Playing With the Index of M-Theory

Motivated by M-theory, we study rank n K-theoretic Donaldson–Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d...

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Autores principales: Del Zotto, Michele, Nekrasov, Nikita, Piazzalunga, Nicolò, Zabzine, Maxim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9637649/
https://www.ncbi.nlm.nih.gov/pubmed/36366771
http://dx.doi.org/10.1007/s00220-022-04479-7
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author Del Zotto, Michele
Nekrasov, Nikita
Piazzalunga, Nicolò
Zabzine, Maxim
author_facet Del Zotto, Michele
Nekrasov, Nikita
Piazzalunga, Nicolò
Zabzine, Maxim
author_sort Del Zotto, Michele
collection PubMed
description Motivated by M-theory, we study rank n K-theoretic Donaldson–Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is Calabi–Yau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on [Formula: see text] ALE space, thus extending the usual geometric engineering dictionary to [Formula: see text] . We finally speculate about implications for instanton counting on Taub-NUT.
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spelling pubmed-96376492022-11-08 Playing With the Index of M-Theory Del Zotto, Michele Nekrasov, Nikita Piazzalunga, Nicolò Zabzine, Maxim Commun Math Phys Article Motivated by M-theory, we study rank n K-theoretic Donaldson–Thomas theory on a toric threefold X. In the presence of compact four-cycles, we discuss how to include the contribution of D4-branes wrapping them. Combining this with a simple assumption on the (in)dependence on Coulomb moduli in the 7d theory, we show that the partition function factorizes and, when X is Calabi–Yau and it admits an ADE ruling, it reproduces the 5d master formula for the geometrically engineered theory on [Formula: see text] ALE space, thus extending the usual geometric engineering dictionary to [Formula: see text] . We finally speculate about implications for instanton counting on Taub-NUT. Springer Berlin Heidelberg 2022-08-23 2022 /pmc/articles/PMC9637649/ /pubmed/36366771 http://dx.doi.org/10.1007/s00220-022-04479-7 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Del Zotto, Michele
Nekrasov, Nikita
Piazzalunga, Nicolò
Zabzine, Maxim
Playing With the Index of M-Theory
title Playing With the Index of M-Theory
title_full Playing With the Index of M-Theory
title_fullStr Playing With the Index of M-Theory
title_full_unstemmed Playing With the Index of M-Theory
title_short Playing With the Index of M-Theory
title_sort playing with the index of m-theory
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9637649/
https://www.ncbi.nlm.nih.gov/pubmed/36366771
http://dx.doi.org/10.1007/s00220-022-04479-7
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