Quantum Gravity and String Theory

   

On n-ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces

Authors: Carlos Castro

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X1,X2, ......,Xn] with the poly-vector valued coordinates X123...n in noncommutative Clifford spaces is explicitly derived [X1,X2, ......,Xn] = n! X123...n. The large N limit of n-ary commutators of n hyper-matrices Xi1i2....in leads to Eguchi-Schild p-brane actions for p + 1 = n. Noncommutative Clifford-space gravity as a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces would require quantum Hopf algebraic deformations of Clifford algebras.

Comments: 25 Pages. This article has been submitted to the J. Math. Phys.

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Submission history

[v1] 24 Sep 2009

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