BPS spectrum of Argyres-Douglas theory via spectral network

Maruyoshi, Kazunobu; Park, Chan Y.; Yan, Wenbin

doi:10.1007/jhep12(2013)092

Cited by 17 publications

(29 citation statements)

References 38 publications

(129 reference statements)

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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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“…Similar concepts have been pursued in the study of D-branes in Calabi-Yau varieties [22][23][24][25]. There are by now several approaches to determine the BPS degeneracies; for example spectral networks [26][27][28][29][30][31][32][33][34][35], the MPS wall-crossing formula [36][37][38][39][40][41][42], or a direct localization approach [18,43,44].…”

Section: Introductionmentioning

confidence: 99%

Quivers, Line Defects and Framed BPS Invariants

Cirafici

2017

Ann. Henri Poincaré

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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 quivers. The associated spectral problem characterises the line defect completely. Framed BPS states can be thought of as BPS particles bound to the defect. We identify the framed BPS degeneracies with certain enumerative invariants associated with the moduli spaces of stable quiver representations. We develop a formalism based on equivariant localization to compute explicitly such BPS invariants, for a particular choice of stability condition. Our framework gives a purely combinatorial solution of this problem. We detail our formalism with several explicit examples.Once again to construct the pyramid arrangement we have to look at the relevant terms in the Jacobian algebra J W = ⊕ n≥0 J W,n :Now we write down the Jacobian algebra elements corresponding to cyclic modules (6.32) and summands with higher grading do not contribute to the classification of the fixed points due to the condition dim V f = 1 and equations (6.15) and (6.18) evaluated at B =B = 0. To write down J W,4 we have usedthanks to (6.16) and (6.24) respectively, andWe can write the cyclic elements of the Jacobian algebra as A 2ψ A 1 C 3 v} . (6.44) the cyclic vector v. As usual this is graded J W = n≥0 J W,n and the first few terms are is obtained from the analog situation for SU (3), equation (6.14). To build the pyramid arrangement we have to study modules generated by the action of the Jacobian algebra on a single vector v ∈ V f , with V f one dimensional. The Jacobian algebra thus generated is naturally graded J W = n≥0 J W,n , and the first few terms are easy to work outAt the next levels we have four independent vectorswhere we have used the F-term relations obtained from (7.16) to show7.19) 56 Similar arguments give J W,7 = {ψÃ 2 ψ A 3 φÃ 1C v ,ψ A 2 ψ A 3 φÃ 1C v} , J W,8 = {A 3ψÃ2 ψ A 3 φÃ 1C v ,Ã 3ψÃ2 ψ A 3 φÃ 1C v} , J W,9 = {φ A 3ψÃ2 ψ A 3 φÃ 1C v ,φÃ 3ψÃ2 ψ A 3 φÃ 1C v} , J W,10 = {Ã 1φ A 3ψÃ2 ψ A 3 φÃ 1C v , A 1φ A 3ψÃ2 ψ A 3 φÃ 1C v} . (7.20)

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“…The relevant pattern of wall-crossings in the Z-plane is illustrated in figure 7: for 0.2 < m < 1 the spectrum is constant. In the region 0.03 < m < 0.2 a series of wall crossing occurs leading It should be possible to reproduce our results using the spectral networks as in [110].…”

Section: A Details On the Bps Spectrum Of The H 1 Modelmentioning

confidence: 83%

Kinetic mixing at strong coupling

et al. 2017

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A common feature of many string-motivated particle physics models is additional strongly coupled U (1)'s. In such sectors, electric and magnetic states have comparable mass, and integrating out modes also charged under U (1) hypercharge generically yields CP preserving electric kinetic mixing and CP violating magnetic kinetic mixing terms. Even though these extra sectors are strongly coupled, we show that in the limit where the extra sector has approximate N = 2 supersymmetry, we can use formal methods from Seiberg-Witten theory to compute these couplings. We also calculate various quantities of phenomenological interest such as the cross section for scattering between visible sector states and heavy extra sector states, as well as the effects of supersymmetry breaking induced from coupling to the MSSM.

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BPS spectrum of Argyres-Douglas theory via spectral network

Cited by 17 publications

References 38 publications

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

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

Quivers, Line Defects and Framed BPS Invariants

Kinetic mixing at strong coupling

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