Advertisement

Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models

  • Ilka Brunner
  • Jonathan SchulzEmail author
  • Alexander Tabler
Open Access
Regular Article - Theoretical Physics
  • 45 Downloads

Abstract

Theories with 3D \( \mathcal{N} = 2 \) bulk supersymmetry may preserve a 2D \( \mathcal{N} = \left(0,\ 2\right) \) subalgebra when a boundary is introduced, possibly with localized degrees of freedom. We propose generalized supercurrent multiplets with bulk and boundary parts adapted to such setups. Using their structure, we comment on implications for the \( {\overline{Q}}_{+} \)-cohomology. As an example, we apply the developed framework to Landau-Ginzburg models. In these models, we study the role of boundary degrees of freedom and matrix factorizations. We verify our results using quantization.

Keywords

Supersymmetry and Duality Field Theories in Lower Dimensions Boundary Quantum Field 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]
    T. Dimofte, D. Gaiotto and N.M. Paquette, Dual boundary conditions in 3d SCFT’s, JHEP 05 (2018) 060 [arXiv:1712.07654] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Okazaki and S. Yamaguchi, Supersymmetric boundary conditions in three-dimensional N =2 theories, Phys. Rev. D 87 (2013) 125005 [arXiv:1302.6593] [INSPIRE].Google Scholar
  3. [3]
    A. Gadde, S. Gukov and P. Putrov, Fivebranes and 4-manifolds, arXiv:1306.4320 [INSPIRE].
  4. [4]
    Z. Komargodski and N. Seiberg, Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    T.T. Dumitrescu and N. Seiberg, Supercurrents and Brane Currents in Diverse Dimensions, JHEP 07 (2011) 095 [arXiv:1106.0031] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    N. Drukker, D. Martelli and I. Shamir, The energy-momentum multiplet of supersymmetric defect field theories, JHEP 08 (2017) 010 [arXiv:1701.04323] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    D. Gaiotto, S. Gukov and N. Seiberg, Surface Defects and Resolvents, JHEP 09 (2013) 070 [arXiv:1307.2578] [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    M. Dedushenko, Chiral algebras in Landau-Ginzburg models, JHEP 03 (2018) 079 [arXiv:1511.04372] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    E. Witten, On the Landau-Ginzburg description of N = 2 minimal models, Int. J. Mod. Phys. A 9 (1994) 4783 [hep-th/9304026] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    E. Silverstein and E. Witten, Global U(1) R symmetry and conformal invariance of (0,2) models, Phys. Lett. B 328 (1994) 307 [hep-th/9403054] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  11. [11]
    E. Witten, Two-dimensional models with (0, 2) supersymmetry: Perturbative aspects, Adv. Theor. Math. Phys. 11 (2007) 1 [hep-th/0504078] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Y. Yoshida and K. Sugiyama, Localization of 3d \( \mathcal{N} = 2 \) Supersymmetric Theories on S 1 × D 2, arXiv:1409.6713 [INSPIRE].
  13. [13]
    A. Kapustin and Y. Li, D branes in Landau-Ginzburg models and algebraic geometry, JHEP 12 (2003) 005 [hep-th/0210296] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  14. [14]
    I. Brunner, M. Herbst, W. Lerche and B. Scheuner, Landau-Ginzburg realization of open string TFT, JHEP 11 (2006) 043 [hep-th/0305133] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  15. [15]
    L. Di Pietro, N. Klinghoffer and I. Shamir, On Supersymmetry, Boundary Actions and Brane Charges, JHEP 02 (2016) 163 [arXiv:1502.05976] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Bilal, Supersymmetric Boundaries and Junctions in Four Dimensions, JHEP 11 (2011) 046 [arXiv:1103.2280] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M. Magro, I. Sachs and S. Wolf, Superfield Noether procedure, Annals Phys. 298 (2002) 123 [hep-th/0110131] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S. Ferrara and B. Zumino, Transformation Properties of the Supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace Or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [INSPIRE].zbMATHGoogle Scholar
  20. [20]
    N. Drukker, I. Shamir and C. Vergu, Defect multiplets of \( \mathcal{N} = 1 \) supersymmetry in 4d, JHEP 01 (2018) 034 [arXiv:1711.03455] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    I.V. Melnikov, An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry, Lect. Notes Phys. 951 (2019) 1.MathSciNetCrossRefGoogle Scholar
  22. [22]
    M. Bullimore, T. Dimofte, D. Gaiotto and J. Hilburn, Boundaries, Mirror Symmetry and Symplectic Duality in 3d \( \mathcal{N} = 4 \) Gauge Theory, JHEP 10 (2016) 108 [arXiv:1603.08382] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    A. Kapustin and Y. Li, Topological correlators in Landau-Ginzburg models with boundaries, Adv. Theor. Math. Phys. 7 (2003) 727 [hep-th/0305136] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    M. Herbst, K. Hori and D. Page, Phases Of N = 2 Theories In 1 + 1 Dimensions With Boundary, arXiv:0803.2045 [INSPIRE].
  25. [25]
    C.I. Lazaroiu, On the boundary coupling of topological Landau-Ginzburg models, JHEP 05 (2005) 037 [hep-th/0312286] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  26. [26]
    E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    H. Jockers and P. Mayr, A 3d Gauge Theory/Quantum k-theory Correspondence, arXiv:1808.02040 [INSPIRE].
  28. [28]
    M.C.N. Cheng, S. Chun, F. Ferrari, S. Gukov and S.M. Harrison, 3d Modularity, arXiv:1809.10148 [INSPIRE].
  29. [29]
    F. Aprile and V. Niarchos, \( \mathcal{N} = 2 \) supersymmetric field theories on 3-manifolds with A-type boundaries, JHEP 07 (2016) 126 [arXiv:1604.01561] [INSPIRE].
  30. [30]
    C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, Supersymmetric Field Theories on Three-Manifolds, JHEP 05 (2013) 017 [arXiv:1212.3388] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, The Geometry of Supersymmetric Partition Functions, JHEP 01 (2014) 124 [arXiv:1309.5876] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    K. Hori, Linear models of supersymmetric D-branes, in Symplectic geometry and mirror symmetry. Proceedingsof 4th KIAS Annual International Conference, Seoul South Korea (2000), pg. 111 [hep-th/0012179] [INSPIRE].
  33. [33]
    K. Hori et al., Clay mathematics monographs. Vol. 1: Mirror symmetry, AMS Press, Providence U.S.A. (2003).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Arnold Sommerfeld CenterLudwig-Maximilians-UniversitätMünchenGermany

Personalised recommendations