arXiv subjects

Kazunori Takenaga

Publications and source records attributed to Kazunori Takenaga.

At least 19 recordsLinked to original sources

arXiv2026

Nonanalytic Structure of Effective Potential at Finite Temperature on Compactified Space

We thoroughly investigate nonanalytic terms in the finite-temperature effective potential in one-loop approximation on a $D$-dimensional spacetime, $S_τ\times R^{D-(p+1)}\times \prod_{i=1}^p S_i^1$, using a mode recombination formula. Such nonanalytic terms cannot be expressed as positive powers of field-dependent mass squared. The formula provides a clear separation of the effective potential into a part that contains the nonanalytic terms and a part that is purely analytic, and clarifies the origin of the nonanalytic terms. We obtain all the nonanalytic terms and show that only two types of nonanalytic terms arise from the modes with zero Matsubara frequency. For a real scalar field with periodic boundary conditions, if the number of noncompacted spatial dimensions is odd (even), there are odd powers of $M$ ($\log M$ terms) but no $\log M$ terms (no odd powers of $M$). For fermions with general boundary conditions, we find that neither of the two types appears. These results clarify the nonanalytic structure of the finite-temperature effective potential on the spacetime with compactified spatial dimensions.

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arXiv2024

Mode Recombination Formula and Nonanalytic Term in Effective Potential at Finite Temperature on Compactified Space

We develop a new formula called a mode recombination formula, and we can recast the effective potential at finite temperature in one-loop approximation for fermion and scalar fields on the $D$-dimensional spacetime, $S_τ^1 \times R^{D-(p+1)}\times\prod_{i=1}^pS_i^1$ into a convenient form for discussing nonanalytic terms, which cannot be written in the form of any positive integer power of the field-dependent mass squared, in the effective potential. The formula holds irrespective of whether the field is a fermion or a scalar and of boundary conditions for spatial $S_i^1$ directions and clarifies the importance of zero modes in the Matsubara and Kaluza-Klein modes for the existence of the nonanalytic terms. The effective potential is drastically simplified further to obtain the nonanalytic terms in easier and more transparent way. In addition to reproducing previous results, we find that there exists no nonanalytic term for the fermion field with arbitrary boundary condition for the spatial $S_i^1$ direction, which is also the case for the scalar field with the antiperiodic boundary condition for the spatial direction.

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arXiv2023

Grand Gauge-Higgs Unification on $T^2/{\mathbb Z}_3$ via Diagonal Embedding Method

We study a novel six-dimensional gauge theory compactified on the $T^2/{\mathbb Z}_3$ orbifold utilizing the diagonal embedding method. The bulk gauge group is $G\times G\times G$, and the diagonal part $G^{\rm diag}$ remains manifest in the effective four-dimensional theory. Further spontaneous breaking of the gauge symmetry occurs through the dynamics of the zero modes of the extra-dimensional components of the gauge field. We apply this setup to the $SU(5)$ grand unified theory and examine the vacuum structure determined by the dynamics of the zero modes. The phenomenologically viable models are shown, in which the unified symmetry $G^{\rm diag}\cong SU(5)$ is spontaneously broken down to $SU(3)\times SU(2)\times U(1)$ at the global minima of the one-loop effective potential for the zero modes. This spontaneous breaking provides notable features such as a realization of the doublet-triplet splitting without fine tuning and a prediction of light adjoint fields.

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arXiv2022

Non-analytic Term in Effective Potential at Finite Temperature for Scalar Field on Compactified Space

We study non-analytic terms, which cannot be written in the form of any positive integer power of field-dependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the $D$-dimensional space-time, $S_τ^1\times R^{D-(p+1)}\times\prod_{i=1}^pS_i^1$. The effective potential can be recast into the integral form in the complex plane by using the integral representation for the modified Bessel function of the second kind and the analytical extension for multiple mode summations. The pole structure of the mode summations is clarified and all the non-analytic terms are obtained by the residue theorem. We find that the effective potential has a non-analytic term when the dimension of the flat Euclidean space, $D-(p+1)$ is odd. There appears only one non-analytic term for the given values of $D$ and $p$, for which the non-analytic term exists.

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arXiv2019

Dynamical generation of quark/lepton mass hierarchy in an extra dimension

We show that the observed quark/lepton mass hierarchy can be realized dynamically on an interval extra dimension with point interactions. In our model, the positions of the point interactions play a crucial role to control the quark/lepton mass hierarchy and are determined by the minimization of the Casimir energy. By use of the exact extra-dimensional coordinate-dependent vacuum expectation value of a gauge singlet scalar, we find that there is a parameter set, where the positions of the point interactions are stabilized and fixed, which can reproduce the experimental values of the quark masses precisely enough, while the charged lepton part is less relevant. We also show that possible mixings among the charged leptons will improve the situation significantly.

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arXiv2019

5d Dirac fermion on quantum graph

In this paper, we investigate a five-dimensional Dirac fermion on a quantum graph that consists of a single vertex and $N$ loops. We find that the model possesses a rich structure of boundary conditions for wavefunctions on the quantum graph and they can be classified into $(2N+1)$ distinct categories. It is then shown that there appear degenerate four-dimensional chiral massless fermions in the four-dimensional mass spectrum. We briefly discuss how our model could naturally solve the problems of the fermion generation, the fermion mass hierarchy and the origin of the $CP$-violating phase.

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arXiv2017

The Standard Model Gauge Symmetry from Higher-Rank Unified Groups in Grand Gauge-Higgs Unification Models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and $E_6$ models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.

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arXiv2017

Polyakov Loop in Non-covariant Operator Formalism

We discuss a Polyakov loop in non-covariant operator formalism which consists of only physical degrees of freedom at finite temperature. It is pointed out that although the Polyakov loop is expressed by a Euclidean time component of gauge fields in a covariant path integral formalism, there is no direct counterpart of the Polyakov loop operator in the operator formalism because the Euclidean time component of gauge fields is not a physical degree of freedom. We show that by starting with an operator which is constructed in terms of only physical operators in the non-covariant operator formalism, the vacuum expectation value of the operator calculated by trace formula can be rewritten into a familiar form of an expectation value of Polyakov loop in a covariant path integral formalism at finite temperature for the cases of axial and Coulomb gauge.

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arXiv2016

Gauge Symmetry Breaking Patterns in an SU(5) Grand Gauge-Higgs Unification

We study gauge symmetry breaking patterns of the five-dimensional $SU(5)$ grand gauge-Higgs unification compactified on an orbifold $S^1/{\mathbb Z}_2$ with the Hosotani mechanism in the framework of the diagonal embedding method. We find matter contents that lead to the $SU(3)\times SU(2)\times U(1)$ gauge symmetry on the global minimum of the effective potential and also present examples of matter content for which each regular subgroup of $SU(5)$ is realized as vacuum configuration. The finite temperature phase transitions for the models with the gauge symmetry of the standard model at zero temperature and also for supersymmetric models are studied. We show in a certain model with supersymmetry that the vacuum of the standard model selected dynamically before the inflation continues to stay there up to the present.

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arXiv2013

Is the Higgs a sign of extra dimensions?

We introduce a 4-dimensional cutoff in the scenario of gauge-Higgs unification to control the ultraviolet behavior. A one-loop effective potential for a Higgs field and the Higgs mass are obtained with the cutoff. We find an {\it interrelation} between the 4-dimensional cutoff and the scale of extra dimensions, which is concretized through the Higgs mass. Combining this interrelation and the recently discovered Higgs boson at LHC, we obtain an interesting constraint for the 4-dimensional cutoff and the extra dimensional scale.

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arXiv2011

Grand Gauge-Higgs Unification

We propose a novel way to break grand unified gauge symmetries via the Hosotani mechanism in models that can accommodate chiral fermions. Adjoint scalar fields are realized through the so-called diagonal embedding method which is often used in the heterotic string theory. We calculate the one-loop effective potential of the adjoint scalar field in a five dimensional model compactified on an S^1/Z_2 orbifold, as an illustration. It turns out that the potential is basically the same as the one in an S^1 model, and thus the results in literatures, in addition to the chiral fermions, can be realized easily.

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arXiv2011

Gauge-Higgs Unification in Lifshitz Type Gauge Theory

We discuss the gauge-Higgs unification in a framework of Lifshitz type gauge theory. We study a higher dimensional gauge theory on R^{D-1}\times S^{1} in which the normal second (first) order derivative terms for scalar (fermion) fields in the action are replaced by higher order derivative ones for the direction of the extra dimension. We provide some mathematical tools to evaluate a one-loop effective potential for the zero mode of the extra component of a higher dimensional gauge field and clarify how the higher order derivative terms affect the standard form of the effective potential. Our results show that they can make the Higgs mass heavier and change its vacuum expectation value drastically. Some extensions of our framework are briefly discussed.

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arXiv2010

5-dimensional SU(2) lattice gauge theory with Z2 orbifolding and its phase structure

In an SU(2) lattice gauge theory with a Z2 orbifolded extra dimension, the new symmetry which is called as a stick symmetry is useful in understanding the bulk transition. We discuss the relation with the Fradkin-Shenker's phase diagram as well. A remnant of the extra dimension is remained as two U(1) gauge symmetries in two 4-dimensional spaces. We also consider more general bulk gauge groups beyond SU(2).

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arXiv2009

High Temperature Symmetry Nonrestoration and Inverse Symmetry Breaking on Extra Dimensions

We study $D$-dimensional gauge theory with an extra dimension of a circle at finite temperature. We mainly focus on the expectation value of the gauge field for the direction of the extra dimension, which is the order parameter of the gauge symmetry breaking. We evaluate the effective potential in the one-loop approximation at finite temperature. We show that the vacuum configuration of the theory at finite temperature is determined by a $(D-1)$-dimensional gauge theory defined by removing the Euclidean time coordinate as well as all of the fermions from the original $D$-dimensional gauge theory on the circle. It is pointed out that gauge symmetry nonrestoration and/or inverse symmetry breaking can occur at high temperature in a class of gauge theories on circles and that phase transitions (if they occur) are, in general, expected to be first order.

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arXiv2008

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.

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arXiv2007

Large Gauge Hierarchy in Gauge-Higgs Unification

We study a five dimensional nonsupersymmetric SU(3) gauge theory compactified on $M^4\times S^1/Z_2$. The gauge hierarchy is discussed in the scenario of the gauge-Higgs unification. We present two models in which the large gauge hierarchy is realized, that is, the weak scale is naturally is obtained from an unique large scale such as a GUT and the Planck scale. We also study the Higgs mass in each model.

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arXiv2007

Large Gauge Hierarchy in Gauge-Higgs Unification

We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified on $M^4\times S^1/Z_2$ and discuss the gauge hierarchy in the scenario of the gauge-Higgs unification. Making use of calculability of the Higgs potential and a curious feature that coefficients in the potential are given by discrete values, we find two models, in which the large gauge hierarchy is realized, that is, the weak scale is naturally obtained from an unique large scale such as a grand unified theory scale or the Planck scale. The size of the Higgs mass is also discussed in each model. One of the models we find realizes both large gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass becomes heavier as the compactified scale becomes smaller.

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arXiv2006

Bulk Mass Effects in Gauge-Higgs Unification at Finite Temperature

We study the bulk mass effects on the electroweak phase transition at finite temperature in a five dimensional SU(3) gauge-Higgs unification model on an orbifold. We investigate whether the Higgs mass satisfying the experimental lower bound can be compatible with the strong first order phase transition necessary for a successful electroweak baryogenesis. Our numerical results show that the above statement can be realized by matter with bulk mass yielding a viable Higgs mass. We also find an interesting case where the heavier Higgs gives the stronger first order phase transition.

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