Framed BPS states
TLDR
In this paper, a class of line operators in supersymmetric field theories, which leave four supersymmetries unbroken, are considered and a new class of halo bound states called framed BPS states are defined.Abstract:
We consider a class of line operators in $d = 4, \mathcal{N} = 2$ supersymmetric field theories, which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call "framed BPS states." These include halo bound states similar to those of $d = 4, \mathcal{N} = 2$ supergravity, where (ordinary) BPS particles are loosely bound to the line operator. Using this construction, we give a new proof of the Kontsevich-Soibelman wall-crossing formula (WCF) for the ordinary BPS particles, by reducing it to the semiprimitive WCF. After reducing on $S^1$, the expansion of the vevs of the line operators in the IR provides a new physical interpretation of the "Darboux coordinates" on the moduli space M of the theory. Moreover, we introduce a "protected spin character" (PSC) that keeps track of the spin degrees of freedom of the framed BPS states. We show that the generating functions of PSCs admit a multiplication, which defines a deformation of the algebra of holomorphic functions on $\mathcal{M}$. As an illustration of these ideas, we consider the sixdimensional (2, 0) field theory of $A_1$ type compactified on a Riemann surface $\mathcal{C}$. Here, we show (extending previous results) that line operators are classified by certain laminations on a suitably decorated version of $\mathcal{C}$, and we compute the spectrum of framed BPS states in several explicit examples. Finally, we indicate some interesting connections to the theory of cluster algebras.read more
Citations
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Generalized Global Symmetries
TL;DR: A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. strings, membranes, etc. as discussed by the authors, which leads to Ward identities and hence to selection rules on amplitudes.
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Wall-crossing, Hitchin Systems, and the WKB Approximation
TL;DR: In this article, the authors considered BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the RiemANN surface.
Journal ArticleDOI
Generalized Global Symmetries
TL;DR: A global symmetry is a symmetry for which the charged operators are of space-time dimension $q$; e.g., strings, membranes, etc. as mentioned in this paper Theorem 1.
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Gauge Theories Labelled by Three-Manifolds
TL;DR: In this article, a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories is proposed, which can be seen as a way of describing boundary conditions and duality walls in four-dimensional SCFTs.
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Reading between the lines of four-dimensional gauge theories
TL;DR: In this paper, the authors show that the existence of these distinct theories clarifies a number of issues in electric/magnetic dualities of supersymmetric gauge theories, both for the conformal N = 4 theories and for the low-energy duality of N = 1 theories.
References
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