$\alpha$-Symmetries, Coloured Dimensions and Gauge-String Correspondence

TL;DR

This paper proposes a gauge-string correspondence linking SU(3) color symmetry to hidden extra-dimensional isometries in superstring theory, leading to gluon vertex operators with field-theoretic scattering amplitudes and a novel interpretation of extra dimensions.

Contribution

It introduces a new model connecting SU(3) color symmetry to hidden space-time isometries via $ ext{α}$-symmetries, with gluon vertices exhibiting closed operator algebra and field-theoretic scattering.

Findings

Gluon vertex operators form a closed algebra with zigzag symmetry.

Scattering amplitudes resemble field theory, lacking massive string states.

Model suggests three hidden dimensions each associated with SU(3) color and anticolor.

Abstract

We propose a scenario of gauge-string correspondence by relating the SU(3) colour group to hidden space-time isometries originating from extra dimensions. These isometries ($\alpha$-symmetries) are the special symmetries of RNS superstring theories under global non-linear space-time transformations. The vertex operators for the octet of gluons are constructed by the procedure of ``photon painting'', that is, with the SU(3) subgroup of the $\alpha$-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator algebra of these massless gluon vertices is closed and possesses the full zigzag symmetry, crucial for the isomorphism between open strings and QCD. As a result, the scattering amplitudes of the constructed open string vertex operators have a field-theoretic rather than a stringy structure, including the absense of standard tower of massive intermediate states.Our model also suggests that the total number of underlying hidden dimensions is three, with each extra dimension carrying its appropriate SU(3) colour and anticolour.