TY - JOUR

T1 - Drinfeld twist and general relativity with fuzzy spaces

AU - Kürkçüoglu, Seçkin

AU - Saemann, Christian

N1 - 24 pages; uses youngtab.sty; v2: minor changes; version to appear in CQG

PY - 2007/1/21

Y1 - 2007/1/21

N2 - We give a simplified formula for the star product on CP^n_L, 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 CP^n_L. Furthermore, the twist allows us to define a covariant tensor calculus on CP^n_L from the perspective of the standard embedding of CP^n in flat Euclidean space. That is, we find a representation of a truncated subgroup of the diffeomorphisms on CP^n on the algebra of functions on CP^n_L. Using this calculus, we eventually write down an Einstein-Hilbert action on the fuzzy sphere, which is invariant under twisted diffeomorphisms.

AB - We give a simplified formula for the star product on CP^n_L, 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 CP^n_L. Furthermore, the twist allows us to define a covariant tensor calculus on CP^n_L from the perspective of the standard embedding of CP^n in flat Euclidean space. That is, we find a representation of a truncated subgroup of the diffeomorphisms on CP^n on the algebra of functions on CP^n_L. Using this calculus, we eventually write down an Einstein-Hilbert action on the fuzzy sphere, which is invariant under twisted diffeomorphisms.

U2 - 10.1088/0264-9381/24/2/003

DO - 10.1088/0264-9381/24/2/003

M3 - Article

SN - 0264-9381

VL - 24

SP - 291

EP - 312

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 2

ER -