ADE spectral networks

Longhi, Pietro; Park, Chan Y.

doi:10.1007/jhep08(2016)087

Cited by 27 publications

(86 citation statements)

References 60 publications

(270 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…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%

“…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]. Both these tools were used in developing the picture described below.…”

Section: Spectral Networkmentioning

confidence: 99%

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

Hollands¹,

Neitzke

2016

Commun. Math. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…Spectral networks for higher symmetric representations of A 1 have not been investigated in previous literature, therefore we take a short detour and learn a few basic facts about them. We propose a natural definition, slightly generalizing [13], which is in part based on ideas in [43,44]. The main novelty is the appearance of "collinear vacua" for the 2d theory.…”

Section: Spectral Network In Higher Symmetric Representationsmentioning

confidence: 99%

“…A similar relation holds among periods of cycles arising from p R . The existence of these relations reflects the fact that periods of λ lie in a sub-variety of Jac(Σ) [43,52,78], which is a consequence of the fact that the geometry of Σ N is entirely parameterized by a quadratic differential.…”

Section: Surface Defects Near Puncturesmentioning

confidence: 99%

An infrared bootstrap of the Schur index with surface defects

Fluder

Longhi

2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The infrared formula relates the Schur index of a 4d N = 2 theory to its wallcrossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by various types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class S theories of type A 1 engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a "bootstrap" (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.A relation between Schur indices and BPS monodromies was conjectured in [23], following 6 See also [45], for some results of an IR formula for the lens index. 9 The "no-exotics" property asserts that BPS states have R = 0 in 4d N = 2 gauge theories [33,54,55]. 10 In practice, BPS spectra at arbitrary moduli can be rather involved, and by moving onto a "simple" sector of the theory, in which one can explicitly compute the protected spin character, the wall-crossing formulae allow to extract the BPS degeneracies in other sectors. the latter reference are precisely the "vortex defects" considered in [31] via the Higgsing procedure (see also Appendix A.3), and in the present paper via the IR formalism.

show abstract

ADE spectral networks

Cited by 27 publications

References 60 publications

Exploring 5d BPS Spectra with Exponential Networks

Exploring 5d BPS Spectra with Exponential Networks

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

An infrared bootstrap of the Schur index with surface defects

Contact Info

Product

Resources

About