arXiv subjects

Kei-Ichi Kondo

Publications and source records attributed to Kei-Ichi Kondo.

At least 55 records · Page 3Linked to original sources

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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arXiv2018

Mass-deformed Yang-Mills theory in the covariant gauge and its gauge-invariant extension through the gauge-independent BEH mechanism

In this talk we consider the mass-deformed Yang-Mills theory in the covariant gauge which is obtained by just adding a gluon mass term to the Yang-Mills theory with the covariant gauge fixing term and the associated Faddeev-Popov ghost term. First, we reconfirm that the decoupling solution in the Landau gauge Yang-Mills theory is well reproduced from the mass-deformed Yang-Mills theory by taking into account loop corrections. Second, we show that the mass-deformed Yang-Mills theory is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained as a consequence of the gauge-independent Brout-Englert-Higgs mechanism proposed recently by one of the authors. Third, we show that the reflection positivity is violated for any value of the parameters in the mass-deformed Yang-Mills theory to one-loop quantum corrections. Finally, we discuss the implications for the existence of positivity violation/restoration crossover in light of the Fradkin-Shenker continuity between Confinement-like and Higgs-like regions in a single confinement phase in the gauge-scalar model on the lattice.

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arXiv2018

Composite operator and condensate in $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group

Recently, a reformulation of the $SU(N)$ Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition has been developed in order to understand confinement from the viewpoint of the dual superconductivity. The concept of infrared Abelian dominance plays an important role in the realization of this concept and through numerical simulations on the lattice, evidence was found for example in the form of the dynamical mass generation for certain gluon degrees of freedom. A promising analytical attempt to explain the generation of such masses is through condensates of mass dimension two. In this talk, we want to focus on the reformulated $SU(N)$ Yang-Mills theory in the previously overlooked minimal option with the non-Abelian $U(N-1)$ stability group, in contrast to the famous maximal Abelian gauge, where the decomposition corresponds to the Abelian $U(1)^{N-1}$ stability group. We proceed with a thorough one-loop analysis of this novel decomposition, calculating all standard renormalization group functions at one-loop level in light of the renormalizability of this theory. We subsequently define an appropriate mixed gluon-ghost composite operator of mass dimension two as the candidate for the condensate within this theory and prove its (on-shell) BRST invariance and the multiplicative renormalizability. Finally, the existence of the condensate is discussed within the local composite operator formalism.

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arXiv2018

Gauge-independent Brout-Englert-Higgs mechanism and Yang-Mills theory with a gauge-invariant gluon mass term

For the Yang-Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout-Englert-Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang-Mills theory with an adjoint scalar field. Moreover, we show that the Yang-Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin-Shenker continuity and Osterwalder-Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout-Englert-Higgs mechanism by starting with the complementary gauge-scalar model.

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arXiv2018

Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group

Recently, some reformulations of the Yang-Mills theory inspired by the Cho-Faddeev-Niemi decomposition have been developed in order to understand confinement from the viewpoint of the dual superconductivity. In this paper we focus on the reformulated $SU(N)$ Yang-Mills theory in the minimal option with $U(N-1)$ stability group. Despite existing numerical simulations on the lattice we perform the perturbative analysis to one-loop level as a first step towards the non-perturbative analytical treatment. First, we give the Feynman rules and calculate all renormalization factors to obtain the standard renormalization group functions to one-loop level in light of the renormalizability of this theory. Then we introduce a mixed gluon ghost composite operator of mass dimension two and show the BRST invariance and the multiplicative renormalizability. Armed with these results, we argue the existence of the mixed gluon-ghost condensate by means of the so-called local composite operator formalism, which leads to various interesting implications for confinement as shown in preceding works.

hep-th↗

arXiv2018

Magnetic monopoles in pure $SU (2)$ Yang--Mills theory with a gauge-invariant mass

In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining the gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model with the radial length of the scalar field being fixed. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism which neither relies on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. According to these procedures, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ Yang-Mills theory coupled with an adjoint scalar field whose radial degree of freedom is fixed, and obtain a gauge field configuration of magnetic monopole with a minimum magnetic charge in the massive $SU(2)$ Yang-Mills theory. We compare the magnetic monopole obtained in this way in the massive Yang--Mills theory with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow model.

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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

Double-winding Wilson loop in $SU(N)$ Yang-Mills theory: A criterion for testing the confinement models

We examine how the average of double-winding Wilson loops depends on the number of color $N$ in the $SU(N)$ Yang-Mills theory. In the case where the two loops $C_1$ and $C_2$ are identical, we derive the exact operator relation which relates the double-winding Wilson loop operator in the fundamental representation to that in the higher dimensional representations depending on $N$. By taking the average of the relation, we find that the difference-of-areas law for the area law falloff recently claimed for $N=2$ is excluded for $N \geq 3$, provided that the string tension obeys the Casimir scaling for the higher representations. In the case where the two loops are distinct, we argue that the area law follows a novel law $(N - 3)A_1/(N-1)+A_2$ with $A_1$ and $A_2 (A_1<A_2)$ being the minimal areas spanned respectively by the loops $C_1$ and $C_2$, which is neither sum-of-areas ($A_1+A_2$) nor difference-of-areas ($A_2 - A_1$) law when ($N\geq3$). Indeed, this behavior can be confirmed in the two-dimensional $SU(N)$ Yang-Mills theory exactly.

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arXiv2017

Double-winding Wilson loops in the $SU(N)$ Yang-Mills theory

We consider double-winding, triple-winding and multiple-winding Wilson loops in the $SU(N)$ Yang-Mills gauge theory. We examine how the area law falloff of the vacuum expectation value of a multiple-winding Wilson loop depends on the number of color $N$. In sharp contrast to the difference-of-areas law recently found for a double-winding $SU(2)$ Wilson loop average, we show irrespective of the spacetime dimensionality that a double-winding $SU(3)$ Wilson loop follows a novel area law which is neither difference-of-areas nor sum-of-areas law for the area law falloff and that the difference-of-areas law is excluded and the sum-of-areas law is allowed for $SU(N)$ ($N \ge 4$), provided that the string tension obeys the Casimir scaling for the higher representations. Moreover, we extend these results to arbitrary multi-winding Wilson loops. Finally, we argue that the area law follows a novel law, which is neither sum-of-areas nor difference-of-areas law when $N\ge 3$. In fact, such a behavior is exactly derived in the $SU(N)$ Yang-Mills theory in the two-dimensional spacetime.

hep-th↗

arXiv2017

Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation

In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $β$ function.

hep-th↗

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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arXiv2016

Gauge-independent Higgs mechanism and the implications for quark confinement

We propose a gauge-invariant description for the Higgs mechanism by which a gauge boson acquires the mass. We do not need to assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. For concreteness, we discuss the gauge-Higgs models with $U(1)$ and $SU(2)$ gauge groups explicitly. This enables us to discuss the confinement-Higgs complementarity from a new perspective.

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arXiv2016

Gauge-invariant description of Higgs phenomenon and quark confinement

We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant Higgs phenomenon for the relevant Yang-Mills-Higgs model.

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arXiv2016

Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field

We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group $G(2)$, which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the $SU(N)$ Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of $G(2)$. The resulting new form is used to define gauge-invariant magnetic monopoles in the $G(2)$ Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than $SU(N)$ and $G(2)$.

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arXiv2016

Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

We give a gauge-independent definition of magnetic monopoles in the $SU(N)$ Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the $SU(N)$ gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.

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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.

hep-lat↗

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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