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AKSZ–BV Formalism and Courant Algebroid-Induced Topological Field Theories

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Abstract

We give a detailed exposition of the Alexandrov–Kontsevich–Schwarz– Zaboronsky superfield formalism using the language of graded manifolds. As a main illustrating example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin–Vilkovisky master action for the model.

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References

  1. Alexandrov M., Kontsevich M., Schwarz A. and Zaboronsky O. (1997). The geometry of the Master equation and topological quantum field theory. Int. J. Mod. Phys. A 12(7): 1405–1429

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. Batalin I. and Vilkovisky G. (1981). Gauge algebra and quantization. Phys. Lett. 102: 27

    Article  MathSciNet  Google Scholar 

  3. Cattaneo A. and Felder G. (2000). A path integral approach to the Kontsevich quantization formula. Commun. Math. Phys. 212: 591–611

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Cattaneo A. and Felder G. (2001). On the AKSZ formulation of the Poisson sigma model. Lett. Math. Phys. 56: 163–179

    Article  MATH  MathSciNet  Google Scholar 

  5. Hofman, C., Park, J.-S.: Topological open membranes. Preprint hep-th/0209148, 2002

  6. Hofman C. and Park J.-S. (2004). BV quantization of topological open membranes. Comm. Math. Phys. 249(2): 249–271 Preprint hep-th/0209214

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Ikeda N. (2002). Topological field theories and geometry of Batalin-Vilkovisky algebras. JHEP 0210: 076 Preprint hep-th/0209042

    Article  ADS  Google Scholar 

  8. Ikeda N. (2003). Chern–Simons gauge theory coupled with BF theory. Int. J. Mod. Phys. A 18: 2689–2702 Preprint hep-th/0203043

    Article  MATH  ADS  Google Scholar 

  9. Ikeda N. and Izawa K-i. (2004). Dimensional reduction of nonlinear gauge theories.. JHEP 0409: 030 Preprint hep-th/0407243

    Article  ADS  MathSciNet  Google Scholar 

  10. Park, J.-S.: Topological open p-branes. In: Symplectic Geometry and Mirror Symmetry (Seoul, 2000), pp. 311–384. World Scientific River Edge, NJ (2001). Preprint hep-th/0012141

  11. Roytenberg, D.: On the structure of graded symplectic supermanifolds and Courant algebroids. In: Voronov, (ed.) Quantization, Poisson Brackets and Beyond. Contemporary Mathematics American Mathematics Sociecty, vol. 315. Providence, RI (2002). math.SG/0203110

  12. Roytenberg D. (2002). Quasi-Lie bialgebroids and twisted Poisson manifolds. Lett. Math. Phys. 61(2): 123–137 math.QA/0112152

    Article  MATH  MathSciNet  Google Scholar 

  13. Schaller P. and Strobl T. (1994). Poisson structure induced (topological) field theories. Mod. Phys. Lett. A 9: 3129–3136 Preprint hep-th/9405110

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Voronov, T.: Graded manifolds and Drinfeld doubles for Lie bialgebroids. In: Voronov, T. (ed.) Quantization, Poisson Brackets and Beyond. Contemporary Mathematics American Mathematics Sociecty, vol. 315. Providence, RI (2002). Preprint math.DG/0105237

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Correspondence to Dmitry Roytenberg.

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Roytenberg, D. AKSZ–BV Formalism and Courant Algebroid-Induced Topological Field Theories. Lett Math Phys 79, 143–159 (2007). https://doi.org/10.1007/s11005-006-0134-y

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  • DOI: https://doi.org/10.1007/s11005-006-0134-y

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