Current algebras and differential geometry

Journal of High Energy Physics

Volumn , Issue 3, 2005, Pages 777-790

  Alekseev, Anton ^a,b   Strobl, Thomas ^c  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UPPSALA UNIVERSITY   (Sweden)

^c FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

Anomalies in Field and String Theories; Conformal Field Models in String Theory; Differential and Algebraic Geometry

Indexed keywords

EID: 27344449706     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. S.B. Treiman, E. Witten, R. Jackiw, and B. Zumino, Current algebra and anomalies Singapore: World Scientific, Singapore, 1986, p. 537.
2. L.D. Faddeev, Operator anomaly for the gauss law, Phys. Lett. B 145 (1984) 81.
3. L.D. Faddeev and S.L. Shatashvili, Algebraic and hamiltonian methods in the theory of nonabelian anomalies, Theor. Math. Phys. 60 (1985) 770.
4. V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys. B 247 (1984) 83.
5. V.G. Kac, Infinite dimensional Lie algebras, Cambridge, UK: Univ. Pr., 1990, p. 400.
6. Z.J. Liu, A. Weinstein and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 46 (1997) 547.
7. F. Malikov, V. Schechtman, Chiral de Rham complex, 2. Differential topology, infinite-dimensional Lie algebras, and applications, Amer. Math. Soc. Transl, Ser. 2, 194, 149-188, Amer. Math. Soc., Providence, RI, 1999.
8. P. Bressler, Vertex algebroids I, preprint math.AG/02021850202185;
9. Vertex algebroids II, preprint math.AG/03041150304115.
10. E. Witten, Nonabelian bosonization in two dimensions, Commun. Math. Phys. 92 (1984) 455.
11. P. Schaller and T. Strobl, Poisson sigma models: a generalization of 2D gravity Yang-Mills systems, hep-th/9411163.
12. P. Schaller and T. Strobl, Poisson structure induced (topological) field theories, Mod. Phys. Lett. A 9 (1994) 3129 [hep-th/9405110].
13. N. Ikeda, Two-dimensional gravity and nonlinear gauge theory, Ann. Phys. (NY) 235 (1994) 435 [hep-th/9312059].
14. C. Klimčík and T. Strobl, WZW-poisson manifolds, J. Geom. Phys. 43 (2002) 341 math.sg/0104189.
15. J.-S. Park, Topological open p-branes, hep-th/0012141.
16. K. Gawȩdzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B 320 (1989) 625.
17. P. Severa, Letters to Weinstein, http://sophia.dtp.fmph.uniba.sk/~severa/ letters/.
18. T.J. Courant, Dirac manifolds, Trans. AMS 319 (1990) 631-661.
19. Y. Kosmann-Schwarzbach, From Poisson algebras to Gerstenhaber algebras, Ann. Inst. Fourier (Grenoble) 46 (1996) no. 5, 1243-1274.
20. R. Jackiw and K. Johnson, Anomalies of the axial vector current, Phys. Rev. 182 (1969) 1459.
21. V.W. Guillemin and S. Sternberg, Supersymmetry and equivariant de Rham theory, Mathematics Past and Present, Springer-Verlag, Berlin, 1999.
22. C.M. Hull and B. Spence, The gauged nonlinear sigma model with Wess-Zumino term, Phys. Lett. B 232 (1989) 204.
23. J.M. Figueroa-O'Farrill and S. Stanciu, Gauged Wess-Zumino terms and equivariant cohomology, Phys. Lett. B 341 (1994) 153 [hep-th/9407196].
24. P. Severa and A. Weinstein, Poisson geometry with a 3-form background, Prog. Theor. Phys. Suppl. 144 (2001) 146.
25. R. Jackiw, Dirac's magnetic monopoles (again), Int. J. Mod. Phys. A A19S1 (2004) 137.
26. N. Hitchin, Generalized Calabi-Yau manifolds, Q.J. Math., 54 (2003) no. 3 281-308.
27. M. Gualtieri, Generalized complex geometry, Ph.D. thesis, University of Oxford, 2003, math.DG/0401221.
28. A.S. Cattaneo and G. Felder, Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model, math.qa/0309180.
29. I. Calvo and F. Falceto, Poisson reduction and branes in Poisson-sigma models, 2004.
30. U. Lindstrom, R. Minasian, A. Tomasiello, and M. Zabzine, Generalized complex manifolds and supersymmetry, 2004.
31. E. Getzler, Manin triples and N = 2 superconformal field theory, hep-th/9307041.
32. A. Kotov, P. Schaller, and T. Strobl, Dirac sigma models, 2004, to be published in Commun. Math. Phys.