Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-06-19
Nucl.Phys. B715 (2005) 695-712
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, v2: reference added, v3: corrections in sec.3, references added
Scientific paper
10.1016/j.nuclphysb.2005.02.003
We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational degrees of freedom can be performed exactly even in the presence of a matter field. In the matter sector, we study possible choices of the operators describing quantum fluctuations and define their basic properties (e.g., the Lichnerowicz formula). Then we evaluate two leading terms in the heat kernel expansion, calculate the conformal anomaly and the Polyakov action (as an expansion in the conformal field).
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