相关论文: On the FRTS approach to quantized current algebras

We summarise some of our recent works on $L_\infty$-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of $L_\infty$-algebras,…

The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases…

We will construct the Lusztig form for the quantum loop algebra of $\mathfrak{gl}_n$ by proving the conjecture \cite[3.8.6]{DDF} and establish partially the Schur--Weyl duality at the integral level in this case. We will also investigate…

Let $\mathfrak{g}$ be the derived subalgebra of a Kac-Moody Lie algebra of finite type or affine type, $\mu$ a diagram automorphism of $\mathfrak{g}$ and $L(\mathfrak{g},\mu)$ the loop algebra of $\mathfrak{g}$ associated to $\mu$. In this…

We give a realization $\mathcal{A}_0$ of quantum toroidal algebra associated to $\mathfrak{gl}_2$ which can be viewed as an affinization of the Drinfeld new realization of quantum affine $\mathfrak{gl}_2$. We use this realization to define…

We develop a Lagrangian quantization formalism for a class of theories obtained by the restriction of the configuration space of gauge fields from a wider (parental) gauge theory. This formalism is based on application of the…

We use the BRST formalism to classify the gauge orbits of type II string theory's Ramond-Ramond (RR) field strengths under large RR gauge transformations of the RR gauge potentials. We find that this construction is identical to the…

We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in Drinfeld J presentation for all symmetric…

We settle several questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. An important new technical ingredient introduced in this paper is an…

An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…

We address the treatment of gauge theories within the framework that is formed from combining the machinery of noncommutative symplectic geometry, as introduced by Kontsevich, with Costello's approach to effective gauge field theories…

This paper presents a generalized circuit framework for constructing Shih-type fractionalizations of unitary operators of dyadic order, i.e., operators $U$ satisfying $U^{2^n}=I$. Building upon the architecture of the quantum fractional…

In this letter we describe an approach to the current algebra based in the Path Integral formalism. We use this method for abelian and non-abelian quantum field theories in 1+1 and 2+1 dimensions and the correct expressions are obtained.…

This article studies the rearrangement problem for Fourier series introduced by P.L. Ulyanov, who conjectured that every continuous function on the torus admits a rearrangement of its Fourier coefficients such that the rearranged partial…

We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…

Let U_q(sl_2) be the standard Drinfeld-Jimbo quantized universal enveloping algebra over sl_2, let F_q[SL_2] be the corresponding quantum function algebra, and let R be the ring of Laurent polynomials in q with coefficients in the ring of…

Starting from the requirement that a Lagrangian field theory be invariant under both Schwinger-Dyson BRST and Schwinger-Dyson anti-BRST symmetry, we derive the BRST--anti-BRST analogue of the Batalin-Vilkovisky formalism. This is done…

Exact operator quantization is perfomed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to the one proposed by Callan, Giddings, Harvey and Strominger, in the special case with 24 massless…

We show that the local observables of the curved beta gamma system encode the sheaf of chiral differential operators using the machinery of the book "Factorization algebras in quantum field theory", by Kevin Costello and the second author,…

The shift operator for a quantum lattice current algebra associated with sl(2) is produced in the form of product of local factors. This gives a natural deformation of the Sugawara construction for discrete space-time.