S-duality, noncritical open string and noncommutative gauge theory

Abstract

We examine several aspects of S-duality of four-dimensional noncommutative gauge theory. By making duality transformation explicit, we find that S-dual of noncommutative gauge theory is defined in terms of dual noncommutative deformation. In 'magnetic' noncommutative U(1) gauge theory, we show that, in addition to gauge bosons, open D-strings constitute important low-energy excitations: noncritical open D-strings. Upon S-duality, they are mapped to noncritical open F-strings. We propose that, in dual 'electric' noncommutative U(1) gauge theory, the latters are identified with gauge-invariant, open Wilson lines. We argue that the open Wilson lines are chiral due to underlying parity noninvariance and obey spacetime uncertainty relation. We finally argue that, at high energy-momentum limit, the 'electric' noncommutative gauge theory describes correctly dynamics of delocalized multiple F-strings.

IIA/B, wound and wrapped

“…In the case of compact Euclidean time the result of such a Tduality is to map a straight torus with a B-field into a tilted torus without a B-field. The spectrum is of course invariant under this transformation, so it is still given by the mass formula (23), except that w and n are interpreted in the IIA theory as momentum and winding, respectively. One should note that the second term, linear in B 01 , is no longer due to winding and the presence of a B-field, but to a mixing of momentum and energy resulting from the non-diagonal metric (30).…”

On the unitarity of quantum gauge theories on non-commutative spaces

“…By expanding on the complete set of energy eigenfunctions, after time translations, the loop acquires the expression (for Euclidean time) In the non-commutative case the Wilson loop can be defined by means of the Moyal product as [15,16] …”

Open Wilson lines and generalized star product in noncommutative scalar field theories

“…For fields transforming in 'adjoint' representations under the noncommutative gauge group, it has been shown that the only physical observables are the 'open Wilson lines' [6,3,4,5] along an open contour C:…”