Related papers: Multi-matrix loop equations: algebraic & different…
We present first calculations of QCD matrix-elements in perturbation theory at finite Nc beyond 2 loops in the eikonal approximation for e+ e- annihilation processes. For the emission of n soft energy-ordered gluons we solve both the colour…
We consider the question of loop corrections (i.e. 1/N) in the vector model/higher spin duality following the recent work of Giombi and Klebanov. The purpose of this paper is to gain further more precise comparison between the two sides of…
We study the matrix model/gauge theory connection for three different N=1 models: U(N) x U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric…
The recently discovered general formulas for perturbative correlators in basic matrix models can be interpreted as the Schur-preservation property of Gaussian measures. Then substitution of Schur by, say, Macdonald polynomials, defines a…
The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution…
We enlarge the dictionary between matrix models for long linear quivers preserving eight supercharges in $d=5$ and $d=3$ and type IIB supergravity backgrounds with AdS$_{d+1}$ factors. We introduce mass deformations of the field theory that…
We consider a deformation of N=1 supersymmetric gauge theories in four dimensions, which we call the C-deformation, where the gluino field satisfies a Clifford-like algebra dictated by a self-dual two-form, instead of the standard…
We introduce a commutative product of degree $-n$ on the homology $H_\ast(X)$ of an $n$-dimensional special cubical set $X$ and lift it on the free loop homology $H_\ast(\Lambda M)$ for $M=|X|$ to be the geometric realization. These…
It is well known that under the color-decomposition, one-loop amplitude of gluons contains partial amplitudes of single and double trace structures, and particularly all partial amplitudes of double trace structure can be expressed as a…
We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups…
Deformed gauge transformations on deformed coordinate spaces are considered for any Lie algebra. The representation theory of this gauge group forces us to work in a deformed Lie algebra as well. This deformation rests on a twisted Hopf…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We define a path integral over Dirac operators that averages over noncommutative geometries on a fixed graph, as the title reveals, using quiver representations. We prove algebraic relations that are satisfied by the expectation value of…
The non-equilibrium two loop self-energy is reexamined in the framework of a scalar quark and gluon model, with specific attention to terms which do not give rise to the standard two -> two particle collisional terms in the semi-classical…
q-deformed nonlinear field equations are constructed including Klein-Gordon and Maxwell equations. The q-deformation is interpreted as mathematical structure describing specific nonlinearity for which frequency of vibration exponentially…
We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar N=4 super-Yang-Mills theory, as a function of the three dual conformal cross ratios. The…
We describe noncommutative desingularizations of determinantal varieties, determinantal varieties defined by minors of generic symmetric matrices, and pfaffian varieties defined by pfaffians of generic anti-symmetric matrices. For maximal…
The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two…
The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…
We study Brownian loop soup clusters in $\mathbb{R}^3$ for an arbitrary intensity $\alpha>0$. We show the existence of a phase transition for the presence of unbounded clusters and study its basic properties. In particular, we show that,…