zbMATH — the first resource for mathematics

Supersymmetry and the Atiyah-Singer index theorem. (English) Zbl 0528.58034

58J20 Index theory and related fixed-point theorems on manifolds
58D30 Applications of manifolds of mappings to the sciences
81T08 Constructive quantum field theory
58A12 de Rham theory in global analysis
58A14 Hodge theory in global analysis
57R20 Characteristic classes and numbers in differential topology
Full Text: DOI
[1] Witten, E.: Constraints on supersymmetry breaking. Nucl. Phys. B202, 253 (1982) · Zbl 0499.53056
[2] Singer, I.M., McKean, H.P., Jr.: Curvature ? the eigenvalues of the Laplacian. J. Diff. Geom.1, 43-69 (1967) · Zbl 0198.44301
[3] Witten, E.: Supersymmetry and morse theory. J. Diff. Geom.17, 661 (1982) · Zbl 0499.53056
[4] Witten, E.: Holomorphic morse inequalities. Princeton Preprint 1982 · Zbl 0499.53056
[5] Atiyah, M.F., Singer, I.M.: Index of elliptic operators. I. Ann. Math.87, 485 (1968) · Zbl 0164.24301
[6] Atiyah, M.F., Segal, G.B.: Index of elliptic operators. II. Ann. Math.87, 531 (1968) · Zbl 0164.24201
[7] Atiyah, M.F., Singer, I.M.: Index of elliptic operators. III. Ann. Math.87, 546 (1968) · Zbl 0164.24301
[8] Atiyah, M.F., Singer, I.M.: Index of elliptic operators. IV. Ann. Math.93, 119 (1971) · Zbl 0212.28603
[9] Atiyah, M.F., Singer, I.M.: Index of elliptic operators. V. Ann. Math.93, 139 (1971) · Zbl 0212.28603
[10] Atiyah, M.F., Bott, R., Patodi, V.K.: On the heat equation and the index theorem. Invent. Math.19, 279 (1973) · Zbl 0257.58008
[11] Gilkey, P.B.: The index theorem and the heat equation. Boston: Publish or Perish Inc. 1974 · Zbl 0287.58006
[12] Cecotti, S., Girardello, L.: Functional measure, topology, and dynamical supersymmetry breaking. Phys. Lett.110B, 39 (1982) · Zbl 0505.60073
[13] di Vecchia, P., Ferrara, S.: Classical solutions in two dimensional supersymmetric field theories. Nucl. Phys. B130, 93 (1977)
[14] Witten, E.: Supersymmetric form of the non-linear ?-model in two dimensions. Phys. Rev. D16, 2991 (1977)
[15] Freedman, D.Z., Townsend, P.K.: Antisymmetric tensor gauge theories and non-linear ?-models. Nucl. Phys. B177, 282 (1981) · Zbl 0983.81513
[16] Witten, E.: An SU(2) anomaly. Phys. Lett. B117, 324 (1982) · Zbl 0598.92008
[17] Zumino, B.: Supersymmetry and Kähler manifolds. Phys. Lett. B87, 203 (1979)
[18] Lichnerowicz, A.: Global theory of connections and the holonomy group. Leyden: Noordhoof 1976 · Zbl 0337.53031
[19] Alvarez-Gaumé, L., Freedman, D.Z.: Potential terms in two dimensional extended supersymmetry. Harvard Preprint
[20] Chern, S.S.: On the curvature integrals in a Riemannian manifold. Ann. Math.46, 674 (1942) · Zbl 0060.38104
[21] Alvarez-Gaumé, L., Freedman, D.Z., Mukhi, S.: The background field method in supersymmetric ?-models. Ann. Phys.134, 85 (1981)
[22] Milnor, J.W., Stasheff, J.D.: Characteristic classes. Princeton, NJ: Princeton University Press 1974 · Zbl 0298.57008
[23] Eguchi, T., Gilkey, P.B., Hanson, A.J.: Gravitation, gauge theories, and differential geometry. Phys. Rep. 213 (1980)
[24] Atiyah, M.F., Bott, R.: A Lefshetz fixed point formula for elliptic differential operators. Bull. Am. Math. Soc.12, 245 (1966) · Zbl 0151.31801
[25] Atiyah, M.F., Bott, R.: A Lefshetz fixed point formula for elliptic complexes. I, II. Ann. Math.86, 374 (1967);88, 451 (1968) · Zbl 0161.43201
[26] Haag, R., Lopuszanski, J., Sohnius, M.: All possible generators of supersymmetries of theS-matrix. Nucl. Phys. B88, 61 (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.