Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory
Abstract Drinfel’d doubles of Lie bialgebroids play an important role in T-duality of string theories. In the presence of H and R fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel’d double yields a Cou...
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| Format: | Article |
| Language: | English |
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)192 |
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| author | Aybike Çatal-Özer Keremcan Doğan Cem Yetişmişoğlu |
| author_facet | Aybike Çatal-Özer Keremcan Doğan Cem Yetişmişoğlu |
| author_sort | Aybike Çatal-Özer |
| collection | DOAJ |
| description | Abstract Drinfel’d doubles of Lie bialgebroids play an important role in T-duality of string theories. In the presence of H and R fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel’d double yields a Courant algebroid. However for U-duality, more complicated direct sum decompositions that are not described by dual vector bundles appear. In a previous work, we extended the notion of a Lie bialgebroid for vector bundles that are not necessarily dual. We achieved this by introducing a framework of calculus on algebroids and examining compatibility conditions for various algebroid properties in this framework. Here our aim is two-fold: extending our work on bialgebroids to include both H- and R-twists, and generalizing proto Lie bialgebroids to pairs of arbitrary vector bundles. To this end, we analyze various algebroid axioms and derive twisted compatibility conditions in the presence of twists. We introduce the notion of proto bialgebroids and their Drinfel’d doubles, where the former generalizes both bialgebroids and proto Lie bialgebroids. We also examine the most general form of vector bundle automorphisms of the double, related to twist matrices, that generate a new bracket from a given one. We analyze various examples from both physics and mathematics literatures in our framework. |
| format | Article |
| id | doaj-art-098795a41d154fac859e2c0f2e226579 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-098795a41d154fac859e2c0f2e2265792025-02-09T12:07:18ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025115310.1007/JHEP01(2025)192Drinfel’d doubles, twists and all that. . . in stringy geometry and M theoryAybike Çatal-Özer0Keremcan Doğan1Cem Yetişmişoğlu2Department of Mathematics, İstanbul Technical UniversityDepartment of Mathematics, İstanbul Technical UniversityDepartment of Mathematics, İstanbul Technical UniversityAbstract Drinfel’d doubles of Lie bialgebroids play an important role in T-duality of string theories. In the presence of H and R fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two dual vector bundles, and the Drinfel’d double yields a Courant algebroid. However for U-duality, more complicated direct sum decompositions that are not described by dual vector bundles appear. In a previous work, we extended the notion of a Lie bialgebroid for vector bundles that are not necessarily dual. We achieved this by introducing a framework of calculus on algebroids and examining compatibility conditions for various algebroid properties in this framework. Here our aim is two-fold: extending our work on bialgebroids to include both H- and R-twists, and generalizing proto Lie bialgebroids to pairs of arbitrary vector bundles. To this end, we analyze various algebroid axioms and derive twisted compatibility conditions in the presence of twists. We introduce the notion of proto bialgebroids and their Drinfel’d doubles, where the former generalizes both bialgebroids and proto Lie bialgebroids. We also examine the most general form of vector bundle automorphisms of the double, related to twist matrices, that generate a new bracket from a given one. We analyze various examples from both physics and mathematics literatures in our framework.https://doi.org/10.1007/JHEP01(2025)192Differential and Algebraic GeometryM-TheoryString Duality |
| spellingShingle | Aybike Çatal-Özer Keremcan Doğan Cem Yetişmişoğlu Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory Journal of High Energy Physics Differential and Algebraic Geometry M-Theory String Duality |
| title | Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory |
| title_full | Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory |
| title_fullStr | Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory |
| title_full_unstemmed | Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory |
| title_short | Drinfel’d doubles, twists and all that. . . in stringy geometry and M theory |
| title_sort | drinfel d doubles twists and all that in stringy geometry and m theory |
| topic | Differential and Algebraic Geometry M-Theory String Duality |
| url | https://doi.org/10.1007/JHEP01(2025)192 |
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