Fiber-base duality from the algebraic perspective View Full Text


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Article Info

DATE

2019-03

AUTHORS

J.-E. Bourgine

ABSTRACT

Quiver 5D N=1 gauge theories describe the low-energy dynamics on webs of (p, q)-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping (p, q)-branes to branes of charge (−q, p), and, in this way, induces several dualities between 5D gauge theories. On the other hand, these theories can also be obtained from the compactification of topological strings on a Calabi-Yau manifold, for which the S-duality is realized as a fiber-base duality. Recently, a third point of view has emerged in which 5D gauge theories are engineered using algebraic objects from the Ding-Iohara-Miki (DIM) algebra. Specifically, the instanton partition function is obtained as the vacuum expectation value of an operator T constructed by gluing the algebra’s intertwiners (the equivalent of topological vertices) following the rules of the toric diagram/brane web. Intertwiners and T -operators are deeply connected to the co-algebraic structure of the DIM algebra. We show here that S-duality can be realized as the twist of this structure by Miki’s automorphism. More... »

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3

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http://scigraph.springernature.com/pub.10.1007/jhep03(2019)003

DOI

http://dx.doi.org/10.1007/jhep03(2019)003

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https://app.dimensions.ai/details/publication/pub.1112502977


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    "description": "Quiver 5D N=1 gauge theories describe the low-energy dynamics on webs of (p, q)-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping (p, q)-branes to branes of charge (\u2212q, p), and, in this way, induces several dualities between 5D gauge theories. On the other hand, these theories can also be obtained from the compactification of topological strings on a Calabi-Yau manifold, for which the S-duality is realized as a fiber-base duality. Recently, a third point of view has emerged in which 5D gauge theories are engineered using algebraic objects from the Ding-Iohara-Miki (DIM) algebra. Specifically, the instanton partition function is obtained as the vacuum expectation value of an operator T constructed by gluing the algebra\u2019s intertwiners (the equivalent of topological vertices) following the rules of the toric diagram/brane web. Intertwiners and T -operators are deeply connected to the co-algebraic structure of the DIM algebra. We show here that S-duality can be realized as the twist of this structure by Miki\u2019s automorphism.", 
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