Quantum Holonomies from Spectral Networks and Framed BPS States

Gabella, Maxime

doi:10.1007/s00220-016-2729-1

Cited by 29 publications

(70 citation statements)

References 60 publications

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“…For other applications of spectral networks to BPS state counting, see [14,15,16,17]. Two useful tools for exploration of spectral networks are the software package loom described in Section 5.1 of [17] and the Mathematica notebook [18].…”

Section: Spectral Networkmentioning

confidence: 99%

BPS states in the Minahan-Nemeschansky $${E_6}$$ theory

Hollands¹,

Neitzke

2016

Commun. Math. Phys.

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We use the method of spectral networks to compute BPS state degeneracies in the MinahanNemeschansky E 6 theory, on its Coulomb branch, without turning on a mass deformation. The BPS multiplicities come out in representations of the E 6 flavor symmetry. For example, along the simplest ray in electromagnetic charge space, we give the first 14 numerical degeneracies, and the first 7 degeneracies as representations of E 6 . We find a complicated spectrum, exhibiting exponential growth of multiplicities as a function of the electromagnetic charge. There is one unexpected outcome: the spectrum is consistent (in a nontrivial way) with the hypothesis of spin purity, that if a BPS state in this theory has electromagnetic charge equal to n times a primitive charge, then it appears in a spin-n 2 multiplet.

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Section: Spectral Networkmentioning

confidence: 99%

BPS states in the Minahan-Nemeschansky $${E_6}$$ theory

Hollands¹,

Neitzke

2016

Commun. Math. Phys.

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“…From the spectral network one can determine the BPS quiver in some region of the moduli space [24,27]. The core charge can in principle by determined by a careful study of the abelianiziation map for spectral networks [23,25] which relates flat connections on C and on Σ u . There is however no general algorithm to determine the superpotential W L .…”

Section: Framed Bps Quivers From Uv Datamentioning

confidence: 99%

Quantum line defects and refined BPS spectra

Cirafici

2019

Lett Math Phys

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In this note we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class S. Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the K-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.

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“…For our purposes in this paper, this algorithm is not quite sufficient: we also want to know the spin content of the framed BPS spectra. In [55,56] a method for computing such BPS spectra in class S theories has been proposed, extending [15]. 18 What we use in this paper is a slight extension of the method in [56] to treat the case of an irregular singularity.…”

Section: Line Defects and Their Framed Bps States In Class S[a 1 ]mentioning

confidence: 99%

“…In §4.1- §4.2 we review the approach via mutations; in §4.3- §4.5 we review the geometric methods of [15,[55][56][57][58]. These two methods will be used for the examples in §5- §6 below.…”

Section: Line Defects and Their Framed Bps States In Class S[a 1 ]mentioning

confidence: 99%

Line defect Schur indices, Verlinde algebras and U(1)r fixed points

Neitzke

Yan

2017

J. High Energ. Phys.

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Given an N = 2 superconformal field theory, we reconsider the Schur index I L (q) in the presence of a half line defect L. Recently Cordova-Gaiotto-Shao found that I L (q) admits an expansion in terms of characters of the chiral algebra A introduced by Beem et al., with simple coefficients v L,β (q). We report a puzzling new feature of this expansion: the q → 1 limit of the coefficients v L,β (q) is linearly related to the vacuum expectation values L in U(1) r -invariant vacua of the theory compactified on S 1 . This relation can be expressed algebraically as a commutative diagram involving three algebras: the algebra generated by line defects, the algebra of functions on U(1) r -invariant vacua, and a Verlindelike algebra associated to A. Our evidence is experimental, by direct computation in the Argyres-Douglas theories of type (A 1 , A 2 ), (A 1 , A 4 ), (A 1 , A 6 ), (A 1 , D 3 ) and (A 1 , D 5 ). In the latter two theories, which have flavor symmetries, the Verlinde-like algebra which appears is a new deformation of algebras previously considered.

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Quantum Holonomies from Spectral Networks and Framed BPS States

Cited by 29 publications

References 60 publications

BPS states in the Minahan-Nemeschansky $${E_6}$$ theory

BPS states in the Minahan-Nemeschansky $${E_6}$$ theory

Quantum line defects and refined BPS spectra

Line defect Schur indices, Verlinde algebras and U(1)r fixed points

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