arXiv subjects
Publications and source records attributed to Martin Schvellinger.
The tree-level type II superstring theory scattering amplitude of two dilatons and two dilatinos is explicitly calculated from the Kawai-Lewellen-Tye relations. The corresponding Regge behavior is obtained.
We calculate the glueball-fermion hard-scattering amplitude from the dilaton-dilatino closed string scattering amplitude in type IIB superstring theory, in the framework of the gauge/string theory duality. We investigate its high-energy scaling at fixed angle and also in the Regge limit. We derive the leading and sub-leading terms contributing to the scattering cross section. This dual calculation of the glueball-fermion scattering amplitude is particularly interesting since it involves the scattering of two different types of external states. We calculate explicitly some angular integrals for two scalar spherical harmonics and two spinor spherical harmonics on the five-sphere, leading to selection rules.
An explicit derivation of the four-dilatino scattering amplitude from type II superstring theory is presented. This is obtained by using the Kawai-Lewellen-Tye relations for closed string scattering amplitudes in terms of the product of two open string scattering amplitudes. We also investigate its Regge limit.
We study high-energy scattering at fixed angle in the planar limit of non-Abelian gauge field theories from type IIB superstring theory scattering amplitudes. Firstly, we consider four-glueball scattering described in terms of the four-dilaton string theory scattering amplitude. We explicitly calculate some angular integrals of four scalar spherical harmonics on the five sphere leading to selection rules for several scattering processes. Then, we consider the high-energy limit of the four-dilatino scattering amplitude in type IIB superstring theory, which allows to describe four spin-1/2 fermions scattering in the dual gauge field theory. In both cases the partonic structure of the scattering cross sections is obtained. The Regge behavior is also obtained. In addition, we study certain related aspects by considering the effective action constructed from IIB supergravity.
We present a detailed analysis of the polarized and the unpolarized deep inelastic scattering structure functions of the proton, g_1^p and F_2^p respectively, in the context of a holographic dual description based on type IIB superstring theory. We compare this description with experimental data and Quantum Chromodynamics estimates computed at leading, next-to-leading and next-to-next-to-leading order in perturbation. We confront the predictions of a holographic dual model and those of perturbative QCD for g_1^p at the kinematics that will be probed by the forthcoming Electron-Ion Collider. We find that the extrapolation of g_1^p to very small values the Bjorken variable computed with a Holographic Pomeron model based on actual data at higher momentum fractions is always positive and differs significantly with standard projections based on perturbative QCD.
Symmetric and antisymmetric structure functions from electromagnetic deep inelastic scattering of charged leptons off spin-1/2 hadrons are investigated in the framework of a top-down holographic dual description. We consider the BPST Pomeron, type IIB superstring theory scattering amplitudes, and type IIB supergravity on AdS$_5 \times S^5$. In all cases it is used the hard-wall prescription. Different kinematic regions of the Bjorken variable $x$, as well as the squared momentum of the virtual photon $Q^2$, are studied in detail for $F_2^P$ and $g_1^P$ structure functions of the proton. Also, the virtual Compton scattering asymmetry of the proton $A_1^P$ is investigated. Comparison with data from several experimental collaborations is presented. In addition, the holographic Pomeron leads to predictions for the mentioned observables for very small $x$ values. In particular, we present predictions for $g_1^P$ at $Q^2$ around 10 GeV$^2$, for data expected to be measured in a future electron-ion collider. Limitations of this holographic dual approach are discussed.
The role of local higher-twist ($τ> 3$) 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 ($τ= 3$) case, and they are studied thoroughly.
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 ${\cal {N}}=4$ 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 $λ^{-1/2}_{SYM} \ll x < 1$ 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.
The structure functions $F_1$ and $F_2$ of the hadronic tensor of vector mesons are obtained at order $1/N$ and strong coupling using the gauge/gravity duality. We find that the large $N$ limit and the high energy one do not commute. Thus, by considering the high energy limit first, our results of the first moments of $F_1$ for the rho meson agree well with those from lattice QCD, with an important improvement of the accuracy with respect to the holographic dual calculation in the planar limit.
We study polarized deep inelastic scattering of charged leptons from spin-$1/2$ hadrons at low values of the Bjorken parameter and large 't Hooft coupling in terms of the gauge/string theory duality. We calculate the structure functions from type IIB superstring theory scattering amplitudes. We discuss the role of the non-Abelian Chern-Simons term and the Pauli term from the five-dimensional $SU(4)$ gauged supergravity. Furthermore, the exponentially small-$x$ regime where Regge physics becomes important is analyzed in detail for the antisymmetric structure functions. In this case the holographic dual picture of the Pomeron exchange is realized by a Reggeized gauge field. We compare our results with experimental data of the proton antisymmetric structure function $g_1$, obtaining a very good level of agreement.
We calculate the structure function $F_3(x,q^2)$ of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of ${\cal {N}}=4$ SYM theory at strong coupling and at small values of the Bjorken parameter in the gauge/string theory duality framework. This is done in terms of type IIB superstring theory scattering amplitudes. From the AdS$_5$ perspective, the relevant part of the scattering amplitude comes from the five-dimensional non-Abelian Chern-Simons terms in the $SU(4)$ gauged supergravity obtained from dimensional reduction on $S^5$. From type IIB superstring theory we derive an effective Lagrangian describing the four-point interaction in the local approximation. The exponentially small regime of the Bjorken parameter is investigated using Pomeron techniques.
Deep inelastic scattering (DIS) of charged leptons off scalar mesons in the $1/N$ expansion is studied by using the gauge/gravity duality. We focus on the D3D7-brane system and investigate the corresponding structure functions by considering both the high energy limit and the $1/N$ expansion. These limits do not commute. From the D7-brane DBI action we derive a Lagrangian at sub-leading order in the D7-brane fluctuations and obtain a number of interactions some of which become relevant for two-hadron final-state DIS. By considering first the high energy limit followed by the large $N$ one, our results fit lattice QCD data within $1.27\%$ for the first three moments of $F_2$ for the lightest pseudoscalar meson.
$1/N^2$ corrections to deep inelastic scattering (DIS) of charged leptons from glueballs at strong coupling are investigated in the framework of the gauge/gravity duality. The structure functions $F_1$ and $F_2$ (and also $F_L$) are studied at subleading order in the $1/N^2$ expansion, in terms of $q^2$ and the Bjorken parameter $x$. The relevant type IIB supergravity one-loop diagrams (which correspond to DIS with two-hadron final states) are studied in detail, while $n$-loop diagrams (corresponding to DIS with $(n+1)$-hadron final states) are briefly discussed. The $1/N^{2n}$ and $Λ^2/q^2$ dependence of the structure functions is analyzed. Within this context two very different limits are considered: one is the large $N$ limit and the other one is when the virtual photon momentum transfer $q$ is much larger than the infrared confining scale $Λ$. These limits do not commute.
Differential cross sections of deep inelastic scattering of charged leptons from hadrons are investigated by using the gauge/string duality. We consider vector mesons derived from different holographic dual models obtaining a general expression. We focus on the strongly coupled regime of dual gauge theories for different values of the Bjorken parameter. We find new predictions which are particularly interesting for differential scattering cross sections of polarized leptons scattered off polarized vector mesons. We also carry out a detailed comparison of the moments of the structure functions with lattice QCD results.
Deep inelastic scattering of leptons from hadrons at small values of the Bjorken parameter $x$ is studied from superstring theory. In particular, we focus on single-flavored scalar and vector mesons in the large $N$ limit. This is studied in terms of different holographic dual models with flavor Dp-branes in type IIA and type IIB superstring theories, in the strong coupling limit of the corresponding dual gauge theories. We derive the hadronic tensor and the structure functions for scalar and polarized vector mesons. In particular, for polarized vector mesons we obtain the eight structure functions at small values of the Bjorken parameter. The main result is that we obtain new relations of the Callan-Gross type for several structure functions. These relations have similarities for all different Dp-brane models that we consider. This would suggest their universal character, and therefore, it is possible that they hold for strongly coupled QCD in the large $N$ limit.
Two-point current correlation functions of the large $N$ limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with $N_f > 1$. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of their moments are also derived. Aspects of the sub-leading contributions in the $1/N$ and $N_f/N$ expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.
We investigate the thermalization time scale in the planar limit of the SU(N) N=4 SYM plasma at strong yet finite 't Hooft coupling by considering its supergravity dual description, including the full O(alpha'^3) type IIB string theory corrections. We also discuss on the effects of the leading non-planar corrections. We use extended geometric probes in the bulk which are dual to different non-local observables in the N=4 SYM theory. This is carried out within the framework of dynamical holographic thermalization.
Dynamical evolution of thin shells composed by different kinds of degrees of freedom collapsing within asymptotically AdS spaces is explored with the aim of investigating models of holographic thermalization of strongly coupled systems. From the quantum field theory point of view this corresponds to considering different thermal quenches. We carry out a general study of the thermalization time scale using different parameters and space-time dimensions, by calculating renormalized space-like geodesic lengths and rectangular minimal area surfaces as extended probes of thermalization, which are dual to two-point functions and rectangular Wilson loops. Different kinds of degrees of freedom in the shell are described by their corresponding equations of state. We consider a scalar field, as well as relativistic matter, a pressureless massive fluid and conformal matter, which can be compared with the collapse of an AdS-Vaidya thin shell. Remarkably, for conformal matter, the thermalization time scale becomes much larger than the others. Furthermore, in each case we also investigate models where the cosmological constants of the inner and outer regions separated by the shell are different. We found that in this case only a scalar field shell collapses, and that the thermalization time scale is also much larger than the AdS-Vaidya case.