Related papers: Topological Basis Associated with B-M-W algebra: T…
We establish that the relevant geometric data for the target space description of world sheet topological defects are submanifolds - which we call bi-branes - in the product M1 x M2 of the two target spaces involved. Very much like branes,…
In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three…
The topology of the Moyal $*$-algebra may be defined in three ways: the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself; or one may…
The conjectured symmetries of M-theory famously involve (1.) brane-extended super-symmetry (the M-algebra) and (2.) exceptional duality-symmetry (the $\mathfrak{e}_{11}$-algebra); but little attention has been given to their inevitable…
We provide explicit presentations of members of a suite of R matrices arising from the (\dot{0}_m|\alpha) representations of the quantum superalgebras U_q[gl(m|1)]. Our algorithm constructs both trigonometric and quantum R matrices; all of…
Scattering of a spin-1/2 particle off a spin-0 target is formulated based on a simple three-dimensional momentum-spin basis. The azimuthal behaviour of both the potential and the T-matrix elements leads to a set of integral equations for…
It was proved by Montaner and Zelmanov that up to classical twisting Lie bialgebra structures on $\mathfrak{g}[u]$ fall into four classes. Here $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra. It turns out that classical…
A new construction method of $R$-matrix is given. Let $A$ be a C$^{*}$-bialgebra with a comultiplication $\Delta$. For two states $\omega$ and $\psi$ of $A$ which satisfy certain conditions, we construct a unitary $R$-matrix…
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…
The spin-charge-orbital complex structures of manganites are studied using topological concepts. The key quantity is the "winding number" w associated with the Berry-phase connection of an e_g electron parallel-transported through…
We explicitly determine all Rota-Baxter operators (of weight zero) on $sl(2,C)$ under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmetric solutions of the classical Yang-Baxter equation in…
We investigate the W-algebra resulting from Drinfel'd-Sokolov reduction of a $B_2$ WZW model with respect to the grading induced by a short root. The quantum algebra, which is generated by three fields of spin-2 and a field of spin-1, is…
These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to…
In this paper I construct lattice models with an underlying $U_q osp(2,2)$ superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These {\it trigonometric} $R$-matrices depend on {\it three} continuous parameters,…
We define an operad in Top, called $\text{FM}_2^W$. The spaces in $\text{FM}_2^W$ come with CW decompositions, such that the operad compositions are cellular. In fact, each space in $\text{FM}_2^W$ is the realization of a simplicial set. We…
An explicit quantization is given of certain skew-symmetric solutions of the classical Yang-Baxter, yielding a family of $R$-matrices which generalize to higher dimensions the Jordanian $R$-matrices. Three different approaches to their…
Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for…
It is suggested that topological membranes play a fundamental role in the recently proposed topological M-theory. We formulate a topological theory of membranes wrapping associative three-cycles in a seven-dimensional target space with G_2…
A new method for solving the Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the power lambda^6. Using this method the R-matrix for integrable spin ladder is calculated.
The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible…