Related papers: On refined Chern-Simons and refined ABJ matrix mod…
Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation.…
It was proved by Macdonald that the Giambelli identity holds if we define the Schur functions using the Jacobi-Trudi identity. Previously for the super Chern-Simons matrix model (the spherical one-point function of the superconformal…
In this paper, from the $q$-gauge covariant condition we define the $q$-deformed Killing form and the second $q$-deformed Chern class for the quantum group $SU_{q}(2)$. Developing Zumino's method we introduce a $q$-deformed homotopy…
We investigate the possibility of Lorentz and CPT violations in the photon sector, of the Chern-Simons form, be induced by radiative corrections arising from the Lorentz and CPT non-invariant fermionic sector of an extended version of QED.…
We present a new technique for computing supersymmetric Wilson loops in the ABJM theory via supersymmetric localization, valid for arbitrary values of the rank of the gauge group $N$ and the Chern-Simons level $k$. The approach relies on an…
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six…
We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…
Tensor operators in graded representations of Z_{2}-graded Hopf algebras are defined and their elementary properties are derived. Wigner-Eckart theorem for irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of tensor…
We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the…
We consider $U(N)$ $\mathcal N=4$ super Yang-Mills theory and discuss how to extract the strong coupling limit of non-planar corrections to observables involving the $\frac{1}{2}$-BPS Wilson loop. Our approach is based on a suitable saddle…
N=6 superconformal Chern-Simons theory with gauge group U(M)xU(N)} is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We show that, much like its regular counterpart…
We solve for finite $N$ the matrix model of supersymmetric $U(N)$ Chern-Simons theory coupled to $N_{f}$ fundamental and $N_{f}$ anti-fundamental chiral multiplets of $R$-charge $1/2$ and of mass $m$, by identifying it with an average of…
We perform a first step analysis toward generalization of the classification of N=4 linear quiver gauge theories by Gaiotto and Witten including Chern-Simons interaction. For this we investigate minimal N=4 U(N_1)_k x U(N_2)_{-k}…
We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto-Witten theory with linear matter.…
We consider the Gopakumar-Ooguri-Vafa correspondence, relating ${\rm U}(N)$ Chern-Simons theory at large $N$ to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $\mathbb{S}^{\Gamma} =…
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 $\mathfrak{gl}(1)$…
We study three-dimensional {\cal N}=2 U(N) Chern-Simons theory on S^3 coupled to 2N_f chiral multiplets deformed by mass terms. The partition function localizes to a matrix integral, which can be exactly computed in the large N limit. In a…
The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational…
With the introduction of shadow fields, we demonstrate the renormalizability of the N=4 super-Yang--Mills theory in component formalism, independently of the choice of UV regularization. Remarkably, by using twisted representations, one…
We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector…