Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds
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| Format: | Preprint |
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2018
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| _version_ | 1866916102072696832 |
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| author | Nikolić, Bojan Obrić, Danijel |
| author_facet | Nikolić, Bojan Obrić, Danijel |
| contents | In this article we consider closed bosonic string in the presence of constant metric and Kalb-Ramond field with one non-zero component, $B_{xy}=Hz$, where field strength $H$ is infinitesimal. Using Buscher T-duality procedure we dualize along $x$ and $y$ directions and using generalized T-duality procedure along $z$ direction imposing trivial winding conditions. After first two T-dualizations we obtain $Q$ flux theory which is just locally well defined, while after all three T-dualizations we obtain nonlocal $R$ flux theory. Origin of non-locality is variable $ΔV$ defined as line integral, which appears as an argument of the background fields. Rewriting T-dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that $Q$ flux theory is commutative one and the $R$ flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non-locality and closed string noncommutativity and nonassociativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_08772 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds Nikolić, Bojan Obrić, Danijel High Energy Physics - Theory In this article we consider closed bosonic string in the presence of constant metric and Kalb-Ramond field with one non-zero component, $B_{xy}=Hz$, where field strength $H$ is infinitesimal. Using Buscher T-duality procedure we dualize along $x$ and $y$ directions and using generalized T-duality procedure along $z$ direction imposing trivial winding conditions. After first two T-dualizations we obtain $Q$ flux theory which is just locally well defined, while after all three T-dualizations we obtain nonlocal $R$ flux theory. Origin of non-locality is variable $ΔV$ defined as line integral, which appears as an argument of the background fields. Rewriting T-dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that $Q$ flux theory is commutative one and the $R$ flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non-locality and closed string noncommutativity and nonassociativity. |
| title | Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/1801.08772 |