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Deconstructing graviphoton from mass-deformed ABJM

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Abstract

Mass-deformed ABJM theory has a maximally supersymmetric fuzzy two- sphere vacuum solution where the scalar fields are proportional to the TGRVV matrices. We construct these matrices using Schwinger oscillators. This shows that the ABJM gauge group that corresponds to the fuzzy two-sphere geometry is U(N) × U(N − 1). We deconstruct the graviphoton term in the D4 brane theory. The normalization of this term is fixed by topological reasons. This gives us the correct normalization of the deconstructed U(1) gauge field and fixes the Yang-Mills coupling constant to the value which corresponds to M5 brane compactified on \({\mathbb{R}^{1,2}} \times {{{{S^3}}} \left/ {{{\mathbb{Z}_k}}} \right.}\). The graviphoton term also enable us to show that the zero mode contributions to the partition functions for the D4 and the M5 brane agree.

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References

  1. S. Terashima, On M5-branes in N = 6 membrane action, JHEP 08 (2008) 080 [arXiv:0807.0197] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A massive study of M2-brane proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].

    Article  ADS  Google Scholar 

  3. K.-M. Lee, S. Lee and S. Lee, Nonrelativistic superconformal M2-brane theory, JHEP 09 (2009) 030 [arXiv:0902.3857] [INSPIRE].

    Article  ADS  Google Scholar 

  4. N. Lambert and P. Richmond, M2-branes and background fields, JHEP 10 (2009) 084 [arXiv:0908.2896] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. H.-C. Kim and S. Kim, Supersymmetric vacua of mass-deformed M2-brane theory, Nucl. Phys. B 839 (2010) 96 [arXiv:1001.3153] [INSPIRE].

    Article  ADS  Google Scholar 

  6. J. Bagger and N. Lambert, Three-algebras and N = 6 Chern-Simons gauge theories, Phys. Rev. D 79 (2009) 025002 [arXiv:0807.0163] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. A. Gustavsson, Monopoles, three-algebras and ABJM theories with \(\mathcal{N} = 5,6,8\) supersymmetry, JHEP 01 (2011) 037 [arXiv:1012.4568] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. M. Mathur, I. Raychowdhury and R. Anishetty, SU(N) irreducible Schwinger bosons, J. Math. Phys. 51 (2010) 093504 [arXiv:1003.5487] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. H. Nastase, C. Papageorgakis and S. Ramgoolam, The fuzzy S 2 structure of M2-M5 systems in ABJM membrane theories, JHEP 05 (2009) 123 [arXiv:0903.3966] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Lambert, private communication.

  11. N. Lambert, H. Nastase and C. Papageorgakis, 5D Yang-Mills instantons from ABJM monopoles, Phys. Rev. D 85 (2012) 066002 [arXiv:1111.5619] [INSPIRE].

    ADS  Google Scholar 

  12. N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-branes, D4-branes and quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. M.R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].

    ADS  Google Scholar 

  14. A. Gustavsson, A preliminary test of Abelian D4-M5 duality, Phys. Lett. B 706 (2011) 225 [arXiv:1111.6339] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Gustavsson, M5 brane on R 1,2 × S 3, JHEP 01 (2012) 057 [arXiv:1111.5392] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. H. Linander and F. Ohlsson, (2, 0) theory on circle fibrations, JHEP 01 (2012) 159 [arXiv:1111.6045] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. E. Witten, Geometric Langlands from six dimensions, arXiv:0905.2720 [INSPIRE].

  18. S. Mukhi and C. Papageorgakis, M2 to D2, JHEP 05 (2008) 085 [arXiv:0803.3218] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. D. Berenstein and R. Corrado, Matrix theory on ALE spaces and wrapped membranes, Nucl. Phys. B 529 (1998) 225 [hep-th/9803048] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. X. Chu, H. Nastase, B.E.W. Nilsson and C. Papageorgakis, Higgsing M2 to D2 with gravity: N = 6 chiral supergravity from topologically gauged ABJM theory, JHEP 04 (2011) 040 [arXiv:1012.5969] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. Y. Pang and T. Wang, From N M2’s to N D2’s, Phys. Rev. D 78 (2008) 125007 [arXiv:0807.1444] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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  1. Physics Department, University of Seoul, 13 Siripdae, Seoul, 130-743, Korea

    Andreas Gustavsson

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  1. Andreas Gustavsson
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Correspondence to Andreas Gustavsson.

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Gustavsson, A. Deconstructing graviphoton from mass-deformed ABJM. J. High Energ. Phys. 2012, 174 (2012). https://doi.org/10.1007/JHEP06(2012)174

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  • DOI: https://doi.org/10.1007/JHEP06(2012)174

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