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A comment on 4d and 5d BPS states

  • Shamit Kachru
  • Max ZimetEmail author
Open Access
Regular Article - Theoretical Physics
  • 8 Downloads

Abstract

We discuss a phenomenon in supersymmetric field theory and string theory whereby compactifying one of the dimensions of spacetime on an arbitrarily large circle can cause BPS states to become unstable. We exemplify this by considering 5d \( \mathcal{N} \) = 1 theories on a circle and their embeddings into M-theory via geometric engineering. This implicates a subtle relationship between the BPS states of M-theory on a Calabi-Yau threefold, X , and those of type IIA on X with an arbitrary value of the coupling constant. Intuition for this phenomenon is provided by considering F-theory on a complex K3 surface in a limit where it degenerates to a real K3 surface.

Keywords

Brane Dynamics in Gauge Theories 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]
    D. Gaiotto, A. Strominger and X. Yin, New connections between 4 − D and 5 − D black holes, JHEP02 (2006) 024 [hep-th/0503217] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    K. Behrndt, G. Lopes Cardoso and S. Mahapatra, Exploring the relation between 4 − D and 5 − D BPS solutions, Nucl. Phys.B 732 (2006) 200 [hep-th/0506251] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Counting dyons in N = 4 string theory, Nucl. Phys.B 484 (1997) 543 [hep-th/9607026] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    M. Aganagic, H. Ooguri, C. Vafa and M. Yamazaki, Wall crossing and M-theory, Publ. Res. Inst. Math. Sci. Kyoto47 (2011) 569 [arXiv:0908.1194] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    E. Witten, Some comments on string dynamics, hep-th/9507121 [INSPIRE].
  6. [6]
    S.H. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys.B 477 (1996) 105 [hep-th/9601108] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys.B 471 (1996) 195 [hep-th/9603150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys.B 426 (1994) 19 [Erratum ibid.B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
  9. [9]
    S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys.B 450 (1995) 69 [hep-th/9505105] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    S. Kachru et al., Nonperturbative results on the point particle limit of N = 2 heterotic string compactifications, Nucl. Phys.B 459 (1996) 537 [hep-th/9508155] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A.E. Lawrence and N. Nekrasov, Instanton sums and five-dimensional gauge theories, Nucl. Phys.B 513 (1998) 239 [hep-th/9706025] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Alim et al., \( \mathcal{N} \) = 2 quantum field theories and their BPS quivers, Adv. Theor. Math. Phys.18 (2014) 27 [arXiv:1112.3984] [INSPIRE].
  13. [13]
    E. Witten, Small instantons in string theory, Nucl. Phys.B 460 (1996) 541 [hep-th/9511030] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett.B 388 (1996) 753 [hep-th/9608111] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J. Polchinski and E. Witten, Evidence for heterotic-type-I string duality, Nucl. Phys.B 460 (1996) 525 [hep-th/9510169] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    A. Sen, BPS states on a three-brane probe, Phys. Rev.D 55 (1997) 2501 [hep-th/9608005] [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    O. Bergman and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys.B 531 (1998) 108 [hep-th/9802033] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl. Phys.B 531 (1998) 345 [hep-th/9803142] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    A. Sen, F theory and orientifolds, Nucl. Phys.B 475 (1996) 562 [hep-th/9605150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett.B 387 (1996) 278 [hep-th/9605199] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    F.A. Cachazo and C. Vafa, Type I’ and real algebraic geometry, hep-th/0001029 [INSPIRE].
  22. [22]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys.B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
  23. [23]
    V.V. Nikulin, Discrete reflection groups in lobachevsky spaces and algebraic surfaces, in the proceedings of the International Congress of Mathematicians, August 3–11, Berkeley, U.S.A. (1986).Google Scholar
  24. [24]
    A. Fayyazuddin, Results in supersymmetric field theory from three-brane probe in F-theory, Nucl. Phys.B 497 (1997) 101 [hep-th/9701185] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    N. Nekrasov, Five dimensional gauge theories and relativistic integrable systems, Nucl. Phys.B 531 (1998) 323 [hep-th/9609219] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2020

Authors and Affiliations

  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordUSA

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