Syncyclons or Solitonic Signals from Extra Dimensions

TL;DR

This paper explores topological solitons in theories with extra compact dimensions, revealing their properties, quantum numbers, and potential implications for particle physics, such as baryon and lepton number conservation.

Contribution

It introduces and analyzes co-winding solitons in higher-dimensional Yang-Mills theories, highlighting their topological stability and quantum properties.

Findings

Existence of stable solitons with non-trivial winding in extra dimensions

Quantum effects can alter classical quantum numbers of solitons

Solitons carry baryon/lepton number and have mass proportional to 1/(g^2 R)

Abstract

In theories where spacetime is a direct product of Minkowski space ($M^4$) and a d dimensional compact space ($K^d$), there can exist topological solitons that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the compact dimensions. A paradigmatic non-gravitational example of such ``co-winding" solitons is furnished by Yang-Mills theory defined on $M^4 X S^1$. Pointlike, stringlike and sheetlike solitons can be identified by transcribing and generalizing the proceedure used to construct the periodic instanton (caloron) solutions. Asymptotically the classical pointlike objects have non-Abelian magnetic dipole fields together with a non-Abelian scalar potential while the ``color" electric charge is zero. However quantization of collective coordinates associated with zeromodes and coupling to fermions can radically change these quantum numbers due to fermion number fractionalization and its non-Abelian generalization. Interpreting the YM group as color (or the Electroweak SU(2) group) and assuming that an extra circular dimension exists thus implies the existence of topologically stable solitonic objects which carry baryon(lepton) number and a mass O($1/g^2R$), where R is the radius of the compact dimension.