Related papers: Miura operators as R-matrices from M-brane interse…
We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$…
In this work we study the analogues of R-matrices that arise in 5d non-commutative topological-holomorphic Chern-Simons theory, which is known to describe twisted M-theory. We first study the intersections of line and surface operators in…
Recently, Gaiotto and Rapcak proposed a generalization of $W_N$ algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as $Y_{L,M,N}$, is characterized by three…
We determine the mathematical structures which govern the $\Omega$ deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including…
In this paper,we derive a $\hbar$-deformation of the $W_{N}$ algebra and its quantum Miura tranformation. The vertex operators for this $\hbar$-deformed $W_{N}$ algebra and its commutation relations are also obtained.
We further develop the correspondence between representations of Ding-Iohara-Miki (DIM) algebra and Type IIB branes. In particular we explicitly compute the Hanany-Witten type 5-brane crossing operator which plays the role of the $R$-matrix…
We study the algebraic structures which govern the deformation of supersymmetric intersections of M2 and M5 branes. The universal algebras on M2 and M5 branes are deformed double current algebra of $\mathfrak{gl}_K$ and…
We study the quantization of the moduli space of multiplicative Higgs bundles through the lens of five-dimensional $\mathcal{N}=1$ supersymmetric gauge theories in $\Omega$-background. We extend the 4d $\mathcal{N}=2$ gauge theoretical…
We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in $AdS_5 \times S^5 $, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons.…
This thesis is based on two papers by the author and consists of two parts. We review the recent developments in the theory of multiple M2-branes and 3-algebras leading to multiple D2-brane theories. The inclusion of flux terms for the…
We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a…
We give a microscopic two dimensional ${\cal N}=(2,2)$ gauge theory description of arbitrary M2-branes ending on $N_f$ M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional ${\cal N}=2$ field…
In the twisted M-theory setting, various types of fusion of M2 and M5 branes induce coproducts between the algebra of operators on M2 branes and the algebra of operators on M5 branes. By doing a perturbative computation in the gravity side,…
We start from the quantum Miura transformation [7] for the $W$-algebra associated with $GL(n)$ group and find an evident formula for quantum L-operator as well as for the action of $W_l$ currents (l=1,..,n) on elements of the completely…
It was known that the U$(N)^4$ super Chern-Simons matrix model describing the worldvolume theory of D3-branes with two NS5-branes and two $(1,k)$5-branes in IIB brane configuration (dual to M2-branes after taking the T-duality and the…
Si Li and author suggested in that, in some cases, the AdS/CFT correspondence can be formulated in terms of the algebraic operation of Koszul duality. In this paper this suggestion is checked explicitly for $M2$ branes in an…
We consider the problem of the R-matrix of the quantum toroidal algebra $U_{q,t}(\ddot{\mathfrak{gl}}_1)$ in the Fock representation. Using the connection between the R-matrix $R(u)$ ($u$ being the spectral parameter) and the theory of…
Some BPS quantities of $\mathcal{N}=1$ 5D quiver gauge theories, like instanton partition functions or qq-characters, can be constructed as algebraic objects of the Ding-Iohara-Miki (DIM) algebra. This construction is applied here to…
Quiver 5D $\mathcal{N}=1$ gauge theories describe the low-energy dynamics on webs of $(p,q)$-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping $(p,q)$-branes to branes of charge $(-q,p)$, and, in this way,…
It has been known for some time that $W$ algebras can be realised in terms of an energy-momentum tensor together with additional free scalar fields. Some recent results have shown that more general realisations are also possible. In this…