Advertisement

Journal of High Energy Physics

, 2018:183 | Cite as

A note on D0-branes and instantons in 5d supersymmetric gauge theories

  • Eran Avraham
  • Oren Bergman
Open Access
Regular Article - Theoretical Physics
  • 24 Downloads

Abstract

We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.

Keywords

Brane Dynamics in Gauge Theories Field Theories in Lower Dimensions Supersymmetric Gauge Theory 

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]
    M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld and Yu. I. Manin, Construction of Instantons, Phys. Lett. A 65 (1978) 185 [INSPIRE].
  2. [2]
    E. Witten, σ-models and the ADHM construction of instantons, J. Geom. Phys. 15 (1995) 215 [hep-th/9410052] [INSPIRE].
  3. [3]
    N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    N. Nekrasov and S. Shadchin, ABCD of instantons, Commun. Math. Phys. 252 (2004) 359 [hep-th/0404225] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    S. Shadchin, On certain aspects of string theory/gauge theory correspondence, Ph.D. Thesis, Orsay LPT, Paris France (2005) [hep-th/0502180] [INSPIRE].
  6. [6]
    M.R. Douglas, Gauge fields and D-branes, J. Geom. Phys. 28 (1998) 255 [hep-th/9604198] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    H.-C. Kim, S. Kim, E. Koh, K. Lee and S. Lee, On instantons as Kaluza-Klein modes of M5-branes, JHEP 12 (2011) 031 [arXiv:1110.2175] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    H.-C. Kim, S.-S. Kim and K. Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5d SCFT, JHEP 07 (2015) 063 [arXiv:1406.6793] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Y. Hwang, J. Kim and S. Kim, M5-branes, orientifolds and S-duality, JHEP 12 (2016) 148 [arXiv:1607.08557] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
  12. [12]
    O. Bergman and D. Rodriguez-Gomez, 5d quivers and their AdS 6 duals, JHEP 07 (2012) 171 [arXiv:1206.3503] [INSPIRE].
  13. [13]
    O. Aharony, M. Berkooz, S. Kachru and E. Silverstein, Matrix description of (1, 0) theories in six-dimensions, Phys. Lett. B 420 (1998) 55 [hep-th/9709118] [INSPIRE].
  14. [14]
    D. Tong, The holographic dual of AdS 3 × S 3 × S 3 × S 1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
  15. [15]
    D. Tong and K. Wong, Instantons, Wilson lines and D-branes, Phys. Rev. D 91 (2015) 026007 [arXiv:1410.8523] [INSPIRE].
  16. [16]
    Y. Tachikawa, On S-duality of 5d super Yang-Mills on S 1, JHEP 11 (2011) 123 [arXiv:1110.0531] [INSPIRE].
  17. [17]
    B. Collie and D. Tong, Instantons, Fermions and Chern-Simons Terms, JHEP 07 (2008) 015 [arXiv:0804.1772] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    O. Bergman, D. Rodríguez-Gómez and G. Zafrir, Discrete θ and the 5d superconformal index, JHEP 01 (2014) 079 [arXiv:1310.2150] [INSPIRE].
  19. [19]
    A. Keurentjes and S. Sethi, Twisting E8 five-branes, Phys. Rev. D 66 (2002) 046001 [hep-th/0205162] [INSPIRE].
  20. [20]
    D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
  21. [21]
    M.R. Douglas, S.H. Katz and C. Vafa, Small instantons, Del Pezzo surfaces and type-I-prime theory, Nucl. Phys. B 497 (1997) 155 [hep-th/9609071] [INSPIRE].
  22. [22]
    K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
  23. [23]
    O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-Brane Webs, Symmetry Enhancement and Duality in 5d Supersymmetric Gauge Theory, JHEP 03 (2014) 112 [arXiv:1311.4199] [INSPIRE].
  24. [24]
    G. Zafrir, Duality and enhancement of symmetry in 5d gauge theories, JHEP 12 (2014) 116 [arXiv:1408.4040] [INSPIRE].
  25. [25]
    F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].
  26. [26]
    F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic Genera of 2d \( \mathcal{N}=2 \) Gauge Theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
  27. [27]
    O. Bergman and G. Zafrir, Lifting 4d dualities to 5d, JHEP 04 (2015) 141 [arXiv:1410.2806] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsTechnion, Israel Institute of TechnologyHaifaIsrael

Personalised recommendations