Open Wilson Lines as States of Closed String

TL;DR

This paper explores the relationship between open Wilson lines and closed string states in a bosonic string theory with a B field, revealing insights into non-commutative field theories and bulk-boundary duality at a trans-string scale.

Contribution

It establishes a novel correspondence between open Wilson lines and closed string states, and analyzes the UV behavior of non-commutative field theories using boundary states and zero-slope limits.

Findings

Field theories at a trans-string scale may be topological.

Generating functions factorize into open Wilson lines with Gaussian path distributions.

Proof of the Dhar-Kitazawa conjecture via explicit state-path correspondence.

Abstract

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. UV behaviors of field theories on the non-commutative world-volume are investigated by using these states. We take zero-slope limits of 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. Existence of $B$ field allows the limits to be slightly different from the standard field theory limits of closed-string. They enable us to capture world-volume theories at a trans-string scale. In this limit the generating functions are shown to be factorized by two curved open Wilson lines (and their analogues) and become integrals on the space of paths with a Gaussian distribution around straight lines. These indicate a 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 making 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.