Related papers: Eigenvalue Distributions in Yang-Mills Integrals

We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…

We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…

We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3+1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number…

In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric $\mathcal{N}=4$ Yang-Mills. We use the `soft-collinear bootstrap'…

We study complex eigenvalues of large $N\times N$ symmetric random matrices of the form ${\cal H}=\hat{H}-i\hat{\Gamma}$, where both $\hat{H}$ and $\hat{\Gamma}$ are real symmetric, $\hat{H}$ is random Gaussian and $\hat{\Gamma}$ is such…

We develop a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the…

Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…

We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…

We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the…

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

We study two-dimensional integrable $N=1$ supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and…

In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the…

The gauge-independent phenomenon of color confinement in Yang-Mills theory manifests itself differently in different gauges. Therefore, the gauge dependence of quantities related to the infrared structure of the theory becomes important for…

Covariance matrix of heights measured relative to the average height of a growing self-affine surface in the steady state are investigated in the framework of random matrix theory. We show that the spectral density of the covariance matrix…

For an $n \times n$ independent-entry random matrix $X_n$ with eigenvalues $\lambda_1, \ldots, \lambda_n$, the seminal work of Rider and Silverstein asserts that the fluctuations of the linear eigenvalue statistics $\sum_{i=1}^n…

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to…

We review the recent developments in the theory of normal, normal self-dual and general complex random matrices. The distribution and correlations of the eigenvalues at large scales are investigated in the large $N$ limit. The 1/N expansion…

We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has…

A recent paper proposes a way of constructing infinite dimensional symmetries of the non-supersymmetric self-dual Yang-Mills action using isometries of the space-time. We review the Lagrangian formulation of N = 4 super Yang-Mills MHV rules…

We compute the exact all-orders perturbative expansion for the partition function of 2d $\mathrm{SU}(2)$ Yang-Mills theory on closed surfaces around higher critical points. We demonstrate that the expansion can be derived from the lattice…