Duality symmetry of the p-form effective action and supertrace of the twisted de Rham complex

Nuclear Physics B

Volumn 648, Issue 3, 2003, Pages 542-556

  Gilkey, P ^a   Kirsten, K ^a,b   Vassilevich, D ^a,c   Zelnikov, A ^d,e  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b BAYLOR UNIVERSITY   (United States)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^d UNIVERSITY OF ALBERTA   (Canada)

^e LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

Author keywords

Dilaton; Dualities; Euler Poincar characteristics; Heat trace asymptotics; Pfaffian

Indexed keywords

EID: 0037433934     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(02)00975-6     Document Type: Article

References (37)

1. A.A. Andrianov, N.V. Borisov, M.V. Ioffe, Factorization method and Darboux transformation for multidimensional Hamiltonians, Theor. Math. Phys. 61 (1984) 1078, Teor. Mat. Fiz. 61 (1984) 183 (in Russian).
2. M.F. Atiyah, R.H. Bott, V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 13 (1973) 279
3. M.F. Atiyah, R.H. Bott, V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 28 (1975) 277, Erratum.
4. M.F. Atiyah, V.K. Patodi, I.M. Singer, Spectral asymmetry and Riemannian geometry, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71.
5. J.L. Barbon, Generalized Abelian S duality and coset constructions, Nucl. Phys. B 452 (1995) 313, hepth/9506137.
6. N. Berline, N. Getzler, M. Vergne, Heat Kernels and Dirac Operators, Grundlehren Band, Springer-Verlag, Berlin, 1991, p. 298.
7. T. Branson, P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary, Commun. Partial Differential Equations 15 (1990) 245.
8. S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. Math. 45 (1944) 741.
9. S. Chern, On the curvature integral in a Riemmanian manifold, Ann. Math. 46 (1945) 674
10. E. Cremmer, J. Scherk, S. Ferrara, SU(4) invariant supergravity theory, Phys. Lett. B 74 (1978) 61.
11. J.S. Dowker, R. Critchley, Effective Lagrangian and energy momentum tensor in de Sitter space, Phys. Rev. D 13 (1976) 3224.
12. M.J. Duff, P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179.
13. E. Elizalde, M. Lygren, D.V. Vassilevich, Antisymmetric tensor fields on spheres: functional determinants and non-local counterterms, J. Math. Phys. 37 (1996) 3105, hep-th/9602113.
14. G. Esposito, A. Kamenshchik, G. Pollifrone, Euclidean Quantum Gravity on Manifolds with Boundary, Kluwer, Dordrecht, 1997.
15. E.S. Fradkin, A.A. Tseytlin, Quantum equivalence of dual field theories, Ann. Phys. 162 (1985) 31.
16. P. Gilkey, Curvature and the eigenvalues of the Laplacian for elliptic complexes, Adv. Math. 10 (1973) 344.
17. P. Gilkey, The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary, Adv. Math. 15 (1975) 334.
18. P. Gilkey, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, 2nd Edition, CRC Press, 1994.
19. P.B. Gilkey, K. Kirsten, D.V. Vassilevich, Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario, Nucl. Phys. B 601 (2001) 125, hep-th/0101105.
20. P.B. Gilkey, K. Kirsten, D.V. Vassilevich, Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary, math-ph/0211020.
21. D. Grumiller, W. Kummer, D.V. Vassilevich, Dilaton gravity in two dimensions, Phys. Rep. 369 (2002) 327, hep-th/0204253.
22. Y.V. Gusev, A.I. Zelnikov, Two-dimensional effective action for matter fields coupled to the dilaton, Phys. Rev. D 61 (2000) 084010, hep-th/9910198.
23. S.W. Hawking, Zeta function regularization of path integrals in curved spacetime, Commun. Math. Phys. 55 (1977) 133.
24. G.T. Horowitz, L. Susskind, Bosonic M theory, J. Math. Phys. 42 (2001) 3152, hep-th/0012037.
25. I.R. Klebanov, A.A. Tseytlin, D-branes and dual gauge theories in type 0 strings, Nucl. Phys. B 546 (1999) 155, hep-th/9811035.
26. W. Kummer, D.V. Vassilevich, Effective action and Hawking radiation for dilaton coupled scalars in two dimensions, Phys. Rev. D 60 (1999) 084021, hep-th/9811092.
27. H.P. McKean, I.M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geom. 1 (1967) 43.
28. Y.N. Obukhov, The geometrical approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195.
29. V.K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970) 269.
30. D.B. Ray, I.M. Singer, Analytic torsion for complex manifolds, Ann. Math. 98 (1973) 154.
31. V.N. Romanov, A.S. Schwarz, Anomalies and elliptic operators, Teor. Mat. Fiz. 41 (1979) 190.
32. A.S. Schwarz, The partition function of a degenerate functional, Commun. Math. Phys. 67 (1979) 1.
33. A.S. Schwarz, A.A. Tseytlin, Dilaton shift under duality and torsion of elliptic complex, Nucl. Phys. B 399 (1993) 691, hep-th/9210015.
34. W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170.
35. D. Vassilevich, A. Zelnikov, Discrete symmetries of functional determinants, Nucl. Phys. B 594 (2000) 501, hep-th/0009084.
36. H. Weyl, The Classical Groups, Princeton Univ. Press, Princeton, 1946.
37. E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982) 661.