Related papers: BPS spectra from BPS graphs

We develop geometric techniques for counting BPS states in five-dimensional gauge theories engineered by M theory on a toric Calabi-Yau threefold. The problem is approached by studying framed 3d-5d wall-crossing in presence of a single M5…

In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…

We propose a new approach to studies on partial Steiner triple systems consisting in determining complete graphs contained in them. We establish the structure which complete graphs yield in a minimal PSTS that contains them. As a by-product…

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural…

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…

The vacuum structure and spectra of two-dimensional gauge theories with N=(2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral…

The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph is distance-biregular when it is…

This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states…

BPS quivers for N=2 SU(N) gauge theories are derived via geometric engineering from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of previous low energy constructions, the geometric approach leads to…

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…

Based on basis path set, G-SGD algorithm significantly outperforms conventional SGD algorithm in optimizing neural networks. However, how the inner mechanism of basis paths work remains mysterious. From the aspect of graph theory, this…

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…

We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which…

We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well as recent advances.

This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the foundational background needed to approach the frontiers of…

For the hypergeometric spectral curve and its confluent degenerations (spectral curves of "hypergeometric type"), we obtain a simple formula expressing the topological recursion free energies as a sum over BPS states (degenerate spectral…

The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special…

In this paper we construct a class of bounded degree bipartite graphs with a small separator and large bandwidth. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly…