相关论文: BPS spectra from BPS graphs
We define "BPS graphs" on punctured Riemann surfaces associated with $A_{N-1}$ theories of class $\mathcal{S}$. BPS graphs provide a bridge between two powerful frameworks for studying the spectrum of BPS states: spectral networks and BPS…
BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is…
A new construction of BPS monodromies for 4d ${\mathcal N}=2$ theories of class S is introduced. A novel feature of this construction is its manifest invariance under Kontsevich-Soibelman wall crossing, in the sense that no information on…
The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…
We apply the techniques provided by the recent works Gaiotto, Moore and Neitzke, to derive the most general spectrum generating functions for coupled 2d-4d $A_1$ theories of class ${\cal S}$, in presence of surface and line defects. As an…
A large class of N=2 quantum field theories admits a BPS quiver description and the study of their BPS spectra is then reduced to a representation theory problem. In such theories the coupling to a line defect can be modelled by framed…
We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ superconformal field theory of Argyres-Douglas type, obtained via twisted compactification of six-dimensional $A_{N-1}$ $(2,0)$ theory on a sphere with an irregular puncture, by…
It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of…
We introduce a new perspective and a generalization of spectral networks for 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ associated to Lie algebras $\mathfrak{g} = \textrm{A}_n$, $\textrm{D}_n$, $\textrm{E}_{6}$, and…
In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class $\mathcal{S}$. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain…
We propose a method for determining the spins of BPS states supported on line defects in 4d $\mathcal{N}=2$ theories of class S. Via the 2d-4d correspondence, this translates to the construction of quantum holonomies on a punctured Riemann…
We study BPS line defects in N=2 supersymmetric four-dimensional field theories. We focus on theories of "quiver type," those for which the BPS particle spectrum can be computed using quiver quantum mechanics. For a wide class of models,…
We study the geometric description of BPS states in supersymmetric theories with eight supercharges in terms of geodesic networks on suitable spectral curves. We lift and extend several constructions of Gaiotto-Moore-Neitzke from gauge…
We investigate BPS states in 4d N=4 supersymmetric Yang-Mills theory and the corresponding (p, q) string networks in Type IIB string theory. We propose a new interpretation of the algebra of line operators in this theory as a tensor product…
We study cubic differentials and their spectral networks on Riemann surfaces, focusing on the polynomial case on the Riemann sphere. We introduce the notion of spectral core as the primary tool for our study, refining the classical notion…
The infrared formula relates the Schur index of a 4d $\mathcal{N}=2$ theory to its wall-crossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by C\'ordova, Gaiotto and Shao, includes contributions by…
We study the BPS spectra of N=2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and…
The BPS spectrum of d=4 N=2 field theories in general contains not only hyper- and vector-multipelts but also short multiplets of particles with arbitrarily high spin. This paper extends the method of spectral networks to give an algorithm…
Spectral hypergraph theory mainly concerns using hypergraph spectra to obtain structural information about the given hypergraphs. The study of cospectral hypergraphs is important since it reveals which hypergraph properties cannot be…
BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can be represented as planar string networks with ends lying on D3-branes. We introduce several protected indices which capture information on the spectrum and various…