Hooft Tensor Research Articles

Non-Abelian monopoles as the origin of dark matter

We suggest that dark matter may be partially constituted by a dilute ’t Hooft–Polyakov monopoles gas. We reach this conclusion by using the Georgi–Glashow model coupled to a dual kinetic mixing term [Formula: see text] where [Formula: see text] is the electromagnetic field and [Formula: see text] the ’t Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi–Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.

Monopoles, Abelian projection, and gauge invariance

A direct connection is proved between the Non-Abelian Bianchi Identities(NABI), and the abelian Bianchi identities for the 't Hooft tensor. As a consequence the existence of a non-zero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows to show that not all abelian projections can be used to expose monopoles in lattice configurations: each field configuration with non-zero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-abelian gauge is a legitimate choice. It is also proved, starting from the NABI, that monopole condensation is a physical gauge invariant phenomenon, independent of the choice of the abelian projection.

't Hooft Tensor for generic Gauge Groups

We study monopoles in gauge theories with generic gauge group. Magnetic charges are in one-to-one correspondence with the second homotopy classes at spatial infinity (Π 2 ), which are therefore identified by the 't Hooft tensor. We determine the 't Hooft tensor in the general case. These issues are relevant to the understanding of Color Confinement.

Homotopy, monopoles and 't Hooft tensor in QCD with generic gauge group

We study monopoles and corresponding 't Hooft tensor in QCD with a generic compact gauge group. This issue is relevant to the understanding of color confinement in terms of dual symmetry.

MAGNETIC BRANES FROM GENERALIZED 't HOOFT TENSOR

't Hooft–Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, the so-called 't Hooft tensor in 3D space. Based on the Chern kernel method, we propose the arbitrary rank 't Hooft tensors, which universally determine the quantized low energy boundaries of generalized Georgi–Glashow models under asymptotic conditions. Furthermore, the dual magnetic branes theory is built up in terms of ϕ-mapping theory.

Regular Magnetic Monopole from Generalized 't Hooft Tensor

It is well known that 't Hooft–Polykov magnetic monopole regularlyrealizes the Dirac magnetic monopole in terms of a two-rank tensor, i.e.the so-called 't Hooft tensor in three-dimensional space, which has beengeneralized to all even rank ones. We propose an arbitrary odd rank 'tHooft tensor, which universally determines the quantized low-energyboundaries of the even dimensional Georgi–Glashow models underasymptotic conditions. Furthermore, the dual magnetic monopole theory isbuilt up in terms of the ϕ-mapping theory.

’t Hooft tensors as Kalb-Ramond fields of generalized monopoles in all odd dimensions:d=3andd=5

Rank $d\ensuremath{-}1$ antisymmetric tensor fields in d Euclidean dimensions, known as Kalb-Ramond fields, can describe monopole-like solutions. In $d=3$ dimensions this Kalb-Ramond monopole is the (singular) Dirac monopole, which in turn can be described by the (regular) 't Hooft-Polyakov monopole, via the 't Hooft tensor construction. This construction is extended to arbitrary odd dimensions by performing the $d=5$ case explicitly, exploiting the (regular) ``monopoles'' of generalized Georgi-Glashow models and identifying their 't Hooft tensors as the Kalb-Ramond fields. The relevant ``magnetic charges'' are expressed as topological invariants.

Non-Abelian Stokes Theorem for Wilson Loops Associated with General Gauge Groups

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the 't Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the case of the fundamental representation of the group SU(N) is pointed out.

N-monopole soliton-type solutions of the self-duality equations for an SU (2) gauge theory in Minkowski space-time

A technique is introduced allowing one to represent the Wu-Yang ansatz, the 't Hooft tensor, and spherical-symmetric functions in a covariant form (for an arbitrary frame). Monopole solutions (including N-soliton-type solutions) of the self-duality equations in Minkowski space-time are constructed in covariant form.