| 1. |
- Bundzik, Daniel, et al.
(författare)
-
The general Leigh-Strassler deformation and integrability
- 2006
-
Ingår i: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. ; :1
-
Tidskriftsartikel (refereegranskat)abstract
- The success of the identification of the planar dilatation operator of N = 4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.
|
|
| 2. |
|
|
| 3. |
- Månsson, Teresia, 1974-
(författare)
-
Is there a tower of charges to be discovered?
- 2007
-
Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 41, s. 194014-
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate higher-loop integrability for a q-deformation of the -sector of SYM theory. First we construct a generalization of the long-range spin chain, which for the lowest orders describes the non-deformed dilatation operator. This generalized model is built up from Temperley–Lieb algebra generators and describes the deformed theory to at least two loops. When constructing the model we have demanded the existence of one commuting charge, which puts strong constraints on the parameters to three-loop orders. We also write the five first charges for this model at two-loops order. Our main goal is to obtain an explicit expression for an infinite number of commuting charges, all commuting with the dilatation operator. This would imply integrability. As a step towards this goal we present in this paper an expression for a generic local charge of the one-loop dilatation operator, which happens to be a generator of the Temperley–Lieb algebra.
|
|
| 4. |
- Månsson, Teresia, 1974-
(författare)
-
The Liegh-Strassler deformation and the quest for integrability
- 2007
-
Ingår i: Journal of High Energy Physics (JHEP). - : Institute of Physics Publishing (IOPP). - 1126-6708 .- 1029-8479.
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the one-loop dilatation operator of the full scalar field sector of Leigh-Strassler deformed =4 SYM theory. In particular we map it onto a spin chain and find the parameter values for which the Reshetikhin integrability criteria are fulfilled. Some years ago Roiban found an integrable subsector, consisting of two holomorphic scalar fields, corresponding to the XXZ model. He was pondering about the existence of a subsector which would form generalisation of that model to an integrable q(3) model. Later Berenstein and Cherkis added one more holomorphic field and showed that the subsector obtained this way cannot be integrable except for the case when q = eiβ, β. In this work we show if we add an anti-holomorphic field to the two holomorphic ones, we get indeed an integrable q(3) subsector. We find it plausible that a direct generalisation to a q(2|3) one-loop sector will exist, and possibly beyond one-loop.
|
|
