Related papers: Emergent Phase Space Description of Unitary Matrix…
We analyze the dynamics of weakly coupled finite temperature $U(N)$ gauge theories on $S^3$ by studying a class of effective unitary matrix model. Solving Dyson-Schwinger equation at large $N$, we find that different phases of gauge…
We present the partition function of a most generic $U(N)$ single plaquette model in terms of representations of unitary group. Extremising the partition function in large N limit we obtain a relation between eigenvalues of unitary matrices…
We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing…
A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent…
We explicitly find representations for different large $N$ phases of Chern-Simons matter theory on $S^2\times S^1$. These representations are characterised by Young diagrams. We show that no-gap and lower-gap phase of Chern-Simons-matter…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
A matrix model is constructed which describes a chiral version of the large $N$ $U(N)$ gauge theory on a two-dimensional sphere of area $A$. This theory has three separate phases. The large area phase describes the associated chiral string…
Chern-Simons (CS) theories with rank $N$ and level $k$ on Seifert manifold are discussed. The partition functions of such theories can be written as a function of modular transformation matrices summed over different integrable…
The large-N behavior of the quartic-cubic generalized two dimensional Yang Mills U(N) on the sphere is investigated, for small cubic couplings. It is shown that single transition at the critical area which is present for the quartic model,…
We study ${\mathcal{N}}=2$ supersymmetric $U(N)$ Chern-Simons with $N_{f}$ fundamental and $N_{f}$ antifundamental chiral multiplets of mass $m$ in the complete parameter space spanned by $(g,\,m,\,N,\,N_{f})$, where $g$ denotes the…
We investigate the different large $N$ phases of a generalized Gross-Witten-Wadia $U(N)$ matrix model. The deformation mimics the one-loop determinant of fermion matter with a particular coupling to gauge fields. In one version of the…
We construct noncommutative U(1) gauge theory on the fuzzy sphere S^2_N as a unitary 2N x 2N matrix model. In the quantum theory the model is equivalent to a nonabelian U(N) Yang-Mills theory on a 2 dimensional lattice with 2 plaquettes.…
We review recent results of emergent geometries in the BMN matrix model, a one-dimensional gauge theory considered as a non-perturbative formulation of M-theory on the plane-wave geometry. A key to understand the emergent geometries is the…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
Phase separation of two phase separating solutes in a common solvent can result in mesoscale (micron-sized) droplets with complex topologies of the domains of each solute within each droplet. Such topologies have been observed in-vitro in…
Applying the machinery of random matrix theory and Toeplitz determinants we study the level $k$, $U(N)$ Chern-Simons theory coupled with fundamental matter on $S^2\times S^1$ at finite temperature $T$. This theory admits a discrete matrix…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
We derive expressions for the phase-space of a particle of momentum $p$ decaying into $N$ particles, that are valid for any number of dimensions. These are the imaginary parts of so-called `sunset' diagrams, which we also obtain. The…