Higher-twist fermionic operators and DIS structure functions from the AdS/CFT duality

David Jorrin,Martin Schvellinger

doi:10.1103/physrevd.103.106012

Abstract

The role of local higher-twist ($\tau > 3$) spin-1/2 fermionic operators of the strongly coupled ${\cal {N}}=4$ supersymmetric Yang-Mills theory on the symmetric and antisymmetric deep inelastic scattering (DIS) structure functions is investigated. The calculations are carried out in terms of the duality between ${\cal {N}}=4$ SYM theory and type IIB supergravity on AdS$_5 \times S^5$. Particularly, we explicitly obtain the structure functions for single-trace spin-1/2 fermionic operators in the 20$^*$ and 60$^*$ irreducible representations of $SU(4)_R$, corresponding to twists 4 and 5, respectively. We also calculate the contributions of other single-trace spin-1/2 fermionic operators in the 4, 20 and 60 irreducible representations of $SU(4)_R$. New important effects are found in comparison with the minimal twist ($\tau = 3$) case, and they are studied thoroughly.

Highlights

Deep inelastic scattering (DIS) cross sections of charged leptons by hadrons are expressed as the contraction of a leptonic tensor with a hadronic one
In [10] we have shown that for τ 1⁄4 3 spin-1=2 fermionic operators the effects due to Pauli terms account for about 90% of each structure function, they play a very important role in the DIS process of SUðNÞ N 1⁄4 4 SYM theory at strong coupling in the planar limit
In the present work we investigate the contributions given by local single-trace higher-twist (τ > 3) spin-1=2 fermionic operators of the strongly coupled SUðNÞ N 1⁄4 4 SYM theory on both the symmetric and the antisymmetric structure functions of a polarized spin-1=2 hadron

Summary

INTRODUCTION

Deep inelastic scattering (DIS) cross sections of charged leptons by hadrons are expressed as the contraction of a leptonic tensor with a hadronic one. This means that in terms of the AdS=CFT duality one has to deal with an increasing number of operators on the gauge theory side, and with the same number of Kaluza-Klein dilatino modes on the type IIB supergravity side For this reason, and in order to show explicitly the new effects we find for higher-twist operators we only carry out the explicit calculations of the hadronic tensor in the cases of twist-4 and twist-5 spin-1=2 fermionic operators. Another important point that will be specified later is the relation between l1 and the charge Q given in Eq (3.5)

THE DUAL TYPE IIB SUPERGRAVITY CALCULATION OF THE STRUCTURE FUNCTIONS

Findings

COMMENTS ON THE RESULTS AND CONCLUSIONS