Skewness Dependence of GPD / DVCS, Conformal OPE and AdS/CFT Correspondence I: Wavefunctions of Regge Trajectory

TL;DR

This paper explores the skewness dependence of GPDs in DVCS using gravity dual models, identifying limitations of existing approaches and deriving wavefunctions on AdS5 to improve the theoretical understanding of non-perturbative hadron scattering.

Contribution

It introduces a new method to determine wavefunctions on AdS5 for GPD analysis, extending the gravity dual Pomeron framework to better capture skewness dependence.

Findings

Identified limitations of the BPST Pomeron in modeling skewness dependence.

Derived wavefunctions on AdS5 as holomorphic functions in j.

Proposed a framework for calculating GPDs via inverse Mellin transform.

Abstract

Traditional idea of Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to exchange of spin-j\in 2Z states in the graviton trajectory. Deeply virtual compton scattering (DVCS) is essentially a 2 to 2 scattering process of a hadron and a photon, and hence one should be able to study non-perturbative aspects (GPD) of this process by the "Pomeron" process in gravity dual. We find, however, that even the most developed formulation of gravity dual Pomeron (Brower--Polchinski--Strassler--Tan (BPST) 2006) is not able to capture skewness dependence of GPD properly. Conformal operator product expansion allows us to determine DVCS amplitude in terms of matrix elements of primary operators, which should then be given by wavefunctions on warped spacetime. We determined all the necessary wavefunctions on AdS$_5$ as an expression holomorphic in $j$, which will then be used (in our forthcoming publication) to determine GPD through inverse Mellin transformation. This approach will extend the formulation of BPST.