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Note about string theory with deformed dispersion relations

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Abstract

The goal of this short paper is to find Lagrangian for bosonic string with deformed dispersion relation proposed by J. Magueijo and L. Smolin in 2004. We also show that in the preferred case \(f=g\) this Lagrangian reduces into Nambu-Gotto form of relativistic string without modification of the dispersion relation.

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Notes

  1. See also [4,5,6, 16, 17].

  2. We introduced the vector \(K^M\) in order to deal with covariant prescription that could simplify calculations and hence we can set \(K^M\) to be equal \(\delta ^M_0\) in the end. In other words, \(K^M\) is not related to any possible Killing vectors of the background metric.

  3. More generally we could consider situation when \(f=Dg\) where D is constant. Then (17) implies that B is equal to zero and (16) reduces to Nambu-Gotto action with prefactor \(\sqrt{D}\) that could be eliminated by appropriate rescaling of \(x^\mu \) coordinates.

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Acknowledgements

This work is supported by the grant “Integrable Deformations” (GA20-04800S) from the Czech Science Foundation (GACR).

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  1. Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    J. Klusoň

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Klusoň, J. Note about string theory with deformed dispersion relations. Gen Relativ Gravit 54, 61 (2022). https://doi.org/10.1007/s10714-022-02945-0

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