Non-Abelian wormholes threaded by a Yang-Mills-Higgs field in the BPS limit

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

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Analytic non-Abelian gravitating solitons in the Einstein–Yang–Mills–Higgs theory and transitions between them

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09197-3 ◽

2021 ◽

Vol 81 (5) ◽

Author(s):

Fabrizio Canfora ◽

Seung Hun Oh

Keyword(s):

Energy Levels ◽

Higgs Field ◽

Scalar Fields ◽

Family Type ◽

Type I ◽

Type Ii ◽

Yang Mills ◽

Completely Regular ◽

The Difference ◽

Abelian Fields

AbstractTwo analytic examples of globally regular non-Abelian gravitating solitons in the Einstein–Yang–Mills–Higgs theory in (3 + 1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang–Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $$X_{0} = 1/2$$ X 0 = 1 / 2 (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $$X_{0} = 1/2$$ X 0 = 1 / 2 is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein–Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D’Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifests itself in a difference between the degeneracies of the corresponding energy levels.

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JACOBI ELLIPTIC MONOPOLE–ANTIMONOPOLE PAIR SOLUTIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x12501485 ◽

2012 ◽

Vol 27 (26) ◽

pp. 1250148 ◽

Cited By ~ 5

Author(s):

ROSY TEH ◽

PEI-YEN TAN ◽

KHAI-MING WONG

Keyword(s):

Total Energy ◽

Equations Of Motion ◽

Higgs Field ◽

Elliptic Functions ◽

Finite Energy ◽

Generalized Solutions ◽

Winding Number ◽

Yang Mills ◽

Total Energies ◽

Map Solution

We present new classical generalized Jacobi elliptic one monopole–antimonopole pair (MAP) solutions of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with θ-winding number m = 1 and ϕ-winding number n = 1, 2, 3,…,6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behavior of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing (λ = 0) and nonvanishing (λ = 1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the 1-MAP solution with winding number m = 1. However these total energies are significantly lower than the total energy of the 1-MAP solution with winding number m = 2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang–Mills–Higgs field theory.

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Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781950049x ◽

2019 ◽

Vol 16 (03) ◽

pp. 1950049

Author(s):

Marcella Palese ◽

Ekkehart Winterroth

Keyword(s):

Symmetry Breaking ◽

Spontaneous Symmetry Breaking ◽

Higgs Field ◽

Field Theories ◽

Conserved Quantities ◽

Principal Bundles ◽

Yang Mills ◽

Covariant Gauge ◽

Higgs Fields ◽

Natural Bundle

We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang–Mills type Lagrangian field theories through the requirement of the existence of canonical covariant gauge-natural conserved quantities. As an illustrative example, we consider the ‘gluon Lagrangian’, i.e. a Yang–Mills Lagrangian on the [Formula: see text]-order gauge-natural bundle of [Formula: see text]-principal connections, and canonically define a ‘gluon’ classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.

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YANG–MILLS FIELD AS A SUBSET OF COVARIANT DERIVATIVE — A UNIFIED YANG–MILLS FIELD AND HIGGS FIELD

Proceedings of the Conference in Honour of the 90th Birthday of Freeman Dyson ◽

10.1142/9789814590112_0032 ◽

2014 ◽

Author(s):

WOON SIONG GAN

Keyword(s):

Covariant Derivative ◽

Higgs Field ◽

Yang Mills ◽

Mills Field

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VORTEX SOLUTION IN (2+1)-DIMENSIONAL PURE YANG–MILLS THEORY AT HIGH TEMPERATURES

Modern Physics Letters A ◽

10.1142/s0217732399001978 ◽

1999 ◽

Vol 14 (27) ◽

pp. 1909-1916 ◽

Cited By ~ 5

Author(s):

DMITRI DIAKONOV

Keyword(s):

High Temperatures ◽

Higgs Field ◽

Higgs Potential ◽

Yang Mills ◽

Vortex Solution ◽

The One ◽

Mills Field ◽

Stable Vortex

At high temperatures the A0 component of the Yang–Mills field plays the role of the Higgs field, and the one-loop potential V(A0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov–Nielsen–Olesen type, and discuss its properties and possible implications.

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GENERALIZED JACOBI ELLIPTIC ONE-MONOPOLE: TYPE A

International Journal of Modern Physics A ◽

10.1142/s0217751x10051062 ◽

2010 ◽

Vol 25 (31) ◽

pp. 5731-5746 ◽

Cited By ~ 9

Author(s):

ROSY TEH ◽

KHAI-MING WONG ◽

KOK-GENG LIM

Keyword(s):

Equations Of Motion ◽

Higgs Field ◽

Elliptic Functions ◽

Finite Energy ◽

Generalized Solution ◽

Adjoint Representation ◽

Winding Number ◽

Axially Symmetric ◽

Yang Mills ◽

Monopole Solution

We present a new classical generalized one-monopole solution of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. We show that this generalized solution with θ-winding number m = 1 and ϕ-winding number n = 1 is an axially symmetric Jacobi elliptic generalization of the 't Hooft–Polyakov one-monopole. We construct this axially symmetric one-monopole solution by generalizing the large distance asymptotic solution of the 't Hooft–Polyakov one-monopole to the Jacobi elliptic functions and solving the second-order equations of motion numerically when the Higgs potential is vanishing and nonvanishing. These solutions are regular non-BPS finite energy solutions.

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