Supergravity couplings to Noncommutative Branes, Open Wilson Lines and Generalised Star Products

TL;DR

This paper identifies gauge-invariant operators involving open Wilson lines on noncommutative D-branes that couple to supergravity backgrounds, clarifying the role of generalized star products and their relation to string amplitudes.

Contribution

It proposes a construction of supergravity coupling operators on noncommutative D-branes using lower-dimensional gauge theories and the Seiberg-Witten map, including their relation to generalized star products.

Findings

Operators involving open Wilson lines couple to supergravity backgrounds.

The generalized star product appears in open Wilson line expansions and string amplitude computations.

The approach can produce operators holographically dual to supergravity modes.

Abstract

Noncommutative gauge theories can be constructed from ordinary $U(\infty)$ gauge theories in lower dimensions. Using this construction we identify the operators on noncommutative D-branes which couple to linearized supergravity backgrounds, from a knowledge of such couplings to lower dimensional D-branes with no $B$ field. These operators belong to a class of gauge invariant observables involving open Wilson lines. Assuming a DBI form of the coupling we show, to second order in the gauge potential but to all orders of the noncommutativity parameter, that our proposal agrees with the operator obtained in terms of ordinary gauge fields by considering brane actions in backgrounds and then using the Seiberg-Witten map to rewrite this in terms of noncommutative gauge fields. Our result clarify why a certain {\it commutative} but {\it non-associative} ``generalized star product'' appears both in the expansion 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 used to obtain operators in the noncommutative theory which are holographically dual to supergravity modes.