Related papers: Courant-Hilbert deformations of Yang-Baxter sigma …

We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…

We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations.…

We study deformation of N=2 and N=4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at…

We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…

Conformally invariant sigma models in $D=2n$ dimensions with target non-compact O(2n,1) groups are studied. It is shown that despite the non-compact nature of the O(2n,1) groups, the classical action and Hamiltonian are positive definite.…

Let $(M, \omega)$ be a compact connected K\"ahler manifold of complex dimension four and let $[\chi] \in H^{1,1}(M; \mathbb{R})$. We confirmed the conjecture by Collins--Jacob--Yau [arXiv:1508.01934] of the solvability of the deformed…

We analyse in detail the local BRST cohomology in Einstein-Yang-Mills theory using the antifield formalism. We do not restrict the Lagrangian to be the sum of the standard Hilbert and Yang-Mills Lagrangians, but allow for more general…

In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between…

We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with…

Modified $r$-matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this paper, first we introduce a cohomology theory for modified…

An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…

The recent papers arXiv:1110.0971 and arXiv:1201.5431 have provided a superfield description for vector-tensor multiplets and their Chern-Simons couplings in 4D N = 2 conformal supergravity. Here we develop a superform formulation for these…

This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the…

A topological model in three dimensions is proposed. It combines the Chern-Simons action with a BFK-model which was investigated recently by the authors of hep-th/9906146. The finiteness of the model to all orders of perturbation theory is…

We consider the problem of exact integration of the $T\bar{T}$-deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of $\det T$-deformations. When the action can be shown to only…

Given a rack Q and a ring A, one can construct a Yang-Baxter operator c_Q: V tensor V --> V tensor V on the free A-module V = AQ by setting c_Q(x tensor y) = y tensor x^y for all x,y in Q. In answer to a question initiated by D.N. Yetter…

In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in arXiv:1908.02289 for describing integrable field theories. We work out explicitly the case of the lambda deformed…

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in…

In this work we study the main properties and the one-loop renormalization of a Yang-Mills theory in which the kinetic term contains also a fourth-order differential operator; in particular, we add to the Yang-Mills Lagrangian the most…

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…