arXiv subjects

Seikou Kato

Publications and source records attributed to Seikou Kato.

At least 19 recordsLinked to original sources

arXiv2024

Gauge-independent transition separating confinement and Higgs phases in lattice SU(2) gauge theory with a scalar field in the fundamental representation

According to the preceding studies, the lattice SU(2) gauge-scalar model with a single scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase where confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamic phase transitions, which is a well-known consequence of the Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, we show that we can define new types of gauge-invariant operators by combining the original fundamental scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. By performing the numerical simulations on the lattice without any gauge fixing, we reproduce the conventional thermodynamic transition line in the weak gauge coupling, and moreover we find a new transition line detected by the new gauge-invariant operators which separates the confinement-Higgs phase into two parts, confinement phase and the Higgs phase, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we discuss a physical interpretation for the new transition from the viewpoint of the realization of a global symmetry.

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arXiv2023

New gauge-independent transition separating confinement-Higgs phase in the lattice gauge-fundamental scalar model

The lattice gauge-scalar model with the scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase which is well-known as the Fradkin-Shenker-Osterwalder-Seiler analytic continuity theorem: Confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamics phase transitions between them. In this talk, however, we show that we can define new type of operators which enable to separate completely the confinement phase and the Higgs phase. In fact, they are constructed in the gauge-invariant procedure by combining the original scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. We perform the numerical simulations for the model with SU(2) gauge group without any gauge fixing and find a new transition line which agrees with the conventional thermodynamic transition line in the weak gauge coupling and divides the confinement-Higgs phase into two separate phases, confinement and the Higgs, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we give a physical interpretation for the new transition from the viewpoint of the spontaneous breaking of a global symmetry. This talk is based on the preprint [1].

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arXiv2021

Magnetic monopole dominance for the Wilson loops in higher representations

The dual superconductor picture is one of the most promising scenarios for quark confinement. To investigate this picture in a gauge-invariant manner, we have proposed a new formulation of Yang-Mills theory, named the decomposition method, on the lattice. The so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. It has been known by preceding works that the restricted-field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is obtained by adopting the Abelian projection or the field decomposition naively in the same way as done in the fundamental representation. Recently, through the non-Abelian Stokes theorem (NAST) for the Wilson loop operator, we have proposed suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. We have demonstrated the numerical evidence for the restricted-field dominance in the string tension. In this talk, we focus on the magnetic monopole. According to this picture, magnetic monopoles causing the dual superconductivity are the dominant degrees of freedom responsible for confinement. With the help of the NAST, we define the magnetic monopole and the string tension extracted from the magnetic-monopole part of the Wilson loop in a gauge-invariant manner. We will further perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators and examine the magnetic monopole dominance in the string tension, which means that the string tension extracted from the magnetic-monopole part of the Wilson loop reproduces the proper string tension obtained from the original Wilson loop.

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arXiv2020

Double-winding Wilson loops in SU(N) lattice Yang-Mills gauge theory

We study double-winding Wilson loops in $SU(N)$ lattice Yang-Mills gauge theory by using both strong coupling expansions and numerical simulations. First, we examine how the area law falloff of a ``coplanar'' double-winding Wilson loop average depends on the number of color $N$. Indeed, we find that a coplanar double-winding Wilson loop average obeys a novel ``max-of-areas law'' for $N=3$ and the sum-of-areas law for $N\geq 4$, although we reconfirm the difference-of-areas law for $N=2$. Second, we examine a ``shifted'' double-winding Wilson loop, where the two constituent loops are displaced from one another in a transverse direction. We evaluate its average by changing the distance of a transverse direction and we find that the long distance behavior does not depend on the number of color $N$, while the short distance behavior depends strongly on $N$.

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arXiv2020

Type of dual superconductivity for the $SU(2)$ Yang--Mills theory

We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ gauge-scalar model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau parameter to reconfirm the type I dual superconductivity for quark confinement which was claimed by preceding works based on a fitting using the Clem ansatz. Moreover, we calculate the Maxwell stress tensor to obtain the distribution of the force around the flux tube. This result suggests that the attractive force acts among chromoelectric flux tubes, in agreement with the type I dual superconductivity.

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arXiv2019

Confinement/deconfinement phase transition and dual Meissner effect in SU(3) Yang-Mills theory

We investigate the confinement-deconfinement phase transition at finite temperature of the SU(3) Yang-Mills(YM) theory on the lattice from a viewpoint of the dual superconductor picture based on the novel reformulation of the YM theory. In particular, we compare the conventional Abelian dual superconductor picture with the non-Abelian dual superconductor picture proposed in our previous works as the mechanism of quark confinement in the SU(3) YM theory. For the SU(3) YM theory, the reformulation allows two possible options called maximal and minimal. The maximal option corresponds to the manifestly gauge-invariant extension of the Abelian projection scheme, while the minimal option is really new to give the non-Abelian dual superconductor picture. Keeping these differences in mind, we present the numerical evidences that the confinement/deconfinement phase transition is caused by appearance/disappearance of the dual Meissner effects. First, we measure the Polyakov loop average at various temperatures to determine the critical temperature separating the low-temperature confined phase and the high-temperature deconfined phase. Second, we measure the static quark-antiquark potential. Third, we measure the chromoelectric and chromomagnetic flux created by a pair of quark and antiquark at temperatures below and above the critical temperature. We observe no more squeezing of the chromoelectric flux tube above the critical temperature. Finally, we measure the associated magnetic--monopole current induced around the chromo-flux tube and observe that the confinement/deconfinement phase transition is associated with the appearance/disappearance of the induced magnetic--monopole current, respectively. We confirm that these results are also obtained by the restricted field alone in both options, indicating the restricted field dominance in quark confinement at finite temperature.

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arXiv2019

Confinement/deconfinement phase transition in SU(3) Yang-Mills theory and non-Abelian dual Meissner effect

The dual superconductivity is a promising mechanism of quark confinement. In the preceding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we focus on the the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. By using our new formulation of lattice Yang-Mills theory and numerical simulations on the lattice, we extract the dominant mode for confinement by decomposing the Yang-Mills field, and we investigate the Polyakov loop average, static quark potential, chromoelectric flux, and induced monopole current for both Yang-Mills field and decomposed restricted field in both confinement and deconfinement phase at finite temperature. We further discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

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arXiv2019

Type of dual superconductivity for $SU(2)$ and $SU(3)$ Yang--Mills theories

We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ Abelian--Higgs model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ and $SU(3)$ Yang--Mills theories on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau parameter to reconfirm the type I dual superconductivity for quark confinement, which was claimed by preceding works based on an approximate method based on the Clem ansatz. Moreover, we calculate the Maxwell stress tensor for the fitted model to obtain the distribution of the force around the flux tube. This suggests that the attractive force acts on the surface perpendicular to the chromoelectric flux tube, in agreement with the type I dual superconductivity.

hep-lat↗

arXiv2019

How to extract the dominant part of the Wilson loop average in higher representations

In previous works, we have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. This framework improves the Abelian projection in the gauge-independent manner. For quarks in the fundamental representation, we have demonstrated some numerical evidences for the restricted field dominance in the string tension, which means that the string tension extracted from the restricted part of the Wilson loop reproduces the string tension extracted from the original Wilson loop. However, it is known that the restricted field dominance is not observed for the Wilson loop in higher representations if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this paper, therefore, we focus on confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable gauge-invariant operators constructed from the restricted field to reproduce the correct behavior of the original Wilson loop averages for higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the behavior of the original Wilson loop average, namely, the linear part of the static potential with the correct value of the string tension, which overcomes the problem that occurs in naively applying Abelian-projection to the Wilson loop operator for higher representations.

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arXiv2018

Confinement of quarks in higher representations in view of dual superconductivity

Dual superconductor picture is one of the most promising scenarios for quark confinement. We have proposed a new formulation of Yang-Mills theory on the lattice so that the so-called restricted field obtained from the gauge-covariant decomposition plays the dominant role in quark confinement. This framework improves the Abelian projection in the gauge-independent manner. For quarks in the fundamental representation, we have demonstrated some numerical evidences for the dual superconductivity. However, it is known that the expected behavior of the Wilson loop in higher representations cannot be reproduced if the restricted part of the Wilson loop is extracted by adopting the Abelian projection or the field decomposition naively in the same way as in the fundamental representation. In this talk, therefore, we focus on confinement of quarks in higher representations. By virtue of the non-Abelian Stokes theorem for the Wilson loop operator, we propose suitable operators constructed from the restricted field only in the fundamental representation to reproduce the correct behavior of the original Wilson loop in higher representations. Moreover, we perform lattice simulations to measure the static potential for quarks in higher representations using the proposed operators. We find that the proposed operators well reproduce the expected behavior of the original Wilson loop average, which overcomes the problem that occurs in naively applying Abelian-projection to the Wilson loop operator for higher representations.

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arXiv2018

Correct way to extract dominant part of the Wilson loop in higher representations

The Abelian dominance for the string tension was shown for the fundamental sources in MA gauge in the lattice simulations. For higher representations, however, it is also known that the naive "Abelian" Wilson loop, which is defined by using the diagonal part of the gauge field, does not reproduce the correct behavior. To solve this problem, for an arbitrary representation of an arbitrary compact gauge group, we propose to redefine the "Abelian" Wilson loop. By using this redefined operator, we demonstrate the "Abelian" dominance for sources in the adjoint representation and the sextet representation of $SU(3)$ gauge group in lattice simulations.

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arXiv2017

Lattice study of area law for double-winding Wilson loops

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.

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arXiv2017

Quark confinement to be caused by Abelian or non-Abelian dual superconductivity in the SU(3) Yang-Mills theory

The dual superconductivity is a promising mechanism for quark confinement. We have presented a new formulation of the Yang-Mills theory on the lattice that enables us to change the original non-Abelian gauge field into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge independent way. We have pointed out that the SU(3) Yang-Mills theory has another reformulation using new field variables (minimal option), in addition to the way adopted by Cho, Faddeev and Niemi (maximal option). In the past lattice conferences, we have shown the numerical evidences that support the non-Abelian dual superconductivity using the minimal option for the SU(3) Yang-Mills theory. This result should be compared with Abelian dual superconductivity obtained in the maximal option which is a gauge invariant extension of the conventional Abelian projection method in the maximal Abelian gauge. In this talk, we focus on discriminating between two reformulations, i.e., maximal and minimal options of the $SU(3)$ Yang-Mills theory from the viewpoint of dual superconductivity for quark confinement. We investigate the confinement/deconfinement phase transitions at finite temperature in both options, which are compared with the original Yang-Mills theory. For this purpose, we measure the distribution of Polyakov-loops and the Polyakov-loop average, the correlation function of the Polyakov loops and the distribution of the chromoelectric flux connecting a quark and antiquark in both confinement and deconfinement phases.

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arXiv2015

Abelian monopole or non-Abelian monopole responsible for quark confinement

We have pointed out that the $SU(3)$ Yang-Mills theory has a new way of reformulation using new field variables (minimal option), in addition to the conventional option adopted by Cho, Faddeev and Niemi (maximal option). The reformulation enables us to change the original non-Abelian gauge field into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. In the minimal option, especially, the restricted field is non-Abelian $U(2)$ and involves the non-Abelian magnetic monopole. In the preceding lattice conferences, we have accumulated the numerical evidences for the non-Abelian magnetic-monopole dominance in addition to the restricted non-Abelian field dominance for quark confinement supporting the non-Abelian dual superconductivity using the minimal option for the SU(3) Yang-Mills theory. This should be compared with the maximal option which is a gauge invarient version of the Abelian projection in the maximal Abelian gauge: the restricted field is Abelian $U(1) \times U(1)$ and involves only the Abelian magnetic monopole, just like the Abelian projection. In this talk, we focus on discriminating between two reformulations, i.e., maximal and minimal options of $SU(3)$ Yang-Mills theory for quark confinement from the viewpoint of dual superconductivity. For this purpose, we measure the distribution of the chromoelectric flux connecting a quark and an antiquark and the induced magnetic-monopole current around the flux tube.

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arXiv2015

Confinement/deconfinement phase transition in SU(3) Yang-Mills theory in view of dual superconductivity

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

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arXiv2015

Magnetic monopole versus vortex as gauge-invariant topological objects for quark confinement

First, we give a gauge-independent definition of chromomagnetic monopoles in $SU(N)$ Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of $U(N)$ gauge-Higgs model, which is to be compared with numerical simulations of the $SU(N)$ Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

hep-th↗

arXiv2015

Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the $SU(N)$ Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the $SU(N)$ Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.

hep-th↗

arXiv2015

Magnetic monopole and confinement/deconfinement phase transition in SU(3) Yang-Mills theory

We have proposed the non-Abelian dual superconductivity in SU(3) Yang-Mills theory for the mechanism of quark confinement,and we presented the numerical evidences in preceding lattice conferences by using the proposed gauge link decomposition to extract magnetic monopole in the gauge invariant way. In this talk, we focus on the dual Meissner effects in view of the magnetic monopole in SU(3) Yang-Mills theory. We measure the chromoelectric and chromomagnetic flux due to a pair of quark and antiquark source at finite temperature. Then, we measure the correlation function of Polyakov loops and Polyakov loop average at various temperatures, and investigate chromomagnetic monopole current induced by chromo-magnetic flux in both confinement and deconfinement phase. We will discuss the role of the chromoelectric monopole in confinement/deconfinement phase transition.

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