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Phase structure of lattice \(\mathcal{N}=4\) super Yang-Mills

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Abstract

We make a first study of the phase diagram of four-dimensional \(\mathcal{N}=4\) super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consistent with the existence of a single deconfined phase at all observed values of the bare coupling.

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References

  1. D.B. Kaplan, Recent developments in lattice supersymmetry, Nucl. Phys. Proc. Suppl. 129 (2004) 109 [hep-lat/0309099] [INSPIRE].

    Article  ADS  Google Scholar 

  2. J. Giedt, Deconstruction and other approaches to supersymmetric lattice field theories, Int. J. Mod. Phys. A 21 (2006) 3039 [hep-lat/0602007] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. S. Catterall, D.B. Kaplan and M. Ünsal, Exact lattice supersymmetry, Phys. Rept. 484 (2009) 71 [arXiv:0903.4881] [INSPIRE].

    Article  ADS  Google Scholar 

  4. A. Joseph, Supersymmetric Yang-Mills theories with exact supersymmetry on the lattice, Int. J. Mod. Phys. A 26 (2011) 5057 [arXiv:1110.5983] [INSPIRE].

    ADS  Google Scholar 

  5. F. Sugino, A lattice formulation of super Yang-Mills theories with exact supersymmetry, JHEP 01 (2004) 015 [hep-lat/0311021] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. F. Sugino, Super Yang-Mills theories on the two-dimensional lattice with exact supersymmetry, JHEP 03 (2004) 067 [hep-lat/0401017] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. A. D’Adda, I. Kanamori, N. Kawamoto and K. Nagata, Exact extended supersymmetry on a lattice: Twisted N = 2 super Yang-Mills in two dimensions, Phys. Lett. B 633 (2006) 645 [hep-lat/0507029] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. A. D’Adda, I. Kanamori, N. Kawamoto and K. Nagata, Exact extended supersymmetry on a lattice: twisted N = 4 super Yang-Mills in three dimensions, Nucl. Phys. B 798 (2008) 168 [arXiv:0707.3533] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. I. Kanamori and H. Suzuki, Restoration of supersymmetry on the lattice: two-dimensional N = (2,2) supersymmetric Yang-Mills theory, Nucl. Phys. B 811 (2009) 420 [arXiv:0809.2856] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Hanada and I. Kanamori, Lattice study of two-dimensional N = (2, 2) super Yang-Mills at large-N, Phys. Rev. D 80 (2009) 065014 [arXiv:0907.4966] [INSPIRE].

    ADS  Google Scholar 

  11. M. Hanada, S. Matsuura and F. Sugino, Two-dimensional lattice for four-dimensional N = 4 supersymmetric Yang-Mills, Prog. Theor. Phys. 126 (2011) 597 [arXiv:1004.5513] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  12. M. Hanada, A proposal of a fine tuning free formulation of 4d N = 4 super Yang-Mills, JHEP 11 (2010) 112 [arXiv:1009.0901] [INSPIRE].

    Article  ADS  Google Scholar 

  13. M. Hanada, S. Matsuura and F. Sugino, Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges, Nucl. Phys. B 857 (2012) 335 [arXiv:1109.6807] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. M. Ünsal, Twisted supersymmetric gauge theories and orbifold lattices, JHEP 10 (2006) 089 [hep-th/0603046] [INSPIRE].

    Article  Google Scholar 

  16. P.H. Damgaard and S. Matsuura, Relations among supersymmetric lattice gauge theories via orbifolding, JHEP 08 (2007) 087 [arXiv:0706.3007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Catterall, From twisted supersymmetry to orbifold lattices, JHEP 01 (2008) 048 [arXiv:0712.2532] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. T. Takimi, Relationship between various supersymmetric lattice models, JHEP 07 (2007) 010 [arXiv:0705.3831] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. S. Elitzur, E. Rabinovici and A. Schwimmer, Supersymmetric models on the lattice, Phys. Lett. B 119 (1982) 165 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  21. N. Marcus, The other topological twisting of N = 4 Yang-Mills, Nucl. Phys. B 452 (1995) 331 [hep-th/9506002] [INSPIRE].

    Article  ADS  Google Scholar 

  22. A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  23. H. Aratyn, M. Goto and A. Zimerman, A lattice gauge theory for fields in the adjoint representation, Nuovo Cim. A 84 (1984) 255 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A.G. Cohen, D.B. Kaplan, E. Katz and M. Ünsal, Supersymmetry on a euclidean space-time lattice. 1. A target theory with four supercharges, JHEP 08 (2003) 024 [hep-lat/0302017] [INSPIRE].

    Article  ADS  Google Scholar 

  25. A.G. Cohen, D.B. Kaplan, E. Katz and M. Unsal, Supersymmetry on a euclidean space-time lattice. 2. Target theories with eight supercharges, JHEP 12 (2003) 031 [hep-lat/0307012] [INSPIRE].

    Article  ADS  Google Scholar 

  26. D.B. Kaplan and M. Ünsal, A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges, JHEP 09 (2005) 042 [hep-lat/0503039] [INSPIRE].

    Article  ADS  Google Scholar 

  27. P.H. Damgaard and S. Matsuura, Geometry of orbifolded supersymmetric lattice gauge theories, Phys. Lett. B 661 (2008) 52 [arXiv:0801.2936] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. J.M. Rabin, Homology theory of lattice fermion doubling, Nucl. Phys. B 201 (1982) 315 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. P. Becher and H. Joos, The Dirac-Kähler equation and fermions on the lattice, Z. Phys. C 15 (1982) 343 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. T. Banks, Y. Dothan and D. Horn, Geometric fermions, Phys. Lett. B 117 (1982) 413 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. I. Kanamori, Lattice formulation of two-dimensional N = (2, 2) super Yang-Mills with SU(N) gauge group, JHEP 07 (2012) 021 [arXiv:1202.2101] [INSPIRE].

    Article  ADS  Google Scholar 

  32. M. Hanada and I. Kanamori, Absence of sign problem in two-dimensional N = (2, 2) super Yang-Mills on lattice, JHEP 01 (2011) 058 [arXiv:1010.2948] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. S. Catterall, R. Galvez, A. Joseph and D. Mehta, On the sign problem in 2D lattice super Yang-Mills, JHEP 01 (2012) 108 [arXiv:1112.3588] [INSPIRE].

    Article  ADS  Google Scholar 

  34. D. Mehta, S. Catterall, R. Galvez and A. Joseph, Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem, PoS(LATTICE 2011)078 [arXiv:1112.5413] [INSPIRE].

  35. R. Galvez, S. Catterall, A. Joseph and D. Mehta, Investigating the sign problem for two-dimensional \(\mathcal{N}=\left( {2,2} \right)\) and \(\mathcal{N}=\left( {8,8} \right)\) lattice super Yang-Mills theories, PoS(LATTICE 2011)064 [arXiv:1201.1924] [INSPIRE].

  36. S. Catterall, E. Dzienkowski, J. Giedt, A. Joseph and R. Wells, Perturbative renormalization of lattice N = 4 super Yang-Mills theory, JHEP 04 (2011) 074 [arXiv:1102.1725] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. D. Mehta, Lattice vs. continuum: landau gauge fixing and ’t Hooft-Polyakov monopoles, Ph.D. thesis, The University of Adelaide, Adelaide, Australia (2009).

  38. L. von Smekal, A. Jorkowski, D. Mehta and A. Sternbeck, Lattice Landau gauge via stereographic projection, PoS(CONFINEMENT8)048 [arXiv:0812.2992] [INSPIRE].

  39. L. von Smekal, D. Mehta, A. Sternbeck and A.G. Williams, Modified lattice Landau gauge, PoS(LATTICE 2007)382 [arXiv:0710.2410] [INSPIRE].

  40. S. Catterall and A. Joseph, An object oriented code for simulating supersymmetric Yang-Mills theories, Comput. Phys. Commun. 183 (2012) 1336 [arXiv:1108.1503] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. R. Galvez and G. van Anders, Accelerating the solution of families of shifted linear systems with CUDA, arXiv:1102.2143 [INSPIRE].

  42. W. Krauth and M. Staudacher, Eigenvalue distributions in Yang-Mills integrals, Phys. Lett. B 453 (1999) 253 [hep-th/9902113] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Syracuse University, Syracuse, NY, 13244, U.S.A.

    Simon Catterall, Richard Galvez & Dhagash Mehta

  2. Niels Bohr International Academy and Discovery Center, Niels Bohr Instiutute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

    Poul H. Damgaard

  3. Department of Physics, University of Colorado, Boulder, CO, 80309, U.S.A.

    Thomas DeGrand

Authors
  1. Simon Catterall
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  2. Poul H. Damgaard
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  3. Thomas DeGrand
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  4. Richard Galvez
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  5. Dhagash Mehta
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Correspondence to Simon Catterall.

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ArXiv ePrint: 1209.5285

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Catterall, S., Damgaard, P.H., DeGrand, T. et al. Phase structure of lattice \(\mathcal{N}=4\) super Yang-Mills. J. High Energ. Phys. 2012, 72 (2012). https://doi.org/10.1007/JHEP11(2012)072

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