| Autor: |
Ralph Blumenhagen, Michael Fuchs, Matthias Traube |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
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| Zdroj: |
Journal of High Energy Physics, Vol 2017, Iss 10, Pp 1-21 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
1029-8479 |
| DOI: |
10.1007/JHEP10(2017)163 |
| Popis: |
Abstract It is believed that any classical gauge symmetry gives rise to an L∞ algebra. Based on the recently realized relation between classical W $$ \mathcal{W} $$ algebras and L∞ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum W algebras, we provide a physically well motivated definition of quantum L∞ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces X 0 and X −1 containing the symmetry variations and the symmetry generators. This quantum L∞ algebra structure is explicitly exemplified for the quantum W 3 $$ {\mathcal{W}}_3 $$ algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L∞ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L∞ algebra of closed string field theory. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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