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Matching quantum string corrections and circular Wilson loops in AdS4 × CP3

  • Daniel Medina-RinconEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in AdS4 × CP3. For this, the ratio of \( \frac{1}{2} \)-BPS circular and \( \frac{1}{6} \)-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism in-variant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fermions. In the limit for which the latitude Wilson loop has a trivial expectation value, the long known localization result for the \( \frac{1}{2} \)-BPS fermionic circular Wilson loop in ABJM is recovered.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence Wilson ’t Hooft and Polyakov loops 

Notes

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

References

  1. [1]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  2. [2]
    O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP10 (2008) 091 [arXiv:0806.1218] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett.80 (1998) 4859 [hep-th/9803002] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large N gauge theory and anti-de Sitter supergravity, Nucl. Phys.B 527 (1998) 171 [hep-th/9803135] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71 [arXiv:0712.2824] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    A.M. Polyakov, String theory and quark confinement, Nucl. Phys. Proc. Suppl.68 (1998) 1 [hep-th/9711002] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys.B 582 (2000) 155 [hep-th/0003055] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    N. Drukker and D.J. Gross, An Exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys.42 (2001) 2896 [hep-th/0010274] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    N. Drukker, 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model, JHEP09 (2006) 004 [hep-th/0605151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS 5 × S 5: Semiclassical partition function, JHEP04 (2000) 021 [hep-th/0001204] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Kruczenski and A. Tirziu, Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling, JHEP05 (2008) 064 [arXiv:0803.0315] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    C. Kristjansen and Y. Makeenko, More about One-Loop Effective Action of Open Superstring in AdS 5 × S 5, JHEP09 (2012) 053 [arXiv:1206.5660] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    E.I. Buchbinder and A.A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling, Phys. Rev.D 89 (2014) 126008 [arXiv:1404.4952] [INSPIRE].ADSGoogle Scholar
  14. [14]
    V. Forini, V. Giangreco M. Puletti, L. Griguolo, D. Seminara and E. Vescovi, Precision calculation of 1/4-BPS Wilson loops in AdS 5 × S 5, JHEP02 (2016) 105 [arXiv:1512.00841] [INSPIRE].
  15. [15]
    A. Faraggi, L.A. Pando Zayas, G.A. Silva and D. Trancanelli, Toward precision holography with supersymmetric Wilson loops, JHEP04 (2016) 053 [arXiv:1601.04708] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    J. Aguilera-Damia, A. Faraggi, L.A. Pando Zayas, V. Rathee and G.A. Silva, Zeta-function Regularization of Holographic Wilson Loops, Phys. Rev.D 98 (2018) 046011 [arXiv:1802.03016] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  17. [17]
    V. Forini, A.A. Tseytlin and E. Vescovi, Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS 5 × S 5, JHEP03 (2017) 003 [arXiv:1702.02164] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    A. Cagnazzo, D. Medina-Rincon and K. Zarembo, String corrections to circular Wilson loop and anomalies, JHEP02 (2018) 120 [arXiv:1712.07730] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    D. Medina-Rincon, A.A. Tseytlin and K. Zarembo, Precision matching of circular Wilson loops and strings in AdS 5× S 5, JHEP05 (2018) 199 [arXiv:1804.08925] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons Theory and their string theory duals, JHEP11 (2008) 019 [arXiv:0809.2787] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    B. Chen and J.-B. Wu, Supersymmetric Wilson Loops in N = 6 Super Chern-Simons-matter theory, Nucl. Phys.B 825 (2010) 38 [arXiv:0809.2863] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual, JHEP03 (2009) 127 [arXiv:0809.3786] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    N. Drukker and D. Trancanelli, A Supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP02 (2010) 058 [arXiv:0912.3006] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Mariño and P. Putrov, Exact Results in ABJM Theory from Topological Strings, JHEP06 (2010) 011 [arXiv:0912.3074] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys.306 (2011) 511 [arXiv:1007.3837] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A. Klemm, M. Mariño, M. Schiereck and M. Soroush, Aharony-Bergman-Jafferis-Maldacena Wilson loops in the Fermi gas approach, Z. Naturforsch.A 68 (2013) 178 [arXiv:1207.0611] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    K. Okuyama, Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory, JHEP09 (2016) 125 [arXiv:1607.06157] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    V. Cardinali, L. Griguolo, G. Martelloni and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett.B 718 (2012) 615 [arXiv:1209.4032] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    M.S. Bianchi, L. Griguolo, M. Leoni, S. Penati and D. Seminara, BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis, JHEP06 (2014) 123 [arXiv:1402.4128] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    M.S. Bianchi, L. Griguolo, A. Mauri, S. Penati and D. Seminara, A matrix model for the latitude Wilson loop in ABJM theory, JHEP08 (2018) 060 [arXiv:1802.07742] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  31. [31]
    D.H. Correa, J. Aguilera-Damia and G.A. Silva, Strings in AdS 4 × ℂℙ3Wilson loops in \( \mathcal{N} \) = 6 super Chern-Simons-matter and bremsstrahlung functions, JHEP06(2014) 139 [arXiv:1405.1396] [INSPIRE].ADSzbMATHGoogle Scholar
  32. [32]
    H. Kim, N. Kim and J. Hun Lee, One-loop corrections to holographic Wilson loop in AdS4xCP3, J. Korean Phys. Soc.61 (2012) 713 [arXiv:1203.6343] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    J. Aguilera-Damia, A. Faraggi, L.A. Pando Zayas, V. Rathee and G.A. Silva, Toward Precision Holography in Type IIA with Wilson Loops, JHEP08 (2018) 044 [arXiv:1805.00859] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    K. Zarembo, Supersymmetric Wilson loops, Nucl. Phys.B 643 (2002) 157 [hep-th/0205160] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    X. Chen-Lin, D. Medina-Rincon and K. Zarembo, Quantum String Test of Nonconformal Holography, JHEP04 (2017) 095 [arXiv:1702.07954] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    N. Sakai and Y. Tanii, Supersymmetry in Two-dimensional Anti-de Sitter Space, Nucl. Phys.B 258 (1985) 661 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    D. Fursaev and D. Vassilevich, Operators, Geometry and Quanta Springer, Berlin, Germany (2011) [INSPIRE].CrossRefGoogle Scholar
  38. [38]
    J. Aguilera-Damia, D.H. Correa and G.A. Silva, Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM, JHEP03 (2015) 002 [arXiv:1412.4084] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    V. Forini, V.G.M. Puletti and O. Ohlsson Sax, The generalized cusp in AdS 4× CP 3and more one-loop results from semiclassical strings, J. Phys.A 46 (2013) 115402 [arXiv:1204.3302] [INSPIRE].ADSzbMATHGoogle Scholar
  40. [40]
    K. Okuyama, private communication.Google Scholar
  41. [41]
    R. Bergamin and A.A. Tseytlin, Heat kernels on cone of AdS 2and k-wound circular Wilson loop in AdS 5× S 5superstring, J. Phys.A 49 (2016) 14LT01 [arXiv:1510.06894] [INSPIRE].zbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikEidgenössische Technische Hochschule ZürichZürichSwitzerland

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