Skip to main content
SpringerLink
Log in

Manifestly supersymmetric RG flows

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Renormalisation group (RG) equations in two-dimensional \( \mathcal{N} = 1 \) supersymmetric field theories with boundary are studied. It is explained how a manifestly \( \mathcal{N} = 1 \) supersymmetric scheme can be chosen, and within this scheme the RG equations are determined to next-to-leading order. We also use these results to revisit the question of how brane obstructions and lines of marginal stability appear from a world-sheet perspective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [SPIRES].

  2. D. Gaiotto, G.W. Moore and A. Neitzke, Four-dimensional wall-crossing via three-dimensional field theory, arXiv:0807.4723 [SPIRES].

  3. D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, hitchin systems and the WKB approximation, arXiv:0907.3987 [SPIRES].

  4. I. Brunner, M.R. Gaberdiel, S. Hohenegger and C.A. Keller, Obstructions and lines of marginal stability from the world-sheet, JHEP 05 (2009) 007 [arXiv:0902.3177] [SPIRES].

    Article  ADS  Google Scholar 

  5. S. Fredenhagen, M.R. Gaberdiel and C.A. Keller, Bulk induced boundary perturbations, J. Phys. A 40 (2007) F17 [hep-th/0609034] [SPIRES].

    MathSciNet  Google Scholar 

  6. S. Fredenhagen, M.R. Gaberdiel and C.A. Keller, Symmetries of perturbed conformal field theories, J. Phys. A 40 (2007) 13685 [arXiv:0707.2511] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. N.P. Warner, Supersymmetry in boundary integrable models, Nucl. Phys. B 450 (1995) 663 [hep-th/9506064] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. K. Hori and J. Walcher, F-term equations near Gepner points, JHEP 01 (2005) 008 [hep-th/0404196] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. M.R. Gaberdiel, A. Konechny and C. Schmidt-Colinet, Conformal perturbation theory beyond the leading order, J. Phys. A 42 (2009) 105402 [arXiv:0811.3149] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. M. Baumgartl, I. Brunner and M.R. Gaberdiel, D-brane superpotentials and RG flows on the quintic, JHEP 07 (2007) 061 [arXiv:0704.2666] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Baumgartl and S. Wood, Moduli webs and superpotentials for five-branes, JHEP 06 (2009) 052 [arXiv:0812.3397] [SPIRES].

    Article  ADS  Google Scholar 

  12. H. Jockers and M. Soroush, Effective superpotentials for compact D5-brane Calabi-Yau geometries, Commun. Math. Phys. 290 (2009) 249 [arXiv:0808.0761] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. M. Alim, M. Hecht, P. Mayr and A. Mertens, Mirror symmetry for toric branes on compact hypersurfaces, JHEP 09 (2009) 126 [arXiv:0901.2937] [SPIRES].

    Article  Google Scholar 

  14. M. Alim et al., Hints for off-shell mirror symmetry in type-II/F-theory compactifications, arXiv:0909.1842 [SPIRES].

  15. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Computing brane and flux superpotentials in F-theory compactifications, arXiv:0909.2025 [SPIRES].

  16. M. Aganagic and C. Beem, The geometry of D-brane superpotentials, arXiv:0909.2245 [SPIRES].

  17. H. Ooguri, Y. Oz and Z. Yin, D-branes on Calabi-Yau spaces and their mirrors, Nucl. Phys. B 477 (1996) 407 [hep-th/9606112] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Hanany and K. Hori, Branes and N = 2 theories in two dimensions, Nucl. Phys. B 513 (1998) 119 [hep-th/9707192] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247 [SPIRES].

  20. K. Hori, Linear models of supersymmetric D-branes, hep-th/0012179 [SPIRES].

  21. C. Albertsson, U. Lindström and M. Zabzine, N = 1 supersymmetric σ-model with boundaries. I, Commun. Math. Phys. 233 (2003) 403 [hep-th/0111161] [SPIRES].

    MATH  ADS  Google Scholar 

  22. C. Albertsson, U. Lindström and M. Zabzine, N = 1 supersymmetric σ-model with boundaries. II, Nucl. Phys. B 678 (2004) 295 [hep-th/0202069] [SPIRES].

    Article  ADS  Google Scholar 

  23. U. Lindström and M. Zabzine, N = 2 boundary conditions for non-linear σ-models and Landau-Ginzburg models, JHEP 02 (2003) 006 [hep-th/0209098] [SPIRES].

    Article  ADS  Google Scholar 

  24. P. Koerber, S. Nevens and A. Sevrin, Supersymmetric non-linear σ-models with boundaries revisited, JHEP 11 (2003) 066 [hep-th/0309229] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Sevrin, W. Staessens and A. Wijns, The world-sheet description of A and B branes revisited, JHEP 11 (2007) 061 [arXiv:0709.3733] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. A. Sevrin, W. Staessens and A. Wijns, An N = 2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields, JHEP 10 (2008) 108 [arXiv:0809.3659] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. A. Sevrin, W. Staessens and A. Wijns, An N = 2 worldsheet approach to D-branes in bihermitian geometries: II. The general case, JHEP 09 (2009) 105 [arXiv:0908.2756] [SPIRES].

    Article  Google Scholar 

  28. M. Dörrzapf, The definition of Neveu-Schwarz superconformal fields and uncharged superconformal transformations, Rev. Math. Phys. 11 (1999) 137 [hep-th/9712107] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  29. B. DeWitt, Supermanifolds, 2nd edition, Cambridge University Press, Cambridge U.K. (1992).

    MATH  Google Scholar 

  30. T. Voronov, Geometric integration theory on supermanifolds, Sov. Sci. Rev. C. Math. Phys. 9 (1992) 1.

    Google Scholar 

  31. A. Rogers, Supermanifolds: theory and applications, World Scientific (2007).

  32. F.A. Berezin, The method of second quantisation, Academic, New York U.S.A. (1966).

    Google Scholar 

  33. F.A. Berezin and D.A. Leîtes, Supermanifolds, Sov. Math. Dokl. 16 (1975) 1218.

    MATH  Google Scholar 

  34. I.N. Bernstein and D.A. Leîtes, Integral forms and Stokes’ formula on supermanifolds, Func. Anal. Appl. 11 (1977) 45.

    Article  MATH  Google Scholar 

  35. I.N. Bernstein and D.A. Leîtes, How to integrate differential forms on supermanifolds, Func. Anal. Appl. 11 (1977) 219.

    Article  Google Scholar 

  36. F.A. Berezin, Differential forms on supermanifolds, Sov. J. Nucl. Phys. 30 (1979) 605.

    MATH  MathSciNet  Google Scholar 

  37. A. Rogers, Consistent superspace integration, J. Math. Phys. 26 (1985) 385 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. M. Rothstein, Integration on noncompact supermanifolds, Trans. Americ. Maths. Soc. 299 (1987) 387.

    Article  MATH  MathSciNet  Google Scholar 

  39. A. Recknagel, D. Roggenkamp and V. Schomerus, On relevant boundary perturbations of unitary minimal models, Nucl. Phys. B 588 (2000) 552 [hep-th/0003110] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. A. Recknagel and V. Schomerus, D-branes in Gepner models, Nucl. Phys. B 531 (1998) 185 [hep-th/9712186] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. I. Brunner, M.R. Douglas, A.E. Lawrence and C. Romelsberger, D-branes on the quintic, JHEP 08 (2000) 015 [hep-th/9906200] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. I. Brunner and M.R. Gaberdiel, Matrix factorisations and permutation branes, JHEP 07 (2005) 012 [hep-th/0503207] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, ETH Zürich, 8093, Zürich, Switzerland

    Matthias R. Gaberdiel & Stefan Hohenegger

Authors
  1. Matthias R. Gaberdiel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Hohenegger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthias R. Gaberdiel.

Additional information

ArXiv ePrint: 0910.5122

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gaberdiel, M.R., Hohenegger, S. Manifestly supersymmetric RG flows. J. High Energ. Phys. 2010, 52 (2010). https://doi.org/10.1007/JHEP02(2010)052

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2010)052

Keywords

Search

Navigation