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Duality Cascades and Parallelotopes
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Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. In the setup of the ABJM theory and its generalizations, from the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.
Forward citations
Cited by 2 Pith papers
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Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters
Factorized quantum curves extend to FI parameters in 3D duality cascades, realizing Voronoi polytope vertices of exceptional root lattices as extremal brane configurations.
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Factorized Quantum Curves and Minuscule Vertices in 3D Duality Cascades with FI Parameters
Vertices of fundamental domains for del Pezzo quantum curves with FI parameters are realized as factorized curves from 5-branes dressed by FI parameters, matching minuscule weights.
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