Supermanifolds from Feynman graphs

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 31, 2008, Pages

  Marcolli, Matilde ^a   Rej, Abhijnan ^a  

^a MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48849113991     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/31/315402     Document Type: Article

References (25)

1. Abramovich D, Karu K, Matsuki K and Wlodarczyk J 2002 Torification and factorization of birational maps J. Am. Math. Soc. 15 531-72
2. Aganagic M and Vafa C 2004 Mirror symmetry and supermanifold Adv. Theor. Math. Phys. 8 939-54
3. Belkale P and Brosnan P 2003 Matroids, motives, and a conjecture of Kontsevich Duke Math. J. 116 147-88
4. Bergbauer C and Rej A Insertion of graphs and singularities of graph hypersurfaces Preprint
5. Bernšteǐn I N and Leǐtes D A 1977 Integral forms and the Stokes formula on supermanifolds Functional Anal. Appl. 11 45-7
6. Bjorken J and Drell S 1964 Relativistic Quantum Mechanics (New York: McGraw-Hill)
7. Bjorken J and Drell S 1965 Relativistic Quantum Fields (New York: McGraw-Hill)
8. Bloch S 2007 Motives associated to graphs Japan J. Math. 2 165-96
9. Bloch S, Esnault E and Kreimer D 2006 On motives associated to graph polynomials Commun. Math. Phys. 267 181-225
10. Broadhurst D and Kreimer D 1997 Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops Phys. Lett. B 393 403-12
11. Connes A and Kreimer D 2000 Renormalization in quantum field theory and the Riemann-Hilbert problem: I. The Hopf algebra structure of graphs and the main theorem Commun. Math. Phys. 210 249-73
12. Connes A and Marcolli M 2004 Renormalization and motivic Galois theory Int. Math. Res. Not. 4073-91
13. Kashiwara M and Shapira P 1990 Sheaves on Manifolds (Berlin: Springer)
14. Kumar S P and Policastro G 2005 Strings in twistor superspace and mirror symmetry Phys. Lett. B 619 163-70
15. Larsen M and Lunts V 2003 Motivic measures and stable birational geometry Moscow Math. J. 3 85-95
16. LeBrun C, Poon Y S and Wells R O 1990 Projective embeddings of complex supermanifolds Commun. Math. Phys. 126 433-52
17. Manin Yu I 1988 Gauge Field Theory and Complex Geometry (Berlin: Springer)
18. Medvedev P B 1978 α representation in scalar supersymmetric theory Teo. Mat. Fiz. 35 37-47 (Institute of Theoretical and Experimental Physics (transl.))
19. Nakanishi N 1971 Graph Theory and Feynman Integrals (London: Gordon and Breach)
20. Penkov I B and Skornyakov I A 1987 Projectivity and D-affinity of flag supermanifolds Russ. Math. Surv. 40 233-4
21. Ramond P 1990 Field Theory: a Modern Primer (Reading, MA: Addison-Wesley)
22. Rosly A A, Schwarz A S and Voronov A A 1988 Geometry of superconformal manifolds Commun. Math. Phys. 119 129-52
23. Schwarz A and Shapiro I 2006 Supergeometry and arithmetic geometry Nucl. Phys. B 756 207-18
24. Sethi S 1994 Supermanifolds, rigid manifolds and mirror symmetry Nucl. Phys. B 430 31-50
25. van Suijlekom W 2006 The Hopf algebra of Feynman graphs in quantum electrodynamics Lett. Math. Phys. 77 265-81