Abstract
We calculate the structure function F3(x, q2) of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of \( \mathcal{N}=4 \) 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski and M.J. Strassler, Deep inelastic scattering and gauge/string duality, JHEP 05 (2003) 012 [hep-th/0209211] [INSPIRE].
H.J. Kim, L.J. Romans and P. van Nieuwenhuizen, The mass spectrum of chiral N = 2 D=10 supergravity on S 5, Phys. Rev. D 32 (1985) 389 [INSPIRE].
M. Gunaydin, L.J. Romans and N.P. Warner, Gauged N = 8 supergravity in five-dimensions, Phys. Lett. B 154 (1985) 268.
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 supergravity, Nucl. Phys. B 259 (1985) 460 [INSPIRE].
M. Günaydin, L.J. Romans and N.P. Warner, Compact and noncompact gauged supergravity theories in five-dimensions, Nucl. Phys. B 272 (1986) 598 [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A. Bilal and C.-S. Chu, A note on the chiral anomaly in the AdS/CFT correspondence and 1/N 2 correction, Nucl. Phys. B 562 (1999) 181 [hep-th/9907106] [INSPIRE].
D. Jorrin, N. Kovensky and M. Schvellinger, Towards 1/N corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 [arXiv:1601.01627] [INSPIRE].
J.-H. Gao and Z.-G. Mou, Structure functions in deep inelastic scattering from gauge/string duality beyond single-hadron final states, Phys. Rev. D 90 (2014) 075018 [arXiv:1406.7576] [INSPIRE].
E. Koile, S. Macaluso and M. Schvellinger, Deep inelastic scattering from holographic spin-one hadrons, JHEP 02 (2012) 103 [arXiv:1112.1459] [INSPIRE].
E. Koile, S. Macaluso and M. Schvellinger, Deep inelastic scattering structure functions of holographic spin-1 hadrons with N f ≥ 1, JHEP 01 (2014) 166 [arXiv:1311.2601] [INSPIRE].
E. Koile, N. Kovensky and M. Schvellinger, Hadron structure functions at small x from string theory, JHEP 05 (2015) 001 [arXiv:1412.6509] [INSPIRE].
C. Best et al., Pion and rho structure functions from lattice QCD, Phys. Rev. D 56 (1997) 2743 [hep-lat/9703014] [INSPIRE].
E. Koile, N. Kovensky and M. Schvellinger, Deep inelastic scattering cross sections from the gauge/string duality, JHEP 12 (2015) 009 [arXiv:1507.07942] [INSPIRE].
D. Jorrin, M. Schvellinger and N. Kovensky, Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system, JHEP 12 (2016) 003 [arXiv:1609.01202] [INSPIRE].
S. Ferrara, C. Fronsdal and A. Zaffaroni, On N = 8 supergravity on AdS 5 and N = 4 superconformal Yang-Mills theory, Nucl. Phys. B 532 (1998) 153 [hep-th/9802203] [INSPIRE].
E.J. Schreier, Conformal symmetry and three-point functions, Phys. Rev. D 3 (1971) 980 [INSPIRE].
D.Z. Freedman, G. Grignani, K. Johnson and N. Rius, Conformal symmetry and differential regularization of the three gluon vertex, Annals Phys. 218 (1992) 75 [hep-th/9204004] [INSPIRE].
Y. Hatta, T. Ueda and B.-W. Xiao, Polarized DIS in N = 4 SYM: where is spin at strong coupling?, JHEP 08 (2009) 007 [arXiv:0905.2493] [INSPIRE].
M. Anselmino, A. Efremov and E. Leader, The theory and phenomenology of polarized deep inelastic scattering, Phys. Rept. 261 (1995) 1 [Erratum ibid. 281 (1997) 399] [hep-ph/9501369] [INSPIRE].
B. Lampe and E. Reya, Spin physics and polarized structure functions, Phys. Rept. 332 (2000) 1 [hep-ph/9810270] [INSPIRE].
S. Caron-Huot et al., Photon and dilepton production in supersymmetric Yang-Mills plasma, JHEP 12 (2006) 015 [hep-th/0607237] [INSPIRE].
J. Polchinski and M.J. Strassler, Hard scattering and gauge/string duality, Phys. Rev. Lett. 88 (2002) 031601 [hep-th/0109174] [INSPIRE].
R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].
J.-H. Gao and B.-W. Xiao, Nonforward Compton scattering in AdS/CFT correspondence, Phys. Rev. D 81 (2010) 035008 [arXiv:0912.4333] [INSPIRE].
A. Baguet, O. Hohm and H. Samtleben, Consistent type IIB reductions to maximal 5D supergravity, Phys. Rev. D 92 (2015) 065004 [arXiv:1506.01385] [INSPIRE].
E. D’Hoker et al., Graviton and gauge boson propagators in AdS d+1, Nucl. Phys. B 562 (1999) 330 [hep-th/9902042] [INSPIRE].
J. Bartels, J. Kotanski, A.M. Mischler and V. Schomerus, Regge limit of R-current correlators in AdS supergravity, Nucl. Phys. B 830 (2010) 153 [arXiv:0908.2301] [INSPIRE].
L. Cornalba, M.S. Costa, J. Penedones and R. Schiappa, Eikonal approximation in AdS/CFT: from shock waves to four-point functions, JHEP 08 (2007) 019 [hep-th/0611122] [INSPIRE].
M. Cvetič, H. Lü, C.N. Pope, A. Sadrzadeh and T.A. Tran, Consistent SO(6) reduction of type IIB supergravity on S 5, Nucl. Phys. B 586 (2000) 275 [hep-th/0003103] [INSPIRE].
H.R. Bakhtiarizadeh and M.R. Garousi, Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism, Nucl. Phys. B 884 (2014) 408 [arXiv:1312.4703] [INSPIRE].
M.R. Garousi and R.C. Myers, Superstring scattering from D-branes, Nucl. Phys. B 475 (1996) 193 [hep-th/9603194] [INSPIRE].
K. Becker, M. Becker, I.V. Melnikov, D. Robbins and A.B. Royston, Some tree-level string amplitudes in the NSR formalism, JHEP 12 (2015) 010 [arXiv:1507.02172] [INSPIRE].
J.-H. Gao and B.-W. Xiao, Polarized deep inelastic and elastic scattering from gauge/string duality, Phys. Rev. D 80 (2009) 015025 [arXiv:0904.2870] [INSPIRE].
Y. Hatta, E. Iancu and A.H. Mueller, Deep inelastic scattering at strong coupling from gauge/string duality: the saturation line, JHEP 01 (2008) 026 [arXiv:0710.2148] [INSPIRE].
R.C. Brower, M.J. Strassler and C.-I. Tan, On the eikonal approximation in AdS space, JHEP 03 (2009) 050 [arXiv:0707.2408] [INSPIRE].
R.C. Brower, M.J. Strassler and C.-I. Tan, On the Pomeron at large ’t Hooft coupling, JHEP 03 (2009) 092 [arXiv:0710.4378] [INSPIRE].
R.C. Brower, M. Djuric, I. Sarcevic and C.-I. Tan, String-gauge dual description of deep inelastic scattering at small-x, JHEP 11 (2010) 051 [arXiv:1007.2259] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].
L. Cornalba and M.S. Costa, Saturation in deep inelastic scattering from AdS/CFT, Phys. Rev. D 78 (2008) 096010 [arXiv:0804.1562] [INSPIRE].
N. Kovensky, G. Michalski and M. Schvellinger, Deep inelastic scattering from polarized spin-1/2 hadrons at small-x from string theory, in preparation.
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS 5 × T 1 1: Predictions on N = 1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
Y. Hatta, E. Iancu and A.H. Mueller, Deep inelastic scattering off a N = 4 SYM plasma at strong coupling, JHEP 01 (2008) 063 [arXiv:0710.5297] [INSPIRE].
B. Hassanain and M. Schvellinger, Holographic current correlators at finite coupling and scattering off a supersymmetric plasma, JHEP 04 (2010) 012 [arXiv:0912.4704] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1711.06171
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kovensky, N., Michalski, G. & Schvellinger, M. DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term. J. High Energ. Phys. 2018, 118 (2018). https://doi.org/10.1007/JHEP04(2018)118
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2018)118