Sum rules and dualities for generalized parton distributions: is there a holographic principle?

TL;DR

This paper explores the relationship between different regions of generalized parton distributions (GPDs) through sum rules and dualities, proposing a potential holographic principle linking their behaviors.

Contribution

It introduces a family of GPD sum rules based on Lorentz covariance and cross-over trajectory relations, offering a new phenomenological perspective on GPDs.

Findings

Derived GPD sum rules analogous to finite energy sum rules.

Applied constraints from JLab data on u-quark GPD H.

Discussed the possibility of a holographic principle governing GPDs.

Abstract

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.