arXiv subjects

Nobuyoshi Ohta

Publications and source records attributed to Nobuyoshi Ohta.

At least 37 records · Page 2Linked to original sources

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.

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arXiv2021

BRST Quantization of General Relativity in Unimodular Gauge and Unimodular Gravity

Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We develop a novel way to gauge fix the transverse diffeomorphism (TDiff) and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the TDiff. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then study a theory derived by making "Fourier transform" of GR in the unimodular gauge with respect to the cosmological constant as a candidate of "quantum UG." We clarify the difference from GR and point out problems in this theory.

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arXiv2021

Quantum improved charged black holes

We consider quantum effects of gravitational and electromagnetic fields in spherically symmetric black hole spacetimes in the asymptotic safety scenario. Introducing both the running gravitational and electromagnetic couplings from the renormalization group equations and applying a physically sensible scale identification scheme based on the Kretschmann scalar, we construct a quantum mechanically corrected, or quantum improved Reissner-Nordstrom metric. We study the global structure of the quantum improved geometry and show, in particular, that the central singularity is resolved, being generally replaced with a regular Minkowski-core, where the curvature tensor vanishes. Exploring cases with more general scale identifications, we further find that the space of quantum improved geometries is divided into two regions: one for geometries with a regular Minkowski-core and the other for those with a weak singularity at the center. At the boundary of the two regions, the geometry has either Minkowski-, de Sitter-, or anti-de Sitter(AdS)-core.

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arXiv2020

General Procedure of Gauge Fixings and Ghosts

We revisit the general procedure of gauge fixings and ghosts based on BRST invariance principle. It is shown that when this is applied to the higher-derivative gauge fixings, it gives the correct structure of gauge fixings and ghosts including "third ghost", previously derived at one-loop level. This procedure is solely based on the symmetry principle and is valid at full order.

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arXiv2020

Effective Action from the Functional Renormalization Group

We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the "exact" or "functional" renormalization group equation to derive the effective action $Γ_0$ by integrating the flow equation from the ultraviolet scale down to $k=0$. The resulting effective action consists of local terms and nonlocal terms with unique coefficients.

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arXiv2020

Towards the determination of the dimension of the critical surface in asymptotically safe gravity

We compute the beta functions of Higher Derivative Gravity within the Functional Renormalization Group approach, going beyond previously studied approximations. We find that the presence of a nontrivial Newtonian coupling induces, in addition to the free fixed point of the one-loop approximation, also two nontrivial fixed points, of which one has the right signs to be free from tachyons. Our results are consistent with earlier suggestions that the dimension of the critical surface for pure gravity is three.

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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.

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arXiv2018

Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames

The $f(R)$ gravity and scalar-tensor theory are known to be equivalent at the classical level. We study if this equivalence is valid at the quantum level. There are two descriptions of the scalar-tensor theory in the Jordan and Einstein frames. It is shown that these three formulations of the theories give the same determinant or effective action on shell, and thus they are equivalent at the quantum one-loop level on shell in arbitrary dimensions. We also compute the one-loop divergence in $f(R)$ gravity.

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arXiv2017

Background Scale Independence in Quantum Gravity

We study the background scale independence in single-metric approximation to the functional renormalization group equation (FRGE) for quantum gravity and show that it is possible to formulate it without using higher-derivative gauge fixing in arbitrary dimensions if we adopt the Landau gauge and suitable cutoff scheme. We discuss this problem for both the linear and exponential splits of the metric into background and fluctuations. The obtained modified Ward identity for the global rescalings of the background metric can be combined with the FRGE to give a manifestly scale-invariant solution. An explicit example of the FRGE is given for four-dimensional $f(R)$ gravity in this framework.

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arXiv2016

Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces

We derive the flow equation for the gravitational effective average action in an $f(R)$ truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to evaluate traces exactly using the optimised cutoff. This reveals in particular that all modes can be integrated out for a finite value of the cutoff due to a gap in the spectrum of the Laplacian, leading to the effective action. Studying polynomial solutions, we find poorer convergence than has been found on compact spacetimes even though at small curvature the equations only differ in the treatment of certain modes. In the vicinity of an asymptotically free fixed point, we find the universal beta function for the $R^2$ coupling and compute the corresponding effective action which involves an $R^2 \log R^2$ quantum correction.

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arXiv2016

Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization

We employ the exponential parametrization of the metric and a "physical" gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an $f(R)$ truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function $f$. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure.

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arXiv2015

Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories

We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful couplings different from linear split, though the fact that there exists nontrivial fixed point remains the same and the fixed points also remain the same.

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arXiv2015

A flow equation for f(R) gravity and some of its exact solutions

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the parameters the solution seems to be continuously deformed.

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arXiv2014

Cosmic acceleration with a negative cosmological constant in higher dimensions

We study gravitational theories with a cosmological constant and the Gauss-Bonnet curvature squared term and analyze the possibility of de Sitter expanding spacetime with a constant internal space. We find that there are two branches of the de Sitter solutions: Both the curvature of the internal space and the cosmological constant are (1) positive and (2) negative. From the stability analysis, we show that the de Sitter solution of the case (1) is unstable, while that in the case (2) is stable. Namely de Sitter solution in the present system is stable if the cosmological constant is negative. We extend our analysis to the gravitational theories with higher-order Lovelock curvature terms. Although the existence and the stability of the de Sitter solutions are very complicated and highly depend on the coupling constants, there exist stable de Sitter solutions similar to the case (2). We also find de Sitter solutions with Hubble scale much smaller than the scale of a cosmological constant, which may explain a discrepancy between an inflation energy scale and the Planck scale.

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arXiv2014

Accelerating Universes in String Theory via Field Redefinition

We study cosmological solutions in the effective heterotic string theory with $α'$-correction terms in string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as "Galileon" field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always the attractors in the present dynamical system.

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arXiv2014

Covariant Approach to the No-ghost Theorem in Massive Gravity

We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and Stückelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we find that the crucial point in the proof is that there is no higher (time) derivative for the Stückelberg `scalar' field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general backgrounds. We end the paper by demonstrating the general results explicitly in a nontrivial example where there apparently appear higher time derivatives for Stückelberg scalar field, but show that this does not introduce the ghost into the theory.

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arXiv2013

Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions

We derive the one-loop beta functions for a theory of gravity with generic action containing up to four derivatives. The calculation is done in arbitrary dimension and on an arbitrary background. The special cases of three, four, near four, five and six dimensions are discussed in some detail. We find that the theories have nontrivial UV fixed points and are asymptotically safe in all dimensions we study. We also find an indication that Weyl-invariant fixed point exists in four dimensions. The new massive gravity in three dimensions does not correspond to any fixed point.

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arXiv2013

Asymptotically AdS Charged Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions

We study charged black hole solutions in Einstein-Maxwell-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$-dimensional and assumed to be static and plane symmetric with the $(D-2)$-dimensional constant curvature space and asymptotically anti-de Sitter. By imposing the boundary conditions of the existence of the regular black hole horizon and proper behavior at infinity where the Breitenlohner-Freedman bound should be satisfied, we construct black hole solutions numerically. We give the relations among the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on. The properties of the black hole do not depend on the dimensions qualitatively, which is different from the spherically symmetric and asymptotically flat case. There is non-zero lower limit for the radius of the event horizon below which no solution exists. The temperature of the black hole becomes smaller as the horizon radius is smaller but remains non-zero when the lower limit is attained.

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