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Drinfeld twist and general relativity with fuzzy spaces
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Date
2007-01-21
Author
Kürkcüoğlu, Seçkin
SAMANN, Christian
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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We give a simplified formula for the star product on CPLn, which enables us to define a twist element suited for discussing a Drinfeld twist like structure on fuzzy complex projective spaces. The existence of such a twist will have several consequences for field theories on fuzzy spaces, some of which we discuss in the present paper. As expected, we find that the twist of the coproduct is trivial for the generators of isometries on CPLn. Furthermore, the twist allows us to define a covariant tensor calculus on CPLn from the perspective of the standard embedding of CPn in flat Euclidean space. That is, we can - in principle - find a representation of a truncated subgroup of the diffeomorphisms on CPn on the algebra of functions on CPLn. Using this calculus, we eventually write down an Einstein - Hilbert action on the fuzzy sphere, which is invariant under twisted diffeomorphisms.
Subject Keywords
Physics and Astronomy (miscellaneous)
URI
https://hdl.handle.net/11511/35523
Journal
CLASSICAL AND QUANTUM GRAVITY
DOI
https://doi.org/10.1088/0264-9381/24/2/003
Collections
Department of Physics, Article