Related papers: Killing spinors from classical r-matrices
It is demonstrated how chains of twists for classical Lie algebras induce the new twist deformations (the deformed Yangians) that quantize the generalized rational solutions of the classical Yang-Baxter equation. For the case of Y(g) with…
Yang--Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang--Baxter equation. For a set $X=\Omega\times V$, where $V$ is a vector space and $\Omega$ is regarded as a space of parameters, a linear parametric YB map is a YB…
Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in…
We investigate how the marginal deformations of N=4 supersymmetric Yang-Mills theory (analysed in particular by Leigh and Strassler) arise within B-model topological string theory on supertwistor space CP(3|4). This is achieved by turning…
The Yang-Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article…
We obtain the effective action for the bosonic string with arbitrary Yang-Mills fields, up to the \alpha' order, in general dimensions. The form of the action is determined by the requirement that the action admit well-defined Killing…
We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extended in the presence of a background gauge connection, allows to fix in a unique way the dependence of the vertex functional on the background, once the 1-PI amplitudes…
Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in…
It is known that the supermultiplet of beta-deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a…
We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the…
Planar N=4 super Yang-Mills appears to be integrable. While this allows to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by…
In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super Yang-Mills theory and discuss a…
It has recently been demonstrated that the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map. Thus, given any solution with an isometry group, there exists a deformed solution based on an…
Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is…
We study Yang-Baxter deformations of the Nappi-Witten model with a prescription invented by Delduc, Magro and Vicedo. The deformations are specified by skew-symmetric classical $r$-matrices satisfying (modified) classical Yang-Baxter…
The Yang-Baxter $\sigma$-model is an integrable deformation of the principal chiral model on a Lie group $G$. The deformation breaks the $G \times G$ symmetry to $U(1)^{\textrm{rank}(G)} \times G$. It is known that there exist non-local…
We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin. One class includes the $T\bar T$-deformation of 1+1 dimensional integrable…
We perform the dynamical change of coordinates to derive a generalization of the trace relation and apply it to the non-linear Schr\"odinger model. After that, we work out the dimensional reduction of the bilinear $T\bar T$ operator and…
We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbour interactions. We find a total of four independent solutions. Two are related to the usual…