Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
BPS states in the Minahan-Nemeschansky E6 theory
2 Pith papers cite this work, alongside 13 external citations. Polarity classification is still indexing.
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abstract
We use the method of spectral networks to compute BPS state degeneracies in the Minahan-Nemeschansky $E_6$ 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-$\frac{n}{2}$ multiplet.
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A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.