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We present a systematic method to derive the chiral kinetic theory from the Wigner equations based on quantum field theory order by order. We take special effort to derive the chiral kinetic theory in seven-dimensional phase space from the eight-dimensional chiral kinetic theory. We give the seven-dimensional chiral kinetic theory up to second order of semiclassical expansion. We find some new second-order contributions compared with other approaches., Comment: 24 pages

We derive self-consistent constraint conditions for collision terms in quantum kinetic theory using the Wigner function formalism. We present specific solutions for these collision terms that align with the constraints. we develop quantum kinetic theory at relaxation-time approximation. With this framework, we discuss spin polarization and electric charge separation effects in relativistic heavy-ion collisions., Comment: 27 pages, other constraint conditions discussed, journal format changed

We have derived the Wigner equations at global equilibrium with constant vorticity but space-time dependent electromagnetic fields up to second order in semiclassical expansion. We obtain the new second-order contributions to the charge currents and energy-momentum tensor from the varying electromagnetic fields. We also compute the new corrections to the spin polarization pesudo-vector from both contant and varying electromagnetic fields. We also find that the space-time dependent electromagnetic field provides a tighter constraint on the solutions of Wigner functions in global equilibrium compared with constant electromagnetic field., Comment: 20 pages, typos corrected, Sec.VI reorganized

We revisit the spin effects induced by thermal vorticity by calculating them directly from the spin-dependent distribution functions. For the spin-1/2 particles, we give the polarization up to the first order of thermal vorticity and compare it with the usual result calculated from the spin vector. For the spin-1 particles, we find that all the non-diagonal elements vanish and there is no spin alignment up the first order of thermal vortcity. We present the spin alignment at second-order contribution from thermal vorticity. We also find that the spin effects for both Dirac and vector particles will receive extra contribution when the spin direction is associated with the particle's momentum., Comment: 23 pages, no figures, the definition of the circular polarization vector for spin-1 changed and non-diagonal elements of spin density matrix for spin-1 changed

We investigate the hydrodynamic helicity polarization of $\Lambda$ hyperons, defined as the projection of the spin polarization vector along the directions of particle momenta, at RHIC-BES energies by utilizing the relativistic (3+1)D CLVisc hydrodynamics framework with SMASH initial conditions. As opposed to local spin polarization at high energy collisions, our hydrodynamic simulations demonstrate that the helicity polarization induced by the kinetic vorticity dominates over other contributions at intermediate and low collision energies. Our findings provide an opportunity to probe the fine structure of local kinetic vorticity as a function of azimuthal angle at intermediate and low collision energies by mapping our predictions to the future measurements in experiments., Comment: 8 pages, 3 figures

We derive the generalized chiral kinetic equations which are applicable to the fermions with arbitrary mass. We show how the dynamical magnetic-moment distribution function could lead to spin polarization and electric charge separation. We also show how the electric/magnetic moment distribution and pseudoscalar distribution could be induced by vorticity and electromagnetic field in global equilibrium., Comment: 6 pages, no figures

The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this paper we will show that how these constraints can be applied to determine the non-dissipative transport coefficients for chiral systems along with the energy-momentum conservation, chiral anomaly for charge current and trace anomaly in energy-momentum tensor., Comment: 9 pages, no figures, submitted to Symmetry for the special issue "Symmetry with Chiral Magnetic Effects and Chiral Transports"

We study helicity polarization through the (3+1) dimensional relativistic viscous hydrodynamic models at $\sqrt{s_{NN}}=200$GeV Au+Au collisions. Similar to the local spin polarization, we consider the helicity polarization beyond global equilibrium and investigate the contributions induced by thermal vorticity, shear viscous tensor, and the fluid acceleration. We find that the local helicity polarization induced by thermal vorticity dominates over other contributions. It also implies that in the low-energy collisions, the the fluid vorticity as part of thermal vorticity may play the crucial role to the total helicity polarization. Such a finding could be useful for probing the local strength of vorticity in rotational quark gluon plasmas by measuring helicity polarization. Our simulation confirms the strict space reversal symmetry, whereas we also compare our numerical results with approximated relations derived from ideal Bjorken flow. Our studies also provide a baseline for the future investigation on local parity violation through the correlations of helicity polarization., Comment: 27 pages, 9 figures

We derive the chiral kinetic equation in 8 dimensional phase space in non-Abelian $SU(N)$ gauge field within the Wigner function formalism. By using the "covariant gradient expansion", we disentangle the Wigner equations in four-vector space up to the first order and find that only the time-like component of the chiral Wigner function is independent while other components can be explicit derivative. After further decomposing the Wigner function or equations in color space, we present the non-Abelian covariant chiral kinetic equation for the color singlet and multiplet phase-space distribution functions. These phase-space distribution functions have non-trivial Lorentz transformation rules when we define them in different reference frames. The chiral anomaly from non-Abelian gauge field arises naturally from the Berry monopole in Euclidian momentum space in the vacuum or Dirac sea contribution. The anomalous currents as non-Abelian counterparts of chiral magnetic effect and chiral vortical effect have also been derived from the non-Abelian chiral kinetic equation., Comment: 19 pages, no figures

We discuss the helicity polarization which can be locally induced from both vorticity and helicity charge in non-central heavy ion collisions. Helicity charge redistribution can be generated in viscous fluid and contributes to azimuthal asymmetry of the polarization along global angular momentum or beam momentum. We also discuss on detecting the initial net helicity charge from topological charge fluctuation or initial color longitudinal field by the helicity polarization correlation of two hyperons and the helicity alignment of vector mesons in central heavy ion collisions., Comment: 5 pages, no figures, some typos corrected, more references added, averaged spin alignment with elliptic flow added

We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which satisfy 32 coupled equations. For massless fermions, the number of independent equations can be significantly reduced due to the decoupling of left-handed and right-handed particles. It can be proved that out of many components of Wigner functions and their coupled equations, only one kinetic equation for the distribution function is independent. This is called the disentanglement theorem for Wigner functions of chiral fermions. For massive fermions, it turns out that one particle distribution function and three spin distribution functions are independent and satisfy four kinetic equations. Various chiral and spin effects such as chiral magnetic and votical effects, the chiral seperation effect, spin polarization effects can be consistently described in the formalism., Comment: 32pages, no figures, published version in IJMPA, more references are added

In non-central high energy heavy ion collisions the colliding system posses a huge orbital angular momentum in the direction opposite to the normal of the reaction plane. Due to the spin-orbit coupling in strong interaction, such huge orbital angular momentum leads to the polarization of quarks and anti-quarks in the same direction. This effect, known as the global polarization effect, has been recently observed by STAR Collaboration at RHIC that confirms the theoretical prediction made more than ten years ago. The discovery has attracted much attention on the study of spin effects in heavy ion collision. It opens a new window to study properties of QGP and a new direction in high energy heavy ion physics -- Spin Physics in Heavy Ion Collisions. In this chapter, we review the original ideas and calculations that lead to the predictions. We emphasize the role played by spin-orbit coupling in high energy spin physics and discuss the new opportunities and challenges in this connection., Comment: prepared for "Lecture Notes in Physics", to appear

We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions. We present updated experimental results for the chiral magnetic effect and related phenomena. The time evolution of the magnetic fields in different models is discussed. The newly developed quantum kinetic theory for massive fermions is reviewed. We present theoretical and experimental results for the polarization of $\Lambda$ hyperons and the $\rho_{00}$ value of vector mesons., Comment: 22 pages, 9 figures. A review article for Nucl. Sci. Tech; more references are added

We construct the grand partition function of the system of chiral fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Taking use of Abel-Plana formula, these thermodynamic quantities can be expanded as series with respect to a dimensionless variable $b=2eB/T^{2}$. We find that the series expansions of energy density, pressure, magnetization intensity and magnetic susceptibility contain a singular term with $\ln b^{2}$, while particle number density, entropy density and heat capacity are power series of $b^{2}$. The asymptotic behaviors of these thermodynamic quantities in extreme conditions are also discussed., Comment: 30 pages, 7 figures

We solve the Wigner equation for massless spin-1/2 charged fermions near global equilibrium. The Wigner function can be obtained order by order in the power expansion of the vorticity and electromagnetic field. The Wigner function has been derived up to the second order from which the non-dissipative charge currents and the stress tensor can be obtained. The charge and energy densities and the pressure have contributions from the vorticity and electromagnetic field at the second order. The vector and axial Hall currents can be induced along the direction orthogonal to the vorticity and electromagnetic field at the second order. We also find that the trace anomaly emerges natually in renormalizing the stress tensor by including the quantum correction from the electromagnetic field., Comment: 31 pages, no figures, accepted version, general solution derived, more detail and more references added

Within Wigner function formalism, the chiral anomaly arises naturally from the Dirac sea contribution in un-normal-ordered Wigner function. For massless fermions, the Dirac sea contribution behaves like a 4-dimensional or 3-dimensional Berry monopole in Euclidian momentum space, while for massive fermions, although Dirac sea still leads to the chiral anomaly but there is no Berry monopole at infrared momentum region. We discuss these points explicitly in a simple and concrete example., Comment: 5 pages, Contribution to the proceedings of XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019)

We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles., Comment: 7 pages, Version submitted to PRD

We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce to 4 independent transport equations. We solve modified on-shell conditions to obtain the general solution and present the corresponding transport equations in three different forms that are suitable for different purposes. We demonstrate how different spin effects arise from the kinetic theory by calculating the chiral separation effect with mass correction, the chiral anomaly from the axial current and the quantum magnetic moment density induced by vorticity and magnetic field. We also show how to generate the global polarization effect due to spin vorticity coupling. The formalism presented may serve as a practical theoretical framework to study different spin effects in relativistic fermion systems encountered in different areas such as heavy ion, astro-particle and condensed matter physics as well., Comment: 5 pages, Typos fixed and references updated

It is more subtle to obtain the chiral vortical effect (CVE) than chiral magnetic effect (CME) in quantum transport approach. To investigate the subtlty of the CVE we present two different derivation in the Wigner function approach. The first one is based on the method in our previous work \cite{Gao:2012ix} in which the CVE was derived under static-equilibrium conditions without details. We provide a detailed derivation using a more transparent and powerful method, which can be easily generalized to higher order calculation. In this derivation of the CVE current, there is an explicit Lorentz covariance. The second derivation is based on a more general chiral kinetic theory in a semi-classical expansion of the Wigner function without assuming static-equilibrium conditions \cite{Gao:2018wmr}. In this derivation, there is a freedom to choose a reference frame for the CVE current, so the explicit Lorentz covariance seems to be lost. Howerver, under static-equilibrium conditions, we show that the CVE current in this derivation can be decomposed into two parts, identified as the normal and magnetization current. Each part depends on the reference frame, but the sum of two parts does give the total CVE current which is independent of the reference frame. In the comoving frame of the fluid, it can be shown that the normal and magnetization current give one-third and two-thirds of the total CVE current respectively. This gives a natural solution to the 'one-third' puzzle in the CVE current in three-dimensional version of the chiral kinetic theory in the literature., Comment: RevTex 4, 13 pages, no figure. The abstract and introduction section have been rewritten to highlight the significance of the main result. The structure of the paper has been re-organized to emphasize two derivations of the CVE. The electromagnetic field contribution in Sec. III has been added. To appear in PRD

We develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant $\hbar$. We demonstrate to any order of $\hbar$ that only the time-component of the Wigner function is independent while other components are explicit derivative. We further demonstrate to any order of $\hbar$ that a system of quantum kinetic equations for multiple-components of Wigner functions can be reduced to one chiral kinetic equation involving only the single-component distribution function. These are remarkable properties of the quantum kinetics of chiral fermions and will significantly simplify the description and simulation of chiral effects in heavy ion collisions and Dirac/Weyl semimetals. We present the unintegrated chiral kinetic equations in four-momenta up to $O(\hbar ^2)$ and the integrated ones in three-momenta up to $O(\hbar)$. We find that some singular terms emerge in the integration over the time component of the four-momentum, which result in a new source term contributing to the chiral anomaly, in contrast to the well-known scenario of the Berry phase term. Finally we rewrite our results in any Lorentz frame with a reference four-velocity and show how the non-trivial transformation of the distribution function in different frames emerges in a natural way., Comment: RevTex 4, 14 pages, no figure. Section II and III have been re-organized and expended to three sections (II-IV) to include more details of calculations. Section V has been expanded to include more discussions. A new section (VI) is added about Wigner functions in a general Lorentz frame. Some references are added

The covariant chiral kinetic equation (CCKE) is derived from the 4-dimensional Wigner function by an improved perturbative method under the static equilibrium conditions. The chiral kinetic equation in 3-dimensions can be obtained by intergation over the time component of the 4-momentum. There is freedom to add more terms to the CCKE allowed by conservation laws. In the derivation of the 3-dimensional equation, there is also freedom to choose coefficients of some terms in $dx_{0}/d\tau$ and $d\mathbf{x}/d\tau$ ($\tau$ is a parameter along the worldline, and $(x_{0},\mathbf{x})$ denotes the time-space position of a particle) whose 3-mometum integrals are vanishing. So the 3-dimensional chiral kinetic equation derived from the CCKE is not uniquely determined in the current approach. To go beyond the current approach, one needs a new way of building up the 3-dimensional chiral kinetic equation from the CCKE or directly from covariant Wigner equations., Comment: ReVTex 4, 23 pages, no figure

We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space-time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields., Comment: RevTex 4, 5 pages, no figure. Appendix A and B are added about derivation of Eq.(7) and about Wigner functions in space-time varying electromagnetic fields. Accepted by PLB

Multiple scattering leads to transverse momentum broadening of the struck quark in semi-inclusive deeply inelastic scatterings (SIDIS). Nuclear broadening of the transverse momentum squared at the leading twist is determined by the twist-four collinear quark-gluon correlation function of the target nucleus that is in turn related to the jet transport parameter inside the nuclear medium. The twist-six contributions to the transverse momentum broadening are calculated as power corrections $\sim 1/Q^2$. Such power corrections are found to have no extra nuclear enhancement beyond the twist-four matrix elements and are determined by the nuclear modification of collinear parton distribution and correlation functions. They become important for an accurate extraction of the jet transport parameter inside large nuclei and its scale evolution at intermediate values of the hard scale $Q^2$., Comment: 11 pages in RevTeX, 1 figure

In this paper, we propose a method of solving the viscous hydrodynamics order by order in a derivative expansion. In such a method, the zero-order solution is just one of the ideal hydrodynamics. All the other higher order corrections satisfy the same first-order partial differential equations but with different inhomogeneous terms. We take the Bjorken flow as an example to test the validity of our method and present how to deal with the problems about the initial condition and perturbation evolution in our formalism., Comment: 17 pages, published version in PRC

We study deep inelastic scattering at large-'t Hooft coupling and finite $x$ from gauge/string duality beyond single-hadron final states which gives the leading large-$N_c$ contribution. Within the supergravity approximation, we calculate the subleading large-$N_c$ contribution by introducing an extra hadron into the final states. We find the contribution from these double-hadron final states will dominate in the Bjorken limit $q^2\rightarrow \infty$ compared with the single-hadron states. We discuss the implications of our results., Comment: 22 pages, 4 figures, published version in PRD

In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogenous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe., Comment: 13 pages, published version in PRD

In this work, we first review the issues on the singularities and the boundary conditions in light cone gauge and how to regularize them properly. Then we will further review how these singularities and the boundary conditions can result in the gauge link at the infinity in the light cone direction in the Drell-Yan process. Except for reviewing, we also have verified that the gauge link at the light cone infinity has no dependence on the path not only for the Abelian field but also for non-Abelian gauge field., Comment: 10 pages, 4 figures. Published version in Phys.Part.Nucl

We study nuclear dependences of azimuthal asymmetries in the Drell-Yan lepton pair production in nucleon-nucleus collisions with polarized nucleons.We use the "maximal two-gluon correlation approximation", so that we can relate the transverse momentum dependent quark distribution in a nucleus to that in a nucleon by a convolution with a Gaussian broadening.We use the Gaussian ansatz for the transverse momentum dependence of such quark distribution functions,and obtain the numerical results for the nuclear dependences.These results show that the averaged azimuthal asymmetries are suppressed., Comment: 17 pages, 2 figures, Published version in PRC

Using the formalism obtained from collinear expansion, we calculate the differential cross section and azimuthal asymmetries in semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process $e^-+N (A) \to e^-+q+X$ with both polarized beam and polarized target up to twist-3. We derive the azimuthal asymmetries in terms of twist-3 parton correlation functions. We simplify the results by using the QCD equation of motion that leads to a set of relationships between different twist-3 functions. We further study the nuclear dependence of azimuthal asymmetries and show that they have similar suppression factors as those in the unpolarized reactions., Comment: version to appear in Phys. Rev. D

We study the kinetic theory for a (2+1)-dimensional fermionic system with special emphasis on the parity violating properties associated with the fermion mass. The Wigner function approach is used to derive hydrodynamical transport coefficients to the first spatial derivative order. As a first attempt, the collisions between fermions are neglected. The resulting system is dissipationless. The parity violating Hall electric conductivity has the same temperature and chemical potential dependence as the quantum field theory result at one-loop. Vorticity dependent transport properties, which were not considered before, also emerge naturally in this approach., Comment: ReVTex 4, 12 pages, no figure. Appendix B and some references are added, the discussion in section III about the Wigner function is improved

A power expansion scheme is set up to determine the Wigner function that satisfies the quantum kinetic equation for spin-1/2 charged fermions in a background electromagnetic field. Vector and axial-vector current induced by magnetic field and vorticity are obtained simultaneously from the Wigner function. The chiral magnetic and vortical effect and chiral anomaly are shown as natural consequences of the quantum kinetic equation. The axial-vector current induced by vorticity is argued to lead to a local polarization effect along the vorticity direction in heavy-ion collisions., Comment: RevTex 4, 4 pages, 1 figure; accepted version in PRL

The energy loss parameter $\hat q$ is one of the fundamental transport parameters of hadronic matter. Using the twist-4 collinear approach, we show that the $\cos \phi$ azimuthal asymmetry in unpolarized semi-inclusive deeply inelastic scattering (SIDIS) off a large nucleus at intermediate transverse momentum is a sensitive observable for its determination. The effect is due to the suppression of the azimuthal asymmetry by final-state multiple scattering., Comment: 9 pages

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering (SIDIS) process $e^-+N \to e^-+q+X$ in leading order (LO) of perturbative QCD and up to twist-4 in power corrections and study in particular the azimuthal asymmetry $$. The final results are expressed in terms of transverse momentum dependent (TMD) parton matrix elements of the target nucleon up to twist-4. %Under the maximal two-gluon correlation approximation, these TMD parton matrix elements in a nucleus %can be expressed terms of a Gaussian convolution of that in a nucleon with the width given by the jet transport %parameter inside cold nuclei. We also apply it to $e^-+A \to e^-+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $$ by using a Gaussian ansatz for the TMD parton matrix elements., Comment: 9 pages, afigure

We provide a consistent description of the kinetic equation with triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for minimum number of unknown coefficients in one charge and two charge cases by solving the constraining equations., Comment: RevTex 4, 11 pages; With minor changes: typos are corrected and one reference is added. Accepted version to PRD

In light cone gauge, a gauge link at light cone infinity is necessary for transverse momentum-dependent parton distribution to restore the gauge invariance in some specific boundary conditions. We derive such transverse gauge link in a more regular and general method. We find the gauge link at light cone infinity naturally arises from the contribution of the pinched poles: one is from the quark propagator and the other is hidden in the gauge vector field in light cone gauge. Actually, in the amplitude level, we have obtained a more general gauge link over the hypersurface at light cone infinity which is beyond the transverse direction. The difference of such gauge link between semi-inclusive deep inelastic scattering and Drell-Yan processes can also be obtained directly and clearly in our derivation., Comment: 18 pages, 5 figures, published version

We investigate deep inelastic scattering off the polarized "neutron" using gauge/string duality. The "neutron" corresponds to a supergravity mode of the neutral dilatino. Through introducing the Pauli interaction term into the action in $\textrm{AdS}_{5}$ space, we calculate the polarized deep inelastic structure functions of the "neutron" in supergravity approximation at large t' Hooft coupling $\lambda$ and finite $x$ with $\lambda^{-1/2}\ll x<1$. In comparison with the charged dilatino "proton," which has been obtained in the previous work by Gao and Xiao, we find the structure functions of the "neutron" are power suppressed at the same order as the ones of the "proton." Especially, we find the Burkhardt-Cottingham-like sum rule, which is satisfied in the work by Gao and Xiao, is broken due to the Pauli interaction term. We also illustrate how such a Pauli interaction term can arise naturally from higher dimensional fermion-graviton coupling through the usual Kaluza-Klein reduction., Comment: 21pages,5figures, published version

Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry $ of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of the azimuthal asymmetry $<\cos\phi>$ is studied. It is shown that the azimuthal asymmetry is suppressed by multiple parton scattering and the transverse momentum dependence of the suppression depends on the relative shape of the twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear dependence of the azimuthal asymmetry and to estimate the smearing effect due to fragmentation., Comment: 9 pages in RevTex with 2 figures

We study the nonforward Compton scattering in particular the deeply virtual Compton scattering from AdS/CFT. We first calculate the contributions from the s-channel and u-channel supergravity diagrams as well as the four point interaction diagram which correspond to the Compton scatterings on a dilaton target in CFT. Furthermore, we study the Compton scattering on a dilatino target. Assuming that protons can be identified as supergravity modes of dilatino, we compare the calculated DVCS cross section to the low-energy experimental data from the H1 and ZEUS collaborations and find good agreement. We also discuss the t-channel graviton exchange contribution and show that it should be dominant in the high-energy limit., Comment: 36 pages, 6 figures, some factors corrected, conclusion not changed

In this paper, we investigate deep inelastic and elastic scattering on a polarized spin-1/2 hadron using gauge/string duality. This spin-1/2 hadron corresponds to a supergravity mode of the dilatino. The polarized deep inelastic structure functions are computed in supergravity approximation at large t' Hooft coupling $\lambda$ and finite $x$ with $\lambda^{-1/2}\ll x<1$. Furthermore, we discuss the moments of all structure functions, and propose an interesting sum rule $\int_{0}^{1} \textrm{d}x g_2(x, q^2) =0$ for $g_2$ structure function which is known as the Burkhardt-Cottingham sum rule in QCD. In the end, the elastic scattering is studied and elastic form factors of the spin-1/2 hadron are calculated within the same framework., Comment: 21 pages, 3 figues.v2:fixed a few typos, ref added. v3: more typos fixed, context edited, ref updated; v4: comments added, 1 more figure added