Report
Braided Symmetries in Noncommutative Field Theory
| العنوان: | Braided Symmetries in Noncommutative Field Theory |
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| المؤلفون: | Giotopoulos, Grigorios, Szabo, Richard J. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematical Physics, Mathematics - Algebraic Topology, Mathematics - Quantum Algebra |
| الوصف: | We give a pedagogical introduction to $L_\infty$-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective field theories in string theory. We review recent developments which formulate field theories with braided gauge symmetries as a new means of overcoming several obstacles in the standard noncommutative theories, such as the restrictions on gauge algebras and matter fields. These theories can be constructed by using techniques from Drinfel'd twist deformation theory, which we review in some detail, and their symmetries and dynamics are controlled by a new homotopy algebraic structure called a 'braided $L_\infty$-algebra'. We expand and elaborate on several novel theoretical issues surrounding these constructions, and present three new explicit examples: the standard noncommutative scalar field theory (regarded as a braided field theory), a braided version of $BF$ theory in arbitrary dimensions (regarded as a higher gauge theory), and a new braided version of noncommutative Yang-Mills theory for arbitrary gauge algebras. Comment: 79 pages; v2: references added; v3: reference added; Final version to appear in the Special Issue of Journal of Physics A on "Noncommutative Geometry in Physics" |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1751-8121/ac5dad |
| URL الوصول: | http://arxiv.org/abs/2112.00541 |
| رقم الانضمام: | edsarx.2112.00541 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1751-8121/ac5dad |
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