Supergravity couplings to noncommutative branes, open Wilson lines and generalized star products

Noncommutative gauge theories can be constructed from ordinary U(infinity) gauge theories in lower dimensions. Using this construction we identify the operators on noncommutative D-branes which couple to linearized supergravi ty backgrounds, from a knowledge of such couplings to lower dimensional D-b ranes with no B-field. These operators belong to a class of gauge invariant observables involving open Wilson lines. Assuming a DBI form of the coupli ng we show, to second order in the gauge potential but to all orders of the noncommutativity parameter, that our proposal agrees with the operator obt ained in terms of ordinary gauge fields by considering brane actions in bac kgrounds and then using the Seiberg-Witten map to rewrite this in terms of noncommutative gauge fields. Our result clarifies why a certain commutative but non-associative "generalized star product" appears both in the expansi on of the open Wilson line, as well as in string amplitude computations of open string-closed string couplings. We outline how our procedure can be us ed to obtain operators in the noncommutative theory which are holographical ly dual to supergravity modes.