2023
DOI: 10.1088/1751-8121/acc2fb
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Duality cascades and parallelotopes

Abstract: 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 b… Show more

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Cited by 2 publications
(12 citation statements)
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“…See figure 5. The results match the picture of duality cascades indicated in [61,62], which shows that the more distant from the origin the relative JHEP08(2023)191 ranks are, the higher overall rank N a non-vanishing partition function requires. Namely, we have found that the results obtained from bilinear relations of q-Painlevé equations are also consistent with duality cascades.…”
Section: Applications Beyond Fundamental Domainsupporting
confidence: 80%
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“…See figure 5. The results match the picture of duality cascades indicated in [61,62], which shows that the more distant from the origin the relative JHEP08(2023)191 ranks are, the higher overall rank N a non-vanishing partition function requires. Namely, we have found that the results obtained from bilinear relations of q-Painlevé equations are also consistent with duality cascades.…”
Section: Applications Beyond Fundamental Domainsupporting
confidence: 80%
“…As in [61,62], under duality cascades the relative ranks (M 0 , M 1 , M 3 ) are shifted translationally with the overall rank N decreasing and finally we arrive at the fundamental domain (2.12) with the lowest overall rank N . It is, however, subtle when the relative ranks are located on the boundaries of the fundamental domain since relative ranks on one boundary are shifted to those on the opposite one and both should be treated on an equal footing.…”
Section: Comparison With [69 74]mentioning
confidence: 77%
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