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We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to…
We show that the duality between the self-dual and Maxwell-Chern-Simons theories in 2+1-dimensions survives when the space-time becomes noncommutative. Existence of the Seiberg-Witten map is crucial in the present analysis. It should be…
The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…
We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of…
In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N \ne 2$. We construct a…
We address the study of the classical Gaudin spin model from the bi-Hamiltonian point of view. We describe in details the sl(2) three particle case.
We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andr\'e model. These spectral and…
Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural nets. In the…
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
We consider the reduction along two compact directions of a twisted N=4 gauge theory on a 4-dimensional orientable manifold which is not a global product of two surfaces but contains a non-orientable surface. The low energy theory is a…
Codimension two defects of the $(0,2)$ six dimensional theory $\mathscr{X}[\mathfrak{j}]$ have played an important role in the understanding of dualities for certain $\mathcal{N}=2$ SCFTs in four dimensions. These defects are typically…
The 2+1 dimensional pure SU(N) gauge theories with N <= 4 are candidates for applying the powerful tools of scaling and universality to their deconfinement transitions at finite temperature. The corresponding 2 dimensional q-state Potts…
To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken)…
Solvable supersymmetric algebraic model for descriptions of the spherical to gama unstable shape- phase transition in even and odd mass nuclei is proposed. This model is based on dual algebraic structure and Richardson - Gaudin method,…
We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
Let $G$ be a $2$-step stratified group of topological dimension $d$ and homogeneous dimension $Q$. Let $L$ be a homogeneous sub-Laplacian on $G$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is of weak…
Kapustin and Witten showed that a twisted version of N=4 gauge theory in four dimensions compactifies to a two-dimensional sigma-model whose target space is the Hitchin moduli space. In this talk, I consider the reduction of the gauge…
We develop a new approach to extracting the physical consequences of S-duality of four-dimensional $\mathcal{N}=4$ super Yang-Mills (SYM) and its string theory dual, based on $SL(2,\mathbb{Z})$ spectral theory. We observe that CFT…
Quark-hadron (QH) duality in lepton scattering off nucleons is studied with the resonance quark model. It is shown that in the case of neutrino scattering off an isoscalar target the duality is simultaneously observed for charged and…