’t Hooft-Polyakov monopoles in latticeSU(N)+adjoint Higgstheory

Abstract

We investigate twisted C-periodic boundary conditions in SU(N ) gauge field theory with an adjoint Higgs field. We show that with a suitable twist for even N one can impose a non-zero magnetic charge relative to residual U(1) gauge groups in the broken phase, thereby creating a 't Hooft-Polyakov magnetic monopole. This makes it possible to use lattice Monte-Carlo simulations to study the properties of these monopoles in the quantum theory.

Properties of Ga2O3‐based (Inx Ga1–x)2O3 alloy thin films grown by molecular beam epitaxy

“…While, at In compositions of 43 % or higher, peaks related to the cubic structure of (In x Ga 1x ) 2 O 3 were apparent, indicating the phase separation. Consequently, it was concluded that the solubility limit was between 35% and 43%, and this value of approximately 40% is similar to those in other reports of powder synthesis [12][13][14][15]. Figure 4 shows the transmission spectra of these films.…”

“…However, β-Ga 2 O 3 and In 2 O 3 belong to different crystal systems, that is, a monoclinic system [10] and a cubic system [11], respectively, and this leads to the phase separation. According to the reports on (In x Ga 1-x ) 2 O 3 powder synthesis, where x represents the In composition, the solubility limit of In 2 O 3 into Ga 2 O 3 without phase separation was found to be about 40% [12][13][14][15]. In contrast, there have been few attempts to grow (In x Ga 1-x ) 2 O 3 thin films [16], and no indication was given on the solubility limit.…”

Lattice Landau Gauge and Algebraic Geometry

“…Though the algorithm works well for the one-dimensional lattice, for the 3 × 3 lattice, it is beyond the capabilities of a standard desktop machine. However, the method can be useful in finding a parametrization of the SU(N) matrices [38] and hence can then be used, for example, to extend the method of restricting a path integral of the SU(N) Georgi-Glashow model to the 't Hooft-Polyakov sectors by using the twisted C-periodic boundary conditions [4] for odd N and to precisely define the modified lattice Landau gauge for the SU(3) case.…”

Nonperturbative study of the ’t Hooft-Polyakov monopole form factors

“…We can derive link variables u corresponding to this smaller gauge group [20,21] u ¼ Å þ ðxÞU ðxÞÅ þ ðx þÞ;…”