A falling magnetic monopole as a holographic local quench

An analytic static monopole solution is found in global AdS4, in the limit of small backreaction. This solution is mapped in Poincaré patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case, where the quench induces always a higher entropy compared to the vacuum, i.e. ∆S > 0. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to ∆S due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.

Gravitating Cho–Maison monopole

We study numerical solutions corresponding to spherically symmetric gravitating electroweak monopole and magnetically charged black holes of the Einstein–Weinberg–Salam theory. The gravitating electroweak monopole solutions are quite identical to the gravitating monopole solution in SU(2) Einstein–Yang–Mills–Higgs theory, but with distinctive characteristics. We also found solutions representing radially excited monopole, which has no counterpart in flat space. Both of these solutions exist up to a maximal gravitational coupling before they cease to exist. Lastly we also report on magnetically charged non-Abelian black holes solutions that is closely related to the regular monopole solutions, which represents counterexample to the ‘no-hair’ conjecture.

Electroweak monopoles with a non-linearly realized weak hypercharge

We present a finite-energy electroweak-monopole solution obtained by considering non-linear extensions of the hypercharge sector of the Electroweak Theory, based on logarithmic and exponential versions of electrodynamics. We find constraints for a class of non-linear extensions and also work out an estimate for the monopole mass in this scenario. We finally derive a lower bound for the energy of the monopole and discuss the simpler case of a Dirac magnetic charge.

The ’t Hooft–Polyakov monopole in the geometric theory of defects

The ’t Hooft–Polyakov monopole solution in Yang–Mills theory is given new physical interpretation in the geometric theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids.

Finite-Energy Dressed String-Inspired Dirac-Like Monopoles

On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter β (of dimensions of [mass] 2 ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed.

On finite energy monopole solutions in Weinberg–Salam model

We study the problem of existence of finite energy monopole solutions in the Weinberg–Salam model starting with the most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of field configurations with various topologies described by the monopole and Hopf charges. We introduce a unique [Formula: see text] gauge invariant definition for the electromagnetic field. It has been proved that the magnetic charge of any finite energy monopole solution must be screened at far distance. This implies nonexistence of finite energy monopole solutions with a nonzero total magnetic charge. In the case of a special axially-symmetric Dashen–Hasslacher–Neveu ansatz, we revise the structure of the sphaleron solution and show that sphaleron represents a nontrivial system of monopole and antimonopole with their centers located in one point. This is different from the known interpretation of the sphaleron as a monopole–antimonopole pair like Nambu’s “dumb-bell.” In general, the axially-symmetric magnetic field may admit a helical structure. We conjecture that such a solution exists and estimate an upper bound for its energy, [Formula: see text].

CHO DECOMPOSITION OF ONE-HALF INTEGER MONOPOLES SOLUTIONS

We performed the Cho decomposition of the SU(2) Yang–Mills–Higgs gauge potentials of the finite energy (1) one-half monopole solution and (2) the one and a half monopoles solution into Abelian and non-Abelian components. We found that the semi-infinite string singularity in the gauge potentials is a contribution from the Higgs field of the one-half monopole in both of the solutions. The non-Abelian components of the gauge potentials are able to remove the point singularity of the Abelian components of the 't Hooft–Polyakov monopole but not the string singularity of the one-half monopole which is topological in nature. Hence the total energy of a one monopole is infinite in the Maxwell electromagnetic theory but the total energy of a one-half monopole is finite. By analyzing the magnetic fields and the gauge covariant derivatives of the Higgs field, we are able to conclude that both the one-half integer monopoles solutions are indeed non-BPS even in the limit of vanishing Higgs self-coupling constant.