Related papers: Deformed Schur indices and Macdonald polynomials

We compute supersymmetric indices which count local operators at certain half-BPS interfaces and quarter-BPS junctions of interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory. We use the indices as very stringent tests of…

We review the general procedure for the field-theoretical computation of wrapping effects in standard and beta-deformed N=4 super Yang-Mills by means of N=1 superspace techniques. In the undeformed theory, these methods allowed to find…

We present the Sudakov form factor in full color $\mathcal{N}=4$ supersymmetric Yang-Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.

We formulate noncommutative self-dual N=4 supersymmetric Yang-Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric…

Thrall's problem asks for the Schur decomposition of the higher Lie modules $\mathcal{L}_\lambda$, which are defined using the free Lie algebra and decompose the tensor algebra as a general linear group module. Although special cases have…

Classical Schur P-functions are the particular case of Hall-Littlewood polynomials when the parameter is equal to -1. We introduce factorial (interpolation) analogues of Schur P-functions. A dimension of a skew shifted Young diagram is the…

The superconformal properties of N=4 Yang-Mills theory are most naturally studied using the formalism of harmonic superspace. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant…

We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N) $Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for…

D=4, N=4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D=10 theory. That superspace, in particular the choice of pure spinor variables, is less…

We construct a gauge invariant regularisation scheme for pure SU(N) Yang-Mills theory in fixed dimension four or less (for N = infinity in all dimensions), with a physical cutoff scale Lambda, by using covariant higher derivatives and…

In this paper the partition function of N=4 D=0 super Yang-Mills matrix theory with arbitrary simple gauge group is discussed. We explicitly computed its value for all classical groups of rank up to 11 and for the exceptional groups G_2,…

We provide a systematic way of dimensional reduction for $(4+2n)$-dimensional $U(N)$ supersymmetric Yang-Mills (SYM) theories ($n=0,1,2,3$) and their mixtures compactified on two-dimensional tori with background magnetic fluxes, which…

Topologically twisted $\mathcal{N} = 4$ super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold $\mathbb{P}^2$ and with gauge group $\mathrm{U}(3)$ this partition function has a…

The complete tree-level S-matrix of four dimensional ${\cal N}=4$ super Yang-Mills and ${\cal N} = 8$ supergravity has compact forms as integrals over the moduli space of certain rational maps. In this note we derive formulas for amplitudes…

A gauge invariant regularisation which can be used for non-perturbative treatment of Yang-Mills theories within the exact renormalization group approach is constructed. It consists of a spontaneously broken SU(N|N) super-gauge extension of…

The conformal index counts the number of exactly marginal deformations. In 4d the index is given by the number of chiral primary operators of dimension 3 moded out by the complexified global group, where the quotient is defined as usual by…

We derive the four-dimensional integrand of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. In our integrand…

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into…

We construct the wave functions in the q-deformed 2d Yang-Mills theory that compute torus correlation functions of affine currents in the VOA associated to a class of 4d $N = 2$ SCFTs. These wave functions are then shown to reduce to the…

The ring of symmetric functions $\Lambda$, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the…