Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians

TL;DR

This paper employs a spacetime dependent Lagrangian approach to derive classical solutions in Yang-Mills theory, estimate the Higgs vacuum expectation value, and analyze dyon charge quantization, connecting boundary non-commutativity with D-brane actions.

Contribution

It introduces a novel application of spacetime dependent Lagrangians to obtain classical solutions, estimate the Higgs vacuum expectation value, and extend dyon charge quantization results to boundary non-commutative geometries.

Findings

Derived a classical solution for Yang-Mills theory.

Estimated the Higgs field vacuum expectation value as φ_a=A/e.

Extended dyon charge quantization to non-commuting boundary coordinates.

Abstract

The spacetime dependent lagrangian formalism of references [1-2] is used to obtain is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field,{\it viz.} $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge).The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct $D$-brane actions. The formalism is also used to obtain the Deser-Gomberoff-Henneaux-Teitelboim results [10] for dyon charge quantisation in abelian $p$-form theories in dimensions $D=2(p+1)$ for both even and odd $p$. PACS: 11.15.-q,11.27.+d,11.10.Ef