Advertisement

An Overview of B-branes in Gauged Linear Sigma Models

Conference paper
  • 672 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 240)

Abstract

We review the BPS D-branes in gauged linear sigma models corresponding to toric Calabi–Yau (CY) varieties preserving \({\mathscr {N}}=2_B\) supersymmetry, and their relation to stable low energy branes. The chiral sectors of these low energy branes are described mathematically by various derived categories in various parts of the CY Kähler moduli space \({\mathscr {M}}_K\). For a fixed \({\mathscr {M}}_K\), all these descriptions should in fact be equivalent in a categorical sense and we review some aspects of this equivalence from a physical perspective. This is a short summary of the results of the comprehensive work by Herbst, Hori and Page [3] with some elementary commentary.

Supplementary material

References

  1. 1.
    Maxim Kontsevich. Homological Algebra of Mirror Symmetry. 1994.Google Scholar
  2. 2.
    Andrew Strominger, Shing-Tung Yau, and Eric Zaslow. Mirror symmetry is T duality. Nucl. Phys., B479:243–259, 1996.Google Scholar
  3. 3.
    Manfred Herbst, Kentaro Hori, and David Page. Phases Of N \(=\) 2 Theories In 1+1 Dimensions With Boundary. 2008.Google Scholar
  4. 4.
    T. Bridgeland, A. King, and M. Reid. Mukai implies McKay: the McKay correspondence as an equivalence of derived categories. ArXiv Mathematics e-prints, August 1999.Google Scholar
  5. 5.
    Y. Kawamata. Log Crepant Birational Maps and Derived Categories. ArXiv Mathematics e-prints, November 2003.Google Scholar
  6. 6.
    D. Orlov. Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities. ArXiv Mathematics e-prints, March 2005.Google Scholar
  7. 7.
    Edward Witten. Phases of N=2 theories in two-dimensions. Nucl. Phys., B403:159–222, 1993. [AMS/IP Stud. Adv. Math.1,143(1996)].Google Scholar
  8. 8.
    Paul S. Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Anton Kapustin, Gregory W. Moore, Mark Gross, Graeme Segal, Balázs Szendröi, and P. M. H. Wilson. Dirichlet branes and mirror symmetry, volume 4 of Clay Mathematics Monographs. AMS, Providence, RI, 2009.Google Scholar
  9. 9.
    A. Schwimmer and N. Seiberg. Comments on the N \(=\) 2, N \(=\) 3, N \(=\) 4 Superconformal Algebras in Two-Dimensions. Phys. Lett., B184:191–196, 1987.Google Scholar
  10. 10.
    Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, and Eric Zaslow. Mirror symmetry, volume 1 of Clay mathematics monographs. AMS, Providence, RI, 2003. With a preface by Vafa.Google Scholar
  11. 11.
    Lance J. Dixon, Jeffrey A. Harvey, C. Vafa, and Edward Witten. Strings on Orbifolds. Nucl. Phys., B261:678–686, 1985.Google Scholar
  12. 12.
    Simeon Hellerman, Shamit Kachru, Albion E. Lawrence, and John McGreevy. Linear sigma models for open strings. JHEP, 07:002, 2002.Google Scholar
  13. 13.
    Kentaro Hori. Linear models of supersymmetric D-branes. In Symplectic geometry and mirror symmetry. Proceedings, 4th KIAS Annual International Conference, Seoul, South Korea, August 14-18, 2000, pages 111–186, 2000.Google Scholar
  14. 14.
    Wolfgang Lerche, Cumrun Vafa, and Nicholas P. Warner. Chiral Rings in N \(=\) 2 Superconformal Theories. Nucl. Phys., B324:427–474, 1989.Google Scholar
  15. 15.
    Edward Witten. Mirror manifolds and topological field theory. 1991. [AMS/IP Stud. Adv. Math.9,121(1998)].Google Scholar
  16. 16.
    Ashoke Sen. Tachyon condensation on the brane anti-brane system. JHEP, 08:012, 1998.Google Scholar
  17. 17.
    Michael R. Douglas. D-branes, categories and N=1 supersymmetry. J. Math. Phys., 42:2818–2843, 2001.Google Scholar
  18. 18.
    Eric R. Sharpe. D-branes, derived categories, and Grothendieck groups. Nucl. Phys., B561:433–450, 1999.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsUniversity of WaterlooWaterlooCanada

Personalised recommendations