J. Bryce McLeod, Chie Bing Wang
In this paper we give a mathematical proof of the existence of the time independent and spherically symmetric solution to the 't Hooft-Polyakov model of magnetic monopole by using 2D-shooting method.
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Existence of Julia-Zee dyon and 't Hooft-Polyakov monopole with new field strength tensor
本文在Georgi-Glashow模型中引入修正阿贝尔场强张量，导出新的Julia-Zee双子方程，并运用三步迭代打靶法与不动点定理证明静态解的存在性，同时揭示总磁荷为常数、总电荷连续依赖于剖面函数。
Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of 't Hooft-Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.
In this article, we carry out the Hamiltonization in the axial gauge, of the t'Hooft-Polyakov monopole field outside the localized region, which represents the monopole's core. One feature of the treatment here, is using the Higgs vacuum condition as both strong and weak equation instead of using it in the degree of freedom reduction.
We present a systematic approach to the linearised Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral properties. We show that a quaternionic formulation allows for a compact and efficient treatment of the linearised equations in the BPS limit of vanishing Higgs self-coupling, and use it to study both scattering and bound states. We focus on the sector of vanishing generalised angular momentum and analyse it numerically, putting zero-energy bound states, Coulomb bound states and infinitely many Feshbach…
We show that based on the general solution, given by Corrigan, Olive, Fairlie and Nuyts, in the region outside the monopole's core; the equations of motion in the Higgs vacuum (i.e. outside the monopole's core) will not allow asymptotically non-singular extended non-trivial non-Dyonic (including, also, all static) solutions of the 't Hooft-Polyakov monopole. In other words, unless the monopole's magnetic charge is shielded (by some mechanism), the Dirac string is inevitable asymptotically, in the region outside the monopole's core, for all non-Dyonic solutions that are admissible by the equati…
We construct exact t Hooft-Polyakov monopole solutions in a non-Hermitian field theory with local non-Abelian SU(2) gauge symmetry and a modified antilinear CPT symmetry. The solutions are obtained in a fourfold Bogomolny-Prasad-Sommerfield scaling limit giving rise to two different types of monopole masses that saturate the lower energy bound. These two masses only coincide in the Hermitian limit and in the limit in which the symmetry breaking vacuum tends to the trivial symmetry preserving vacuum. In the two theories corresponding to the two known Dyson maps these two masses are exchanged, u…
Monopole bubbling contributions to supersymmetric 't Hooft loops in 4d $\mathcal{N}=2$ theories are computed by SQM indices. As recently argued, those indices are hard to compute due to the presence of Coulomb vacua that are not captured by standard localization techniques. We propose an algorithmic method to compute the full bubbling contributions that circumvent this issue, by considering SQM with more matter fields and isolating the bubbling terms as residues in flavor fugacities. The enlarged SQMs are read from brane configurations realizing the bubbling sector of a given 't Hooft loop. We…
Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as instantons. For this purpose, we analyze supersymmetric 't Hooft loop in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories with Lagrangians and non-positive beta functions. We show that the perturbative series of the 't Hooft loop is Borel summable along positive real axis for fixed instanton numbers and screened magnetic charges. It turns out th…
Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in $\mathcal N=4$ SYM
研究正则Nahm极边界条件下四维$\mathcal N=4$ $U(N)$超杨-米尔斯理论中非极小磁荷的半BPS边界't Hooft线，计算鼓泡修正的缺陷半指标并识别为球面DAHA元，通过Macdonald核证明与S对偶Neumann Wilson线半指标相等。
We use the SU(2) 't Hooft-Polyakov monopole configuration, and its BPS version, to test the integral equations of the Yang-Mills theory. Those integral equations involve two (complex) parameters which do not appear in the differential Yang-Mills equations, and if they are considered to be arbitrary it then implies that non-abelian gauge theories (but not abelian ones) possess an infinity of integral equations. For static monopole configurations only one of those parameters is relevant. We expand the integral Yang-Mills equation in a power series of that parameter and show that the 't Hooft-Pol…
Non-BPS Monopoles and Dyons via Resurgent Transseries
该研究通过 resurgence 转换级数构造了非BPS单极子和双极子，揭示了其在BPS极限下的行为特征。
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