Skip to main content
Springer Nature Link
Log in

Relative Quantum Field Theory

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal theory in six dimensions.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Atiyah M.: On framings of 3-manifolds. Topology 29(1), 1–7 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blanchet C., Habegger N., Masbaum G., Vogel P.: Topological quantum field theories derived from the Kauffman bracket. Topology 34(4), 883–927 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Moore, G., Belov, D.: Classification of abelian spin Chern-Simons theories, http://arxiv.org/abs/hep-th/0505235v1, 2005

  4. Freed D.S.: Higher algebraic structures and quantization. Commun. Math. Phys. 159(2), 343–398 (1994)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Freed D.S., Hopkins M.J.: Chern–Weil forms and abstract homotopy theory. Bull. Amer. Math. Soc. (N.S.) 50(3), 431–468 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Freed, D.S., Hopkins, M.J., Lurie, J., Teleman, C.: Topological quantum field theories from compact Lie groups. A celebration of the mathematical legacy of Raoul Bott, CRM Proc. Lecture Notes, Vol. 50, Providence, RI: Amer. Math. Soc., 2010, pp. 367–403

  7. Gaiotto D., Moore G.W., Neitzke A.: Wall-crossing, Hitchin systems, and the WKB approximation. Adv. Math. 234, 239–403 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hopkins M.J., Singer I.M.: Quadratic functions in geometry, topology, and M-theory. J. Diff. Geom. 70, 329–452 (2005)

    MATH  MathSciNet  Google Scholar 

  9. Kapustin, A.: Topological field theory, higher categories, and their applications. In: Proceedings of the International Congress of Mathematicians. Volume III (New Delhi), Hindustan Book Agency, 2010, pp. 2021–2043

  10. Lurie, J.: On the classification of topological field theories. In: Current developments in mathematics, 2008, Somerville, MA: Int. Press, 2009, pp. 129–280

  11. Quinn, F.: Lectures on axiomatic topological quantum field theory. In: Geometry and quantum field theory (Park City, UT, 1991), IAS/Park City Math. Ser., Vol. 1, Providence, RI: Amer. Math. Soc., 1995, pp. 323–453

  12. Strominger A.: Open p-branes. Phys. Lett. B 383, 44–47 (1996)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Segal, G.B.: Felix Klein Lectures 2011. http://www.mpim-bonn.mpg.de/node/3372/abstracts, 2011

  14. Segal, G.: The definition of conformal field theory. In: Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., Vol. 308, Cambridge: Cambridge Univ. Press, 2004, pp. 421–577

  15. Stirling, S.D.: Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories. Ann Arbor, MI: ProQuest LLC, 2008 Thesis (Ph.D.)–The University of Texas at Austin

  16. Turaev, V.: Homotopy quantum field theory. EMS Tracts in Mathematics, Vol. 10, Zürich: European Mathematical Society (EMS), 2010, Appendix 5 by M. Müger and Appendices 6 and 7 by A. Virelizier

  17. Vafa, C., Witten, E.: A strong coupling test of S-duality. Nucl. Phys. B. 431(1–2), 3–77 (1994)

    Google Scholar 

  18. Witten, E.: Some comments on string dynamics. Strings ’95 (Los Angeles, CA, 1995), River Edge, NJ: World Sci. Publ., 1996, pp. 501–523

  19. Witten, E.: Geometric Langlands from six dimensions. In: A celebration of the mathematical legacy of Raoul Bott, CRM Proc. Lecture Notes, Vol. 50, Providence, RI: Amer. Math. Soc., 2010, pp. 281–310

  20. Witten E.: Supersymmetric index in four-dimensional gauge theories. Adv. Theor. Math. Phys. 5(5), 841–907 (2001)

    MATH  MathSciNet  Google Scholar 

  21. Witten E.: On holomorphic factorization of WZW and coset models. Comm. Math. Phys. 144(1), 189–212 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. Walker, K.: On Witten’s 3-manifold invariants. http://tqft.net/other-papers/KevinWalkerTQFT.pdf, 1991

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, RLM 8.100, The University of Texas at Austin, 2515 Speedway Stop C1200, Austin, TX, 78712-1202, USA

    Daniel S. Freed

  2. Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA, 94720-3840, USA

    Constantin Teleman

Authors
  1. Daniel S. Freed
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Constantin Teleman
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Daniel S. Freed.

Additional information

Communicated by N. A. Nekrasov

The work of D.S.F. is supported by the National Science Foundation under grant DMS-1160461.

The work of C.T. is supported by NSF grant DMS-1160461.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freed, D.S., Teleman, C. Relative Quantum Field Theory. Commun. Math. Phys. 326, 459–476 (2014). https://doi.org/10.1007/s00220-013-1880-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-013-1880-1

Keywords