Related papers: ADE Spectral Networks
We define the notion of a Lie superalgebra over a field $k$ of characteristic $2$ which unifies the two pre-existing ones - $\mathbb{Z}/2$-graded Lie algebras with a squaring map and Lie algebras in the Verlinde category ${\rm Ver}_4^+(k)$,…
In a recent paper DeWolfe et al. have shown how to use the self-intersection number of junctions to constrain the BPS spectrum of N=2, D=4 theories with ADE flavor symmetry arising on a single D3-brane probe in a 7-brane background.…
We introduce an approach for solving PDEs over manifolds using physics informed neural networks whose architecture aligns with spectral methods. The networks are trained to take in as input samples of an initial condition, a time stamp and…
This paper proposes an equivariant neural network that takes data in any semi-simple Lie algebra as input. The corresponding group acts on the Lie algebra as adjoint operations, making our proposed network adjoint-equivariant. Our framework…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We…
We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using…
We consider correlation functions in 6d $(2,0)$ theories of two $\frac{1}{2}$-BPS operators inserted away from a $\frac{1}{2}$-BPS surface defect. In the large central charge limit the leading connected contribution corresponds to sums of…
We propose a new way to build networks of defects. The idea takes advantage of the deformation procedure recently employed to describe defect structures, which we use to construct networks, spread from small rudimentary networks that appear…
The algebraic structure and the spectral properties of a special class of multi-component NLS equations, related to the symmetric spaces of {\bf BD.I}-type are analyzed. The focus of the study is on the spectral theory of the relevant Lax…
We study the BPS spectrum of four dimensional N=2 SU(2) theory with massive fundamental matters using the D3-brane probe. Since the BPS states are realized by string webs subject to the BPS conditions, we determine explicitly the…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
Anomaly detection aims to distinguish observations that are rare and different from the majority. While most existing algorithms assume that instances are i.i.d., in many practical scenarios, links describing instance-to-instance…
This paper proposes a novel neural-network-based adaptive hybrid-reflectance three-dimensional (3-D) surface reconstruction model. The neural network combines the diffuse and specular components into a hybrid model. The proposed model…
In this note we consider the set of line operators in theories of class $S$. We show that this set carries the action of a natural discrete dynamical system associated with the BPS spectrum. We discuss several applications of this…
We generalize the non-abelianization of Gaiotto-Moore-Neitzke from the case of $SL(n)$ and $GL(n)$ to arbitrary reductive algebraic groups. This gives a map between a moduli space of certain $N$-shifted weakly $W$-equivariant $T$-local…
We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at…
We propose a generalization of S-folds to 4d $\mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $\mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a…
We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which…