

arXiv2022

Determining wave equations in holographic QCD from Wilsonian renormalization group

We show a possible way to build the AdS/CFT correspondence starting from the quantum field theory side based on renormalization group approach. An extra dimension is naturally introduced in our scheme as the renomalization scale. The holographic wave equations are derived, with the potential term being determined by the QFT properties. We discover that only around the fixed point, i.e. the conformal limit, the potential in the bulk equations can be fully constrained, and upon this foundation, the correspondence is build. We demonstrate this fact using a 3D scalar theory in which, besides the trivial fixed point, there exists the Wilson-Fisher fixed point. From the energy scalings around those fixed points, we determine the behavior of the potential in the bulk equations.

hep-th↗

arXiv2022

Asymptotic freedom and safety in quantum gravity

We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $β$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a scalar field. Quantum gravity can be asymptotically free, based on a flow trajectory from the corresponding ultraviolet fixed point to the infrared region. This flow can also be realized by a scaling solution for varying values of a scalar field. As an alternative possibility, quantum gravity can be realized by asymptotic safety at the other fixed point. There may exist a critical trajectory between the two fixed points, starting in the extreme ultraviolet from asymptotic freedom. We compute critical exponents and determine the number of relevant parameters for the two fixed points. Evaluating the flow equation for constant scalar fields yields the universal gravitational contribution to the effective potential for the scalars.

hep-th↗

arXiv2022

Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

We study the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. We use the exponential parametrization to derive the fixed points for the cosmological constant, Planck mass, Higgs mass and its coupling, keeping arbitrary gauge parameters $α$ and $β$, and compare the results with the linear split. We find that the beta functions for the Higgs potential are expressed in terms of redefined Planck mass such that the apparent gauge dependence is absent. Only the trace mode of the gravity fluctuations couples to the Higgs potential and it tends to decouple in the large $β$ limit, but the anomalous dimension becomes large, invalidating the local potential approximation. This gives the limitation of the exponential parametrization. There are also singularities for some values of the gauge parameters but well away from these, we find rather stable fixed points and critical exponents. We thus find that there are regions for the gauge parameters to give stable fixed points and critical exponents against the change of gauge parameters. The Higgs coupling is confirmed to be irrelevant for the reasonable choice of gauge parameters.

hep-th↗

arXiv2021

Universal gravitational-wave signatures from heavy new physics in the electroweak sector

We calculate the gravitational-wave spectra produced by the electroweak phase transition with TeV-scale Beyond-Standard-Model physics in the early universe. Our study captures the effect of quantum and thermal fluctuations within a non-perturbative framework. We discover a universal relation between the mean bubble separation and the strength parameter of the phase transition, which holds for a wide range of new-physics contributions. The ramifications of this result are three-fold: First, they constrain the gravitational-wave spectra resulting from heavy (TeV-scale) new physics. Second, they contribute to distinguishing heavy from light new physics directly from the gravitational-wave signature. Third, they suggest that a concerted effort of gravitational-wave observations together with collider experiments could be required to distinguish between different models of heavy new physics.

hep-ph↗

arXiv2020

Dynamically emergent gravity from hidden local Lorentz symmetry

Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent.

hep-th↗

arXiv2020

Gravitational instantons and anomalous chiral symmetry breaking

We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $\exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.

hep-th↗

arXiv2020

Scalegenesis and fermionic dark matters in the flatland scenario

We propose an extension of the standard model with Majorana-type fermionic dark matters based on the flatland scenario where all scalar coupling constants, including scalar mass terms, vanish at the Planck scale, i.e. the scalar potential is flat above the Planck scale. This scenario could be compatible with the asymptotic safety paradigm for quantum gravity. We search the parameter space so that the model reproduces the observed values such as the Higgs mass, the electroweak vacuum and the relic abundance of dark matter. We also investigate the spin-independent elastic cross section for the Majorana fermions and a nucleon. It is shown that the Majorana fermions as dark matter candidates could be tested by dark matter direct detection experiments such as XENON, LUX and PandaX-II. We demonstrate that within the minimal setup compatible with the flatland scenario at the Planck scale or asymptotically safe quantum gravity, the extended model could have a strong predictability.

hep-ph↗

arXiv2020

Partial bosonisation for the two-dimensional Hubbard model: How well does it work?

Partial bosonisation of the two-dimensional Hubbard model focuses the functional renormalisation flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the antiferromagnetic phase near the onset of local antiferromagnetic order, the interaction of the electrons is indeed well described by the exchange of collective bosonic degrees of freedom. The residual four-fermion vertex after the subtraction of the bosonic exchange contribution is small. We propose that similar partial bosonisation techniques can improve the accuracy of renormalisation flow studies also for the case of competing order.

cond-mat.str-el↗

arXiv2020

Gauge hierarchy problem and scalegenesis

We review the gauge hierarchy problem in the standard model. We discuss the meaning of the quadratic divergence in terms of the Wilsonian renormalization group. Classical scale symmetry, which prohibits dimensionful parameters in the bare action, could play a key role for the understanding of the origin of the electroweak scale. We discuss the scale-generation mechanism, i.e. scalegenesis in scale invariant theories. In this paper, we introduce a scale invariant extension of the SM based on a strongly interacting scalar-gauge theory. It is discussed that asymptotically safe quantum gravity provides a hint about solutions to the gauge hierarchy problem.

hep-ph↗

arXiv2019

Variable Planck mass from the gauge invariant flow equation

Using the gauge invariant flow equation for quantum gravity we compute how the strength of gravity depends on the length or energy scale. The fixed point value of the scale-dependent Planck mass in units of the momentum scale has an important impact on the question, which parameters of the Higgs potential can be predicted in the asymptotic safety scenario for quantum gravity? For the standard model and a large class of theories with additional particles the quartic Higgs coupling is an irrelevant parameter at the ultraviolet fixed point. This makes the ratio between the Higgs boson and the top-quark mass predictable.

hep-th↗

arXiv2019

On the impact of Majorana masses in gravity-matter systems

We investigate the Higgs-Yukawa system with Majorana masses of a fermion within asymptotically safe quantum gravity. Using the functional renormalization group method we derive the beta functions of the Majorana masses and the Yukawa coupling constant and discuss the possibility of a non-trivial fixed point for the Yukawa coupling constant. In the gravitational sector we take into account higher derivative terms such as $R^2$ and $R_{μν}R^{μν}$ in addition to the Einstein-Hilbert term for our truncation. For a certain value of the gravitational coupling constants and the Majorana masses, the Yukawa coupling constant has a non-trivial fixed point value and becomes an irrelevant parameter being thus a prediction of the theory. We also discuss consequences due to the Majorana mass terms to the running of the quartic coupling constant in the scalar sector.

hep-th↗

arXiv2019

Planck mass and inflation as consequences of dynamically broken scale invariance

Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden SU(N_c) gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at energies below the Planck mass contains two scalar fields: the pseudo-Nambu--Goldstone boson of spontaneously broken scale invariance (the dilaton) and a gravitational scalar degree of freedom that originates from the R^2 term in the effective action (the scalaron). We compute the effective potential for the coupled dilaton-scalaron system at one-loop order and demonstrate that it can be used to successfully realize a stage of slow-roll inflation in the early Universe. Remarkably enough, our predictions for the primordial scalar and tensor power spectra interpolate between those of standard R^2 inflation and linear chaotic inflation. For comparatively small gravitational couplings, we thus obtain a spectral index n_s ~= 0.97 and a tensor-to-scalar ratio as large as r ~= 0.08.

hep-ph↗

arXiv2019

Higgs scalar potential in asymptotically safe quantum gravity

The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an---asymptotically---vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted.

hep-th↗

arXiv2018

Scale and confinement phase transitions in scale invariant $SU(N)$ scalar gauge theory

We consider scalegenesis, spontaneous scale symmetry breaking, by the scalar-bilinear condensation in $SU(N)$ scalar gauge theory. In an effective field theory approach to the scalar-bilinear condensation at finite temperature, we include the Polyakov loop to take into account the confinement effect. The theory with $N=3,4,5$ and $6$ is investigated, and we find that in all these cases the scale phase transition is a first-order phase transition. We also calculate the latent heat at and slightly below the critical temperature. Comparing the results with those obtained without the Polyakov loop effect, we find that the Polyakov effect can considerably increase the latent heat in some cases, which would mean a large increase in the energy density of the gravitational waves background, if it were produced by the scale phase transition.

hep-th↗

arXiv2018

Asymptotic safety and field parametrization dependence in the f(R) truncation

We study the dependence on field parametrization of the functional renormalization group equation in the $f(R)$ truncation for the effective average action. We perform a systematic analysis of the dependence of fixed points and critical exponents in polynomial truncations. We find that, beyond the Einstein-Hilbert truncation, results are qualitatively different depending on the choice of parametrization. In particular, we observe that there are two different classes of fixed points, one with three relevant directions and the other with two. The computations are performed in the background approximation. We compare our results with the available literature and analyze how different schemes in the regularizations can affect the fixed point structure.

hep-th↗

arXiv2018

Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(σ;t)$ is given as a partial differential equation, where $σ:=\bar ψψ$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$χ$SB) occurs at a certain scale $t_c$, $V(σ;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$χ$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

hep-th↗