Spin-1/2 fermionic operators of $$ \mathcal{N} $$ = 4 SYM theory and DIS from type IIB supergravity

Abstract

We study deep inelastic scattering (DIS) of charged leptons from polarised spin-1/2 hadrons in terms of the gauge/gravity duality. We calculate the structure functions related to spin-1/2 fermionic operators of N = 4 SYM theory in the planar limit and at strong coupling. Specifically, we focus on the twist-3 operator which is dual to a certain dilatino mode and gives the leading contribution to the hadronic tensor. We consider the Bjorken variable within the parametric range λ −1/2 SYM ≪ x < 1 where the supergravity dual description holds. From dimensional reduction of type IIB supergravity on the five-sphere, we derive the interaction terms involving two dilatini and a massless vector field mode. This vector field is a linear combination of certain components of the graviton and the four-form potential. The angular integrals on the five-sphere lead to selection rules for the interactions with important consequences on the dynamics. This implies the existence of new terms contributing to the structure functions that we explicitly calculate. The leading contribution comes from the Pauli term, followed by the contributions from the new terms we found.

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

“…In the operator product expansion (OPE) of two electromagnetic currents inside a hadron there are several kinds of contributions from different SYM theory operators, which in certain parametric domains can be relevant depending on the virtual-photon momentum q, the coupling g SY M , the Bjorken parameter x, and the number of color degrees of freedom N. Certain properties of the hadronic tensor as well as relations among different structure functions, such as the Callan-Gross relation and generalizations of it, are valid for different gauge field theories, at least within the same parametric regimes of q, g SY M , x, and N. In particular, this behavior has been found in the framework of the gauge/string theory duality [1,2,3] in diverse situations for the strongly coupled regime of different gauge theories, starting from the pioneering work by Polchinski and Strassler [4]. Structure functions of spin-1/2 hadrons have been investigated in this context in [4,5,6,7,8,9,10]. These techniques have been also applied to the study of the structure functions of scalar and vector mesons from Dp-brane systems with flavor branes preserving some supersymmetries as in the D3D7-brane model [11], or breaking supersymmetry completely as in the Sakai-Sugimoto model [12] and in the D4D6 anti-D6brane model [13], which have been considered in [14,15,16,17,18,19,20].…”

“…These operators transform in the [1, k, 0] irreducible representation of the R-symmetry group of the N = 4 SYM theory, being k ≥ 0 (see for instance [37,38] and references therein). The case for k = 0 has been investigated in detail in [10]. In that situation there are just 4 operators of the form O I 0 ,(6) k=0 (x) = C I 0 , (6) Tr(F + λ N =4 )(x), corresponding to τ = 3, which are in the 4 * irreducible representation of SU(4) R .…”

“…There is a factorization in terms of (Λ 2 /q 2 ) τ −1 . The twist is defined as τ = ∆ − s, for an operator with scaling dimension ∆ and spin s. In a previous paper [10] we have considered single-trace spin-1/2 fermionic operators with τ = 3 which belong to the 4 * irreducible representation of SU(4) R . For that purpose firstly we have derived the corresponding terms in the effective five-dimensional supergravity action containing the coupling of two dilatino modes with a massless vector field.…”

“…Those terms in the five-dimensional action, which we briefly discuss in Section 3 of the present work, are the minimal coupling and two Pauli terms, one of which connects the same incoming and intermediate states (in the forward Compton scattering related to the DIS process via the optical theorem) and a second one which allows for certain different intermediate states that we study in detail. In [10] we have shown that for τ = 3 spin-1/2 fermionic operators the effects due to Pauli terms account for about 90% of each structure function, thus they play a very important role in the DIS process of SU(N) N = 4 SYM theory at strong coupling in the planar limit.…”

Proton structure functions from an AdS/QCD model with a deformed background

“…[24,26] the authors studied DIS for vector particles, while in Refs. [9,14,23,25,38] for baryonic DIS.…”