Affine Toda Solitons and Vertex Operators
| dc.creator | Olive, D. I. | |
| dc.creator | Turok, N. | |
| dc.creator | Underwood, J. W. R. | |
| dc.date | 1993-05-28 | |
| dc.date.accessioned | 2026-07-07T10:58:32Z | |
| dc.date.available | 2026-07-07T10:58:32Z | |
| dc.description | Affine Toda theories with imaginary couplings associate with any simple Lie algebra ${\bf g}$ generalisations of Sine Gordon theory which are likewise integrable and possess soliton solutions. The solitons are \lq\lq created" by exponentials of quantities $\hat F^i(z)$ which lie in the untwisted affine Kac-Moody algebra ${\bf\hat g}$ and ad-diagonalise the principal Heisenberg subalgebra. When ${\bf g}$ is simply-laced and highest weight irreducible representations at level one are considered, $\hat F^i(z)$ can be expressed as a vertex operator whose square vanishes. This nilpotency property is extended to all highest weight representations of all affine untwisted Kac-Moody algebras in the sense that the highest non vanishing power becomes proportional to the level. As a consequence, the exponential series mentioned terminates and the soliton solutions have a relatively simple algebraic expression whose properties can be studied in a general way. This means that various physical properties of the soliton solutions can be directly related to the algebraic structure. For example, a classical version of Dorey's fusing rule follows from the operator product expansion of two $\hat F$'s, at least when ${\bf g}$ is simply laced. This adds to the list of resemblances of the solitons with respect to the particles which are the quantum excitations of the fields. | |
| dc.description | Imperial/TP/92-93/29 SWAT/92-93/5 PU-PH-93/1392, requires newmac | |
| dc.identifier | https://arxiv.org/abs/hep-th/9305160 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9305160 | |
| dc.identifier | Nucl.Phys.B409:509-546,1993 | |
| dc.identifier | doi:10.1016/0550-3213(93)90541-V | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/187133 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Affine Toda Solitons and Vertex Operators | |
| dc.type | text |