Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Holography for \( \mathcal{N} \) = 1∗ on S 4

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 18 October 2016
  • Volume 2016, article number 95, (2016)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Holography for \( \mathcal{N} \) = 1∗ on S 4
Download PDF
  • Nikolay Bobev1,
  • Henriette Elvang2,
  • Uri Kol2,
  • Timothy Olson2 &
  • …
  • Silviu S. Pufu3 

  • 415 Accesses

  • 37 Citations

  • 4 Altmetric

  • Explore all metrics

A preprint version of the article is available at arXiv.

Abstract

We construct the five-dimensional supergravity dual of the \( \mathcal{N} \) = 1∗ mass deformation of the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory on S 4 and use it to calculate the universal contribution to the corresponding S 4 free energy at large ’t Hooft coupling in the planar limit. The holographic RG flow solutions are smooth and preserve four supercharges. As a novel feature compared to the holographic duals of \( \mathcal{N} \) = 1∗ on \( {\mathbb{R}}^4 \), in our backgrounds the five-dimensional dilaton has a non-trivial profile, and the gaugino conden- sate is fixed in terms of the mass-deformation parameters. Important aspects of the analysis involve characterizing the ambiguities in the partition function of non-conformal \( \mathcal{N} \) = 1 supersymmetric theories on S 4 as well as the action of S-duality on the \( \mathcal{N} \) = 1∗ theory.

Article PDF

Download to read the full article text

Similar content being viewed by others

Precision holography for \( \mathcal{N}={2}^{\ast } \) on S4 from type IIB supergravity

Article Open access 27 April 2018

Superconformal indices of 3d \( \mathcal{N} \) = 2 SCFTs and holography

Article Open access 16 October 2024

AdS5 holography and higher-derivative supergravity

Article Open access 14 April 2022
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  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].

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  4. 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].

    Article  MathSciNet  MATH  Google Scholar 

  5. I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].

  7. L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, The supergravity dual of N = 1 super Yang-Mills theory, Nucl. Phys. B 569 (2000) 451 [hep-th/9909047] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. K. Pilch and N.P. Warner, N = 1 supersymmetric renormalization group flows from IIB supergravity, Adv. Theor. Math. Phys. 4 (2002) 627 [hep-th/0006066] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  9. O. Aharony, N. Dorey and S.P. Kumar, New modular invariance in the N = 1∗ theory, operator mixings and supergravity singularities, JHEP 06 (2000) 026 [hep-th/0006008] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. N. Dorey and S.P. Kumar, Softly broken N = 4 supersymmetry in the large-N limit, JHEP 02 (2000) 006 [hep-th/0001103] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. N. Dorey, T.J. Hollowood and S.P. Kumar, An exact elliptic superpotential for N = 1∗ deformations of finite N = 2 gauge theories, Nucl. Phys. B 624 (2002) 95 [hep-th/0108221] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. D.L. Jafferis and S.S. Pufu, Exact results for five-dimensional superconformal field theories with gravity duals, JHEP 05 (2014) 032 [arXiv:1207.4359] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. F. Benini and S. Cremonesi, Partition functions of N = (2, 2) gauge theories on S 2 and vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact results in D = 2 supersymmetric gauge theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere partition functions and the Zamolodchikov metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. J. Gomis and N. Ishtiaque, Kähler potential and ambiguities in 4d N = 2 SCFTs, JHEP 04 (2015) 169 [arXiv:1409.5325] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  20. K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. M. Baggio, V. Niarchos and K. Papadodimas, Exact correlation functions in SU(2) N = 2 superconformal QCD, Phys. Rev. Lett. 113 (2014) 251601 [arXiv:1409.4217] [INSPIRE].

    Article  ADS  Google Scholar 

  22. M. Baggio, V. Niarchos and K. Papadodimas, tt ∗ equations, localization and exact chiral rings in 4d N = 2 SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [INSPIRE].

  23. N. Bobev, H. Elvang, D.Z. Freedman and S.S. Pufu, Holography for N = 2∗ on S 4, JHEP 07 (2014) 001 [arXiv:1311.1508] [INSPIRE].

    Article  ADS  Google Scholar 

  24. J.G. Russo and K. Zarembo, Large-N limit of N = 2 SU(N ) gauge theories from localization, JHEP 10 (2012) 082 [arXiv:1207.3806] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. A. Buchel, J.G. Russo and K. Zarembo, Rigorous test of non-conformal holography: Wilson loops in N = 2∗ theory, JHEP 03 (2013) 062 [arXiv:1301.1597] [INSPIRE].

    Article  ADS  Google Scholar 

  26. J.G. Russo and K. Zarembo, Evidence for large-N phase transitions in N = 2∗ theory, JHEP 04 (2013) 065 [arXiv:1302.6968] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. J.G. Russo and K. Zarembo, Massive N = 2 gauge theories at large-N , JHEP 11 (2013) 130 [arXiv:1309.1004] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. J.G. Russo and K. Zarembo, Localization at large-N , arXiv:1312.1214 [INSPIRE].

  29. A. Buchel, Localization and holography in N = 2 gauge theories, JHEP 08 (2013) 004 [arXiv:1304.5652] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. X. Chen-Lin, J. Gordon and K. Zarembo, N = 2∗ super-Yang-Mills theory at strong coupling, JHEP 11 (2014) 057 [arXiv:1408.6040] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. J.G. Russo, A note on perturbation series in supersymmetric gauge theories, JHEP 06 (2012) 038 [arXiv:1203.5061] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  32. J.G. Russo, N = 2 gauge theories and quantum phases, JHEP 12 (2014) 169 [arXiv:1411.2602] [INSPIRE].

    Article  ADS  Google Scholar 

  33. X. Chen-Lin and K. Zarembo, Higher rank Wilson loops in N = 2∗ super-Yang-Mills theory, JHEP 03 (2015) 147 [arXiv:1502.01942] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  34. X. Chen-Lin, A. Dekel and K. Zarembo, Holographic Wilson loops in symmetric representations in N = 2∗ super-Yang-Mills theory, JHEP 02 (2016) 109 [arXiv:1512.06420] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  35. K. Zarembo, Strong-coupling phases of planar N = 2∗ super-Yang-Mills theory, Theor. Math. Phys. 181 (2014) 1522 [arXiv:1410.6114] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Karch, B. Robinson and C.F. Uhlemann, Supersymmetric D3/D7 for holographic flavors on curved space, JHEP 11 (2015) 112 [arXiv:1508.06996] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  37. A. Karch, B. Robinson and C.F. Uhlemann, Precision test of gauge-gravity duality with flavor, Phys. Rev. Lett. 115 (2015) 261601 [arXiv:1509.00013] [INSPIRE].

    Article  ADS  Google Scholar 

  38. C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. N. Dorey, An elliptic superpotential for softly broken N = 4 supersymmetric Yang-Mills theory, JHEP 07 (1999) 021 [hep-th/9906011] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 supergravity in five-dimensions, Phys. Lett. B 154 (1985) 268 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  42. 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].

    Article  ADS  Google Scholar 

  43. M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged N = 8 D = 5 supergravity, Nucl. Phys. B 259 (1985) 460 [INSPIRE].

    Article  ADS  Google Scholar 

  44. K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N =1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].

  46. D.Z. Freedman, S.S. Gubser, K. Pilch and N.P. Warner, Renormalization group flows from holography supersymmetry and a c theorem, Adv. Theor. Math. Phys. 3 (1999) 363 [hep-th/9904017] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  47. L. Girardello, M. Petrini, M. Porrati and A. Zaffaroni, Novel local CFT and exact results on perturbations of N = 4 super Yang-Mills from AdS dynamics, JHEP 12 (1998) 022 [hep-th/9810126] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. S.S. Gubser, Curvature singularities: the good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  49. D.Z. Freedman and S.S. Pufu, The holography of F -maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. G. Knodel, J.T. Liu and L.A. Pando Zayas, On N = 1 partition functions without R-symmetry, JHEP 03 (2015) 132 [arXiv:1412.4804] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  51. K.A. Intriligator, Bonus symmetries of N = 4 super Yang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. M. Waldschmidt, P. Moussa, J.M. Luck and C. Itzykson eds., From number theory to physics, Les Houches, (1989), Springer, Germany (1992).

  53. K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, arXiv:1401.3360 [INSPIRE].

  54. 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].

    ADS  MathSciNet  Google Scholar 

  55. N.P. Warner, Some new extrema of the scalar potential of gauged N = 8 supergravity, Phys. Lett. B 128 (1983) 169 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  56. K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  57. J. de Boer, E.P. Verlinde and H.L. Verlinde, On the holographic renormalization group, JHEP 08 (2000) 003 [hep-th/9912012] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  58. J. Kalkkinen, D. Martelli and W. Mueck, Holographic renormalization and anomalies, JHEP 04 (2001) 036 [hep-th/0103111] [INSPIRE].

    Article  ADS  Google Scholar 

  59. D. Martelli and W. Mueck, Holographic renormalization and Ward identities with the Hamilton-Jacobi method, Nucl. Phys. B 654 (2003) 248 [hep-th/0205061] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  61. H. Elvang and M. Hadjiantonis, A practical approach to the Hamilton-Jacobi formulation of holographic renormalization, JHEP 06 (2016) 046 [arXiv:1603.04485] [INSPIRE].

    Article  ADS  Google Scholar 

  62. K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  64. A. Khavaev and N.P. Warner, A class of N = 1 supersymmetric RG flows from five-dimensional N = 8 supergravity, Phys. Lett. B 495 (2000) 215 [hep-th/0009159] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Supersymmetric charged clouds in AdS 5, JHEP 03 (2011) 070 [arXiv:1005.3552] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  66. D. Cassani, J. Lorenzen and D. Martelli, Comments on supersymmetric solutions of minimal gauged supergravity in five dimensions, Class. Quant. Grav. 33 (2016) 115013 [arXiv:1510.01380] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  67. B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir energy in curved space and its supersymmetric counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  68. B. Assel, D. Cassani and D. Martelli, Supersymmetric counterterms from new minimal supergravity, JHEP 11 (2014) 135 [arXiv:1410.6487] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. D. Cassani and D. Martelli, The gravity dual of supersymmetric gauge theories on a squashed S 1 × S 3, JHEP 08 (2014) 044 [arXiv:1402.2278] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

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

  1. Instituut voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium

    Nikolay Bobev

  2. Michigan Center for Theoretical Physics, Randall Laboratory of Physics, Department of Physics, University of Michigan, Ann Arbor, MI, 48109, U.S.A.

    Henriette Elvang, Uri Kol & Timothy Olson

  3. Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, U.S.A.

    Silviu S. Pufu

Authors
  1. Nikolay Bobev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henriette Elvang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Uri Kol
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Timothy Olson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Silviu S. Pufu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolay Bobev.

Additional information

ArXiv ePrint: 1605.00656

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bobev, N., Elvang, H., Kol, U. et al. Holography for \( \mathcal{N} \) = 1∗ on S 4 . J. High Energ. Phys. 2016, 95 (2016). https://doi.org/10.1007/JHEP10(2016)095

Download citation

  • Received: 05 August 2016

  • Accepted: 06 October 2016

  • Published: 18 October 2016

  • DOI: https://doi.org/10.1007/JHEP10(2016)095

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • AdS-CFT Correspondence
  • Gauge-gravity correspondence
  • Supergravity Models
  • Supersymmetric gauge theory
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Cancel contracts here

65.254.225.175

Not affiliated

Springer Nature

© 2024 Springer Nature