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Relative Quantum Field Theory

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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.

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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

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Correspondence to Daniel S. Freed.

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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.

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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

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