The characterization of the transverse structure of the QCD string is discussed. We formulate a conjecture as to how the stress-energy tensor of the underlying gauge theory couples to the string degrees of freedom. A consequence of the conjecture is that the energy density and the longitudinal-stress operators measure the distribution of the transverse position of the string, to leading order in the string fluctuations, whereas the transverse-stress operator does not. We interpret recent numerical measurements of the transverse size of the confining string and show that the difference of the energy and longitudinal-stress operators is a particularly natural probe at next-to-leading order. Second, we derive the constraints imposed by open-closed string duality on the transverse structure of the string. We show that a total of three independent “gravitational” form factors characterize the transverse profile of the closed string, and obtain the interpretation of recent effective string theory calculations: the square radius of a closed string of length $\beta$ defined from the slope of its gravitational form factor, is given by $\frac{d-1}{2\pi \sigma }\log \frac{\beta }{4r_0}$ in $d$ space dimensions. This is to be compared with the well-known result that the width of the open string at midpoint grows as $\frac{d-1}{2\pi \sigma }\log \frac{r}{r_0}$. We also obtain predictions for transition form factors among closed-string states.

• Received 16 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.106001