BPS spectra from BPS graphs

Gabella, Maxime

doi:10.48550/arxiv.1710.08449

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…The advantage of geometric approaches to BPS counting in 4d N = 2 quantum field theories was advocated long ago by [47]. This philosophy was turned into a truly powerful framework more recently in [31], and in follow-ups [52][53][54][55][56][57]. The application of geometric techniques to BPS counting in 3d-5d systems was advocated more recently in [33].…”

Section: Geometric Approaches To Bps States From String Theorymentioning

confidence: 99%

Exploring 5d BPS Spectra with Exponential Networks

Banerjee

Longhi

Romo

2019

Ann. Henri Poincaré

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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 brane wrapping a special Lagrangian submanifold L. The spectrum of 3d-5d BPS states is encoded by the geometry of the manifold of vacua of the 3d-5d system, which further coincides with the mirror curve describing moduli of the Lagrangian brane. The information about the BPS spectrum is extracted from the geometry of the mirror curve by construction of a nonabelianization map for the exponential networks. For the simplest Calabi-Yau, C 3 we reproduce the count of 5d BPS states encoded by the Mac Mahon function in the context of topological strings, and match predictions of 3d tt * geometry for the count of 3d-5d BPS states. We comment on applications of our construction to the study of enumerative invariants of toric Calabi-Yau threefolds.

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Section: Geometric Approaches To Bps States From String Theorymentioning

confidence: 99%

Exploring 5d BPS Spectra with Exponential Networks

Banerjee

Longhi

Romo

2019

Ann. Henri Poincaré

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“…The last point of view fits nicely with the 3d/3d correspondence discussed in subsection 9.3, which involves G C Chern-Simons theory. Further works on the Hitchin system, opers, and Darboux coordinates on M include [50,343,356,366,415,488,[524][525][526][527][528][529][530][531][532][533][534][535] (some are reviewed in [536]); a different technique is based on spectral networks, which abelianize flat connections on C [537][538][539][540][541][542][543][544][545][546][547][548][549]; see also [49,[550][551][552].…”

Section: Line Operatorsmentioning

confidence: 99%

A slow review of the AGT correspondence

Floch¹

2022

J. Phys. A: Math. Theor.

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Starting with a gentle approach to the Alday–Gaiotto–Tachikawa (AGT) correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School ‘YRISW 2020’ to appear in a special issue of J. Phys. A. Class S is a wide class of 4d N = 2 supersymmetric gauge theories (ranging from super-QCD (quantum chromodynamics) to non-Lagrangian theories) obtained by twisted compactification of 6d N = ( 2 , 0 ) superconformal theories on a Riemann surface C. This 6d construction yields the Coulomb branch and Seiberg–Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d conformal field theory (CFT) correlators. For instance, the four-sphere partition function of a 4d N = 2 S U ( 2 ) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres–Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as T N correspond to Toda CFT correlators, and nonlocal operators (Wilson–’t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

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“…A BPS graph G is a graph embedded in the UV curve C of a class S theory, and arises as a maximally degenerate spectral network [9] (see also the related works [10,24,25]). The shape of the spectral network reflects the geometry of the Seiberg-Witten curve Σ, which is presented as a N -sheeted ramified covering of C, and depends on a choice of Coulomb vacuum and UV moduli.…”

Section: Bps Graphsmentioning

confidence: 99%

S duality and Framed BPS States via BPS Graphs

Gang,

Longhi,

Yamazaki

2017

Preprint

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We study a realization of S dualities of four-dimensional N = 2 class S theories based on BPS graphs. S duality transformations of the UV curve are explicitly expressed as a sequence of topological transitions of the graph, and translated into cluster transformations of the algebra associated to the dual BPS quiver. Our construction applies to generic class S theories, including those with non-maximal flavor symmetry, generalizing previous results based on higher triangulations. We study the the action of S duality on UV line operators, and show that it matches precisely with the mapping class group, by a careful analysis of framed wall-crossing. We comment on the implications of our results for the computation of three-manifold invariants via cluster partition functions.

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BPS spectra from BPS graphs

Cited by 3 publications

References 21 publications

Exploring 5d BPS Spectra with Exponential Networks

Exploring 5d BPS Spectra with Exponential Networks

A slow review of the AGT correspondence

S duality and Framed BPS States via BPS Graphs

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