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

Hollands, Lotte; Neitzke, Andrew

doi:10.1007/s00220-016-2798-1

Cited by 17 publications

(44 citation statements)

References 30 publications

(133 reference statements)

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“…By combining the BPS indices listed in [26] and table 4 with the tables of the mirror maps listed in the main text, we are able to describe the non-perturbative terms of the ST/TS correspondence for the del Pezzo geometries completely in the group-theoretical language as explained in section 2. Note also that the BPS indices of the E 6 curve matches with [76] if we drop the spins.…”

Section: B Bps Indicesmentioning

confidence: 74%

Spectral theories and topological strings on del Pezzo geometries

Moriyama

2020

J. High Energ. Phys.

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Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

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Section: B Bps Indicesmentioning

confidence: 74%

Spectral theories and topological strings on del Pezzo geometries

Moriyama

2020

J. High Energ. Phys.

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“…Here, in order to determine the equations completely, one needs to find a closed formula for a certain transformation S 0, π 3 relating two different branches of X γ (h); we formulate this problem carefully but do not solve it. We also explain how one can approximate S 0, π 3 using some integer invariants previously computed in [34] (BPS indices in the Minahan-Nemeschansky E 6 theory), and give some numerical evidence that this approximation works.…”

Section: Integral Equations and Analytic Structuresmentioning

confidence: 99%

Exact WKB and Abelianization for the $$T_3$$ Equation

Hollands

Neitzke

2020

Commun. Math. Phys.

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We describe the exact WKB method from the point of view of abelianization, both for Schr ödinger operators and for their higher-order analogues (opers). The main new example which we consider is the "T 3 equation," an order 3 equation on the thrice-punctured sphere, with regular singularities at the punctures. In this case the exact WKB analysis leads to consideration of a new sort of Darboux coordinate system on a moduli space of flat SL(3)-connections. We give the simplest example of such a coordinate system, and verify numerically that in these coordinates the monodromy of the T 3 equation has the expected asymptotic properties. We also briefly revisit the Schr ödinger equation with cubic potential and the Mathieu equation from the point of view of abelianization.

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“…The possibility of such crossings vastly increases the complexity of the higher rank networks. In fact, they are largely unexplored apart from the cases of higher rank generalizations of Fock-Goncharov and Fenchel-Nielsen networks [58,75,76].…”

Section: Higher Rank Generalizationmentioning

confidence: 99%

“…for some one-cycle γ on Σ. These non-generic compact networks were studied in [76]. They are labelled by two coprime integers p and q.…”

Section: Higher Rank Generalizationmentioning

confidence: 99%

“…It turns out to be especially valuable for conformal N = 2 theories with a single infinite BPS chamber. Examples include the intrinsically strongly coupled E 6 and higher rank Minahan-Nemeschansky theories discussed in section 3.2, whose spectra are determined in [69,76], where higher rank Fenchel-Nielsen networks play a crucial role. In these examples one finds not only saddles corresponding to hypermultiplets or closed loops corresponding to vector multiplets, but also more complicated topologies arise, such as the finite webs of figure 30.…”

Section: Jhep12(2021)164mentioning

confidence: 99%

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A geometric recipe for twisted superpotentials

Hollands

Rüter

Szabo

2021

J. High Energ. Phys.

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We give a pedagogical introduction to spectral networks and abelianization, as well as their relevance to $$ \mathcal{N} $$ N = 2 supersymmetric field theories in four dimensions. Motivated by a conjecture of Nekrasov-Rosly-Shatashvili, we detail a geometric recipe for computing the effective twisted superpotential for $$ \mathcal{N} $$ N = 2 field theories of class $$ \mathcal{S} $$ S as a generating function of the brane of opers, with respect to the spectral coordinates found from abelianization. We present two new examples, the simplest Argyres-Douglas theory and the pure SU(2) gauge theory, while we conjecture the E-expansion of the effective twisted superpotential for the E6 Minahan-Nemeschansky theory.

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

Cited by 17 publications

References 30 publications

Spectral theories and topological strings on del Pezzo geometries

Spectral theories and topological strings on del Pezzo geometries

Exact WKB and Abelianization for the $$T_3$$ Equation

A geometric recipe for twisted superpotentials

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