### Abstract

Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality.

Original language | English (US) |
---|---|

Pages (from-to) | 873-892 |

Number of pages | 20 |

Journal | Fortschritte der Physik |

Volume | 61 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Fortschritte der Physik*,

*61*(10), 873-892. https://doi.org/10.1002/prop.201300010

}

*Fortschritte der Physik*, vol. 61, no. 10, pp. 873-892. https://doi.org/10.1002/prop.201300010

**Nonassociativity, Malcev algebras and string theory.** / Günaydin, M.; Minic, D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Nonassociativity, Malcev algebras and string theory

AU - Günaydin, M.

AU - Minic, D.

PY - 2013/10/1

Y1 - 2013/10/1

N2 - Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality.

AB - Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out that under certain assumptions these nonassociative structures coincide with nonassociative Malcev algebras which had appeared in the quantum mechanics of systems with non-vanishing three-cocycles, such as a point particle moving in the field of a magnetic charge. We generalize the corresponding Malcev algebras to include electric as well as magnetic charges. These structures find their classical counterpart in the theory of Poisson-Malcev algebras and their generalizations. We also study their connection to Stueckelberg's generalized Poisson brackets that do not obey the Jacobi identity and point out that nonassociative string theory with a fundamental length corresponds to a realization of his goal to find a non-linear extension of quantum mechanics with a fundamental length. Similar nonassociative structures are also known to appear in the cubic formulation of closed string field theory in terms of open string fields, leading us to conjecture a natural string-field theoretic generalization of the AdS/CFT-like (holographic) duality.

UR - http://www.scopus.com/inward/record.url?scp=84885154876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885154876&partnerID=8YFLogxK

U2 - 10.1002/prop.201300010

DO - 10.1002/prop.201300010

M3 - Article

AN - SCOPUS:84885154876

VL - 61

SP - 873

EP - 892

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

IS - 10

ER -