Skip to main content
SpringerLink
Log in

Defect perturbations in Landau-Ginzburg models

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

Abstract

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.

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. E. Wong and I. Affleck, Tunneling in quantum wires: a boundary conformal field theory approach, Nucl. Phys. B 417 (1994) 403 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. C. Bachas, J. de Boer, R. Dijkgraaf and H. Ooguri, Permeable conformal walls and holography, JHEP 06 (2002) 027 [hep-th/0111210] [SPIRES].

    Article  ADS  Google Scholar 

  3. V.B. Petkova and J.B. Zuber, Generalised twisted partition functions, Phys. Lett. B 504 (2001) 157 [hep-th/0011021] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  4. J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Duality and defects in rational conformal field theory, Nucl. Phys. B 763 (2007) 354 [hep-th/0607247] [SPIRES].

    Article  ADS  Google Scholar 

  5. I. Runkel, Perturbed defects and T-systems in conformal field theory, J. Phys. A 41 (2008) 105401 [arXiv:0711.0102] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  6. C. Bachas and I. Brunner, Fusion of conformal interfaces, JHEP 02 (2008) 085 [arXiv:0712.0076] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. I. Brunner and D. Roggenkamp, B-type defects in Landau-Ginzburg models, JHEP 08 (2007) 093 [arXiv:0707.0922] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. C. Bachas, On the symmetries of classical string theory, arXiv:0808.2777 [SPIRES].

  9. I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. S. Fredenhagen, M.R. Gaberdiel and C. Schmidt-Colinet, Bulk flows in Virasoro minimal models with boundaries, J. Phys. A 42 (2009) 495403 [arXiv:0907.2560] [SPIRES].

    Google Scholar 

  11. I. Brunner, H. Jockers and D. Roggenkamp, Defects and D-brane monodromies, arXiv:0806.4734 [SPIRES].

  12. K. Graham and G.M.T. Watts, Defect lines and boundary flows, JHEP 04 (2004) 019 [hep-th/0306167] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. C. Bachas and M. Gaberdiel, Loop operators and the Kondo problem, JHEP 11 (2004) 065 [hep-th/0411067] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. A. Alekseev and S. Monnier, Quantization of Wilson loops in Wess-Zumino-Witten models, JHEP 08 (2007) 039 [hep-th/0702174] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. D. Manolopoulos and I. Runkel, A monoidal category for perturbed defects in conformal field theory, arXiv:0904.1122 [SPIRES].

  16. M. Kormos, I. Runkel and G.M.T. Watts, Defect flows in minimal models, JHEP 11 (2009) 057 [arXiv:0907.1497] [SPIRES].

    Article  Google Scholar 

  17. J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93 (2004) 070601 [cond-mat/0404051] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. P. Seidel and R.P. Thomas, Braid group actions on derived categories, Duke Math Jour. 108 (2001) 37.

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Kapustin and Y. Li, D-Branes in Landau-Ginzburg models and algebraic geometry, JHEP 12 (2003) 005 [hep-th/0210296] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. I. Brunner, M. Herbst, W. Lerche and B. Scheuner, Landau-Ginzburg realization of open string TFT, JHEP 11 (2006) 043 [hep-th/0305133] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  21. M. Khovanov and L. Rozansky, Topological Landau-Ginzburg models on a world-sheet foam, Adv. Theor. Math. Phys. 11 (2007) 233 [hep-th/0404189] [SPIRES].

    MathSciNet  MATH  Google Scholar 

  22. H. Jockers and W. Lerche, Matrix factorizations, D-branes and their deformations, Nucl. Phys. Proc. Suppl. 171 (2007) 196 [arXiv:0708.0157] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. J. Knapp, D-Branes in topological string theory, arXiv:0709.2045 [SPIRES].

  24. C.I. Lazaroiu, On the boundary coupling of topological Landau-Ginzburg models, JHEP 05 (2005) 037 [hep-th/0312286] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. A. Kapustin and L. Rozansky, On the relation between open and closed topological strings, Commun. Math. Phys. 252 (2004) 393 [hep-th/0405232] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. S.K. Ashok, E. Dell’Aquila and D.-E. Diaconescu, Fractional branes in Landau-Ginzburg orbifolds, Adv. Theor. Math. Phys. 8 (2004) 461 [hep-th/0401135] [SPIRES].

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  28. S.K. Ashok, E. Dell’Aquila, D.-E. Diaconescu and B. Florea, Obstructed D-branes in Landau-Ginzburg orbifolds, Adv. Theor. Math. Phys. 8 (2004) 427 [hep-th/0404167] [SPIRES].

    MathSciNet  Google Scholar 

  29. J. Knapp and H. Omer, Matrix factorizations, minimal models and Massey products, JHEP 05 (2006) 064 [hep-th/0604189] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. N. Carqueville, Matrix factorisations and open topological string theory, JHEP 07 (2009) 005 [arXiv:0904.0862] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980) 35.

    Article  MathSciNet  MATH  Google Scholar 

  32. K. Hori, Boundary RG flows of N = 2 minimal models, hep-th/0401139 [SPIRES].

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

    Article  MathSciNet  ADS  Google Scholar 

  34. H. Enger, A. Recknagel and D. Roggenkamp, Permutation branes and linear matrix factorisations, JHEP 01 (2006) 087 [hep-th/0508053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

  36. P. Seidel, Lagrangian two-spheres can be symplectically knotted, J. Diff. Geom. 52 (1999) 145.

    MathSciNet  MATH  Google Scholar 

  37. P.S. Aspinwall and M.R. Douglas, D-brane stability and monodromy, JHEP 05 (2002) 031 [hep-th/0110071] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. S. Gukov and E. Witten, Gauge theory, ramification and the geometric Langlands program, hep-th/0612073 [SPIRES].

  39. S. Gukov, Surface operators and Knot homologies, arXiv:0706.2369 [SPIRES].

  40. M. Herbst, K. Hori and D. Page, Phases of N = 2 theories in 1+1 dimensions with boundary, arXiv:0803.2045 [SPIRES].

  41. E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. P.S. Aspinwall, Enhanced gauge symmetries and K3 surfaces, Phys. Lett. B 357 (1995) 329 [hep-th/9507012] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  43. I. Brunner, M.R. Gaberdiel and C.A. Keller, Matrix factorisations and D-branes on K3, JHEP 06 (2006) 015 [hep-th/0603196] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. P.S. Aspinwall, The Landau-Ginzburg to Calabi-Yau dictionary for D-branes, J. Math. Phys. 48 (2007) 082304 [hep-th/0610209] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. A. Adams, J. Polchinski and E. Silverstein, Don’t panic! Closed string tachyons in ALE space-times, JHEP 10 (2001) 029 [hep-th/0108075] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  46. J.A. Harvey, D. Kutasov, E.J. Martinec and G.W. Moore, Localized tachyons and RG flows, hep-th/0111154 [SPIRES].

  47. E.J. Martinec and G.W. Moore, On decay of k-theory, hep-th/0212059 [SPIRES].

  48. G.W. Moore and A. Parnachev, Localized tachyons and the quantum McKay correspondence, JHEP 11 (2004) 086 [hep-th/0403016] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  49. S. Rossi, Boundaries and defects in topological Landau-Ginzburg models, Ph. D. Thesis (2009).

Download references

Author information

Authors and Affiliations

  1. Arnold Sommerfeld Center, Ludwig Maximilians Universität, Theresienstr. 37, 80333, München, Germany

    Ilka Brunner

  2. Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748, Garching, Germany

    Ilka Brunner

  3. Department of Physics and Astronomy, Rutgers University, Piscataway, 08855-0849, NJ, U.S.A.

    Daniel Roggenkamp

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

    Sebastiano Rossi

Authors
  1. Ilka Brunner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Roggenkamp
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastiano Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilka Brunner.

Additional information

ArXiv ePrint: 0909.0696

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brunner, I., Roggenkamp, D. & Rossi, S. Defect perturbations in Landau-Ginzburg models. J. High Energ. Phys. 2010, 15 (2010). https://doi.org/10.1007/JHEP03(2010)015

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2010)015

Keywords

Search

Navigation