Towards 1/N corrections to deep inelastic scattering from the gauge/gravity duality

$1/N^2$ 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 $\Lambda^2/q^2$ 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 $\Lambda$. These limits do not commute.Comment: 45 page

Deep inelastic scattering cross sections from the gauge/string duality

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.Comment: 42 pages, 5 tables, 9 figure

Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system

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.Fil: Jorrin, David Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Kovensky, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Schvellinger, Martín Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

On spectrally flowed local vertex operators in AdS3_3

We provide a novel local definition for spectrally flowed vertex operators in the SL(2,$\mathbb{R}$)-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] for the singly-flowed case to all $\omega > 1$. This allows us to establish the precise connection between the computation of correlators using the so-called spectral flow operator, and the methods introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local Ward identities. We show that the auxiliary variable $y$ used in the latter paper arises naturally from a point-splitting procedure in the space-time coordinate. The recursion relations satisfied by spectrally flowed correlators, which take the form of partial differential equations in $y$-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of the SL(2,$\mathbb{R}$) series identifications in this context, and prove the validity of the conjecture put forward in [arXiv:2105.12130] for $y$-space structure constants of three-point functions with arbitrary spectral flow charges.Comment: 25 page

Smearing and Unsmearing KKLT AdS Vacua

Gaugino condensation on D-branes wrapping internal cycles gives a mechanism to stabilize the associated moduli. According to the effective field theory, this gives rise, when combined with fluxes, to supersymmetric AdS$_4$ solutions. In this paper we provide a ten-dimensional description of these vacua. We first find the supersymmetry equations for type II AdS$_4$ vacua with gaugino condensates on D-branes, in the framework of generalized complex geometry. We then solve them for type IIB compactifications with gaugino condensates on smeared D7-branes. We show that supersymmetry requires a (conformal) Calabi-Yau manifold and imaginary self-dual three-form fluxes with an additional (0,3) component. The latter is proportional to the cosmological constant, whose magnitude is determined by the expectation value of the gaugino condensate and the stabilized volume of the cycle wrapped by the branes. This confirms, qualitatively and quantitatively, the results obtained using effective field theory. We find that exponential separation between the AdS and the KK scales seems possible as long as the three-form fluxes are such that their (0,3) component is exponentially suppressed. As for the localized solution, it requires going beyond SU(3)-structure internal manifolds. Nevertheless, we show that the action can be evaluated on-shell without relying on the details of such complicated configuration. We find that no "perfect square" structure occurs, and the result is divergent. We compute the four-fermion contributions, including a counterterm, needed to cancel these divergencies.Comment: 28 page

Spectral flow and string correlators in AdS3×S3×T4_3\times S^3 \times T^4

We consider three-point correlation functions for superstrings propagating in AdS$_3\times S^3 \times T^4$. In the RNS formalism, these generically involve correlators with current insertions. When vertex operators with non-trivial spectral flow charges are present, their complicated OPEs with the currents imply that standard methods can not be used to compute such correlators. Here we develop novel techniques for computing all $m$-basis correlators of the supersymmetric model. We then show how, in some cases, these results can be translated to the $x$-basis. We obtain a new family of holographic three-point functions involving spacetime chiral primaries living in spectrally flowed sectors of the worldsheet CFT. These match precisely the predictions from the holographic dual at the symmetric product orbifold point. Finally, we also consider long strings and compute the probability amplitude associated with the process describing the emission/absorption of fundamental string quanta.Comment: 35 page

A proof for string three-point functions in AdS3_3

Correlation functions of the $\text{SL}(2,\mathbb{R})$-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [arXiv:2105.12130v2]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [arXiv:2208.00978] based on the so-called $\text{SL}(2,\mathbb{R})$ series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the AdS$_3$/CFT$_2$ holographic duality at finite 't Hooft coupling.Comment: 22 page

DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term

We calculate the structure function F3(x, q2) of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of 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 AdS5 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 S5. 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.Fil: Kovensky, Nicolas.Fil: Michalski, Gustavo.Fil: Martin Schvellinger