Open Wilson Lines as States of Closed String

Abstract

A system of a D-brane in bosonic string theory on a constant B field background is studied in order to obtain further insight into the bulk-boundary duality. Boundary states which describe arbitrary numbers of open-string tachyons and gluons are given. The UV behavior of field theories on the non-commutative world-volume is investigated by using these states. We take the zero-slope limits of the generating functions of one-loop amplitudes of gluons (and open-string tachyons) in which the region of the small open-string proper time is magnified. The existence of a B field allows the limits to be slightly different from the standard field theory limits of a closed-string. These limits enable us to obtain world-volume theories at a trans-string scale. In this limit the generating functions are shown to be factorized into two curved open Wilson lines (and their analogues) and become integrals on the space of paths with a Gaussian distribution around straight lines. These facts indicate the possibility that field theories on the non-commutative world-volume are topological at such a trans-string scale. We also give a proof of the Dhar-Kitazawa conjecture by determining an explicit correspondence between the closed-string states and the paths. Momentum eigenstates of closed-string or momentum loops also play an important role in these analyses. §1. IntroductionSystems of interacting open-and closed-strings play important roles in several aspects of string theory. It has been found out that even theories formulated as pure closed-strings have open-string sectors when they are accompanied by D-branes. 1) One of the most important features of such open-closed mixed systems is the duality between open-and closed-strings. This duality becomes manifest, for instance, by seeing one-loop diagrams of an open-string as tree propagations of a closed-string through modular transformations on the string world-sheets. In systems of D-branes, this duality should be a rationale for the correspondence between gauge theory on the world-volumes (the open-string sector) and gravity theory in the bulk space-time (the closed-string sector). The AdS/CFT correspondence 2)−4) may be regarded as one of the most remarkable examples of such a bulk-boundary correspondence. This viewpoint is emphasized also in Ref. 5).Nevertheless, it is very difficult to establish the correspondence between the two. This is essentially because light particles (IR effects) in one sector are realized by summing up whole massive towers (UV effects) in the other sector. When a constant B field background of closed-string is turned on, however, we expect that the situation * )

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“…is the noncommutativity parameter. 25) For these operators, after a straightforward computation, 31) we obtain…”

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“…The gauge invariant observables of NC gauge theory, the Wilson lines were constructed through matrix models [8] [9]. In bosonic string theory, they are the emission vertex operators for the entire closed string modes [10] [11].…”

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“…See[29] for an alternative derivation of an analogous expression in the context of bosonic string theory.…”