We argue that the gauge-invariant operators on non-commutative branes which couple to different modes of the closed bosonic string are in one-to-one correspondence with the operators which appear in a harmonic expansion of an open Wilson line, defined on an arbitrary contour, around a certain straight line contour. An analogue of the level matching condition on the gauge theory operators emerges quite naturally from the cyclic symmetry of the straight Wilson line. Moreover, the generating functional of the correlation functions of these operators has the spacetime gauge symmetry that one expects to find in the closed bosonic string field theory at the linearized level.
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