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Communications in Mathematical Physics

Volumn 106, Issue 1, 1986, Pages 1-40

Theta functions, modular invariance, and strings

(3) Alvarez Gaumé, Luis a Moore, Gregory a Vafa, Cumrun a

a HARVARD UNIVERSITY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002914155 PISSN: 00103616 EISSN: 14320916 Source Type: Journal
DOI: 10.1007/BF01210925 Document Type: Article

Times cited : (372)

References (45)

1
- 84911755322
- World Scientific, New York
- (1985) Superstrings: The first fifteen years, Vol. 5, I, II
- Schwarz, J.¹

2
- 4243226043
- Quantum geometry of bosonic strings
- (1981) Phys. Lett. , vol.103 B , pp. 207
- Polyakov, A.M.¹

3
- 84935753636
- Friedan, D., Martinec, E., Shenker, S.: Conformal innvriance, supersymmetry, and strings. Princeton preprint

4
- 84935748461
- Martinec, E.: Nonrenormalization theorems and fermionic string finiteness. Princeton preprint

5
- 33646073638
- (1985) Phys. Rev. Lett. , vol.54 , pp. 502
- Gross, D.J.¹ Harvey, J.A.² Martinec, E.³ Rohm, R.⁴

6
- 0000346203
- Strings on orbifolds I
- (1985) Nucl. Phys. , vol.261 B , pp. 651
- Dixon, L.¹ Harvey, J.² Vafa, C.³ Witten, E.⁴

7
- 0004152420
- Springer, Berlin, Heidelberg, New York
- (1980) Riemann surfaces
- Farkas, H.M.¹ Kra, I.²

8
- 0041738199
- J., Birman, W.J., Harvey, Academic Press, New York
- (1977) Discrete groups and automorphic functions

9
- 0003430207
- Interscience, New York
- (1966) Combinatorial group theory
- Magnus¹ Karras² Solitar³

10
- 0003864210
- Princeton University Press, Princeton, NJ
- (1974) Characteristic classes. Ann. Math. Studies, Vol. 76
- Milnor, J.W.¹ Stasheff, J.D.²

11
- 85100672658
- Wiley, New York
- (1978) Principles of algebraic geometry
- Griffiths, P.¹ Harris, J.²

12
- 84935746254
- Princeton University Press, Princeton, NJ
- (1966) Introduction to Riemann surfaces princeton Math. Notes
- Gunning, R.¹

13
- 0003983437
- Birkhäuser, Boston
- (1983) Tata lectures on theta, Vols. I, II
- Mumford, D.¹

14
- 0003714785
- Springer, Berlin, Heidelberg, New York
- (1973) Theta functions on Riemann surfaces Springer notes in math., Vol. 352
- Fay, J.¹

15
- 0002216062
- Determinants of Cauchy-Riemann operators on Riemann surfaces
- (1985) Funkts. Anal. Prilozh. , vol.19 , pp. 37
- Quillen, D.¹

16
- 84935743933
- Alvarez, O.: Conformal anomalies and the index theorem. Berkeley preprint

17
- 0002821869
- Strings and supermoduli
- (1986) Phys. Lett. , vol.169 B , pp. 47
- Moore, G.¹ Nelson, P.² Polchinski, J.³

18
- 84935708637
- Belavin, A.A., Knizhnik, V.G.: Algebraic geometry and the geometry of quantum strings. Landau Institute preprint; See also, Catenacci, R., Cornalba, M., Martellini, M., Reina, C.: Algebraic geometry and path integrals for closed strings; Bost, J.B., Jolicoeur, J.: A holomorphy property and critical dimension in string theory from an index theorem. Saclay PhT/86-28

19
- 0010190678
- Gravitational anomalies
- (1984) Nucl. Phys. , vol.234 B , pp. 269
- Alvarez-Gaumé, L.¹ Witten, E.²

20
- 84935743158
- Actually, this particular example is well-known to physicists. See, for example, Jackiw, R.: Topological methods in field theory. Les Houches lectures 1983. What is new here is the better geometrical understanding in terms of holomorphic line bundles, and the idea that holomorphy is a powerful tool for understanding determinants

21
- 84935685520
- The generalization of Quillen's theorem has been independently derived by Belavin and Knizhnik. We thank Stephen Della Pietra for pointing out an error in an earlier version of Eq. (4.15). We also thank Phil Nelson and Joe Polchinski for discussions on the application of Eq. (4.15) to holomorphic factorization on moduli space, and on the important difference between Eq. (4.15) and Eq. (4.16)

22
- 84935689953
- Bismut, J.-M., Freed, D.S.: Geometry of elliptic families: Anomalies and determinants. M.I.T. preprint; The analysis of elliptic families: Metrics and connections on determinant bundles. Commun. Math. Phys. (in press); The analysis of elliptic families: Dirac operators, eta invariants, and the holonomy theorem. Commun. Math. Phys. (in press)

23
- 0009418470
- On obtaining a positive line bundle from the Weil-Petersson class
- (1985) American Journal of Mathematics , vol.107 , pp. 1485
- Wolpert, S.¹

24
- 84966229718
- Finite dimensional Teichmüller spaces and generalizations
- (1981) Bulletin of the American Mathematical Society , vol.5 , pp. 131
- Bers, L.¹

25
- 0001480411
- Introduction to Polyakov's string theory
- J.-B., Zuber, R., Stora, Elsevier, Amsterdam
- (1984) Les Houches 1982. Recent advances in field theory and statistical mechanics
- Friedan, D.¹

26
- 84935690201
- We owe this observation to Phil Nelson

27
- 84935717247
- Atiyah, M.: Riemann surfaces and spin structures. Ann. Sci. Ec. Norm. Super. 4 (1971)

28
- 0000242153
- Theta characteristics of an algebraic curve
- (1971) Ann. Sci. Éc. Norm. Supér. , vol.4 , pp. 24
- Mumford, D.¹

29
- 33646063975
- Harmonic spinors
- (1974) Adv. Math. , vol.14 , pp. 1-55
- Hitchin, N.¹

30
- 27344438814
- Global anomalies in string theory
- W.A., Bardeen, A.R., White, World Scientific, New York
- (1985) Geometry anomalies topology
- Witten, E.¹

31
- 84935747561
- Seiberg, N., Witten, E.: Spin structures in string theory. Princeton preprint

32
- 84935715636
- Alvarez-Gaumé, L., Ginsparg, P., Moore, G., Vafa, C.: An O(16) ×O(16) heterotic string. Harvard preprint HUTP-86/AO13

33
- 84935694237
- For a pedagogical treatment and further references to the literature see Nelson, P., Moore, G.: Heterotic geometry. Harvard preprint HUTP-86/A014

34
- 33645920089
- Theory of strings with boundary: Topology, fluctuations, geometry
- (1983) Nucl. Phys. , vol.216 B , pp. 125
- Alvarez, O.¹

35
- 0003024102
- Evaluation of the one loop string path integral
- (1986) Commun. Math. Phys. , vol.104 , pp. 37
- Polchinski, J.¹

36
- 46149140911
- Measure for moduli: The Polyakov string has no nonlocal anomalies
- (1986) Nucl. Phys. , vol.266 B , pp. 58
- Moore, G.¹ Nelson, P.²

37
- 0001251753
- Multiloop amplitudes for the bosonic string
- (1986) Nucl. Phys. , vol.269 B , pp. 205
- D'Hoker, E.¹ Phong, D.²

38
- 84935720701
- D'Hoker, E., Phong, D.: Loop amplitudes for the fermionic string. CU-TP-340

39
- 0011074361
- Loop graph in the dual-tube model
- (1972) Phys. Rev. , vol.5 D , pp. 1945
- Shapiro, J.¹

40
- 14644386708
- Supersymmetry, supergravity theories and the dual spinor model
- (1977) Nucl. Phys. , vol.122 B , pp. 253
- Gliozzi, F.¹ Scherk, J.² Olive, D.³

41
- 84935723475
- In preparation

42
- 0004135743
- Springer, Berlin, Heidelberg, New York
- (1972) Theta functions
- Igusa, J.¹

43
- 84935729841
- Vafa, C.: Modular invariance and discrete torsion on orbifolds

44
- 84935723042
- Dixon, L., Harvey, J.: String theories in ten dimensions without spacetime supersymmetry. Princeton preprint

45
- 84935713998
- After this work was completed we received a preprint in which this question is answered in the affirmative. See Manin, Yu.I.: The partition function of the Polyakov string can be expressed in terms of theta functions. Phys. Lett. (submitted)

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