Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
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| Format: | Preprint |
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2022
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| _version_ | 1866909079772856320 |
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| author | Nikolic, Bojan Sazdovic, Branislav Obric, Danijel |
| author_facet | Nikolic, Bojan Sazdovic, Branislav Obric, Danijel |
| contents | In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^μ$. The derivative of the RR field $C^{αβ}_μ$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T-dual theory is non-local. It is defined in non-geometric space spanned by Lagrange multipliers $y_μ$. We will apply generalized Buscher procedure once more on T-dual theory and prove that original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates $x^μ$, $θ^α$ and $\barθ^α$, while nonassociativity parameter is a constant tensor containing infinitesimal $C^{αβ}_μ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_11651 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field Nikolic, Bojan Sazdovic, Branislav Obric, Danijel High Energy Physics - Theory In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^μ$. The derivative of the RR field $C^{αβ}_μ$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T-dual theory is non-local. It is defined in non-geometric space spanned by Lagrange multipliers $y_μ$. We will apply generalized Buscher procedure once more on T-dual theory and prove that original theory can be salvaged. Finally, we will use T-dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T-dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates $x^μ$, $θ^α$ and $\barθ^α$, while nonassociativity parameter is a constant tensor containing infinitesimal $C^{αβ}_μ$. |
| title | Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2203.11651 |