The transverse structure of the QCD string

TL;DR

This paper investigates the transverse structure of the QCD string, proposing a coupling between the gauge theory's stress-energy tensor and string degrees of freedom, and derives new theoretical constraints and predictions for string profiles and form factors.

Contribution

It introduces a conjecture on how the stress-energy tensor couples to the string, analyzes the transverse size using operators, and derives constraints from open-closed string duality, providing new insights into string structure.

Findings

Energy density and longitudinal-stress operators measure transverse string distribution.

The difference between energy and longitudinal-stress operators is a key probe for string size.

The transverse profile of the closed string is characterized by three gravitational form factors.

Abstract

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 the appropriate probe to use when comparing with the next-to-leading order string prediction. Secondly 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 (d-1)/(2\pi\sigma)\log(\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 mid-point grows as (d-1)/(2\pi\sigma) log(r/r_0). We also obtain predictions for transition form factors among closed-string states.