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Superconformal geometry and string theory. (English) Zbl 0667.58008

We give a formula for the determinant of the super Laplace operator in a holomorphic hermitian line bundle over a superconformal manifold. This is then used to obtain an expression for the fermion string measure.

MSC:

58C50 Analysis on supermanifolds or graded manifolds
58J90 Applications of PDEs on manifolds
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
58A50 Supermanifolds and graded manifolds
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References:

[1] Baranov, M.A., Schwarz, A.S.: Multiloop contribution to string theory. Pis’ma v ZhETF42:8, 340 (1985) [JETP Letters42, 419 (1986)]
[2] Beilinson, A.A., Manin, Yu.I.: The Mumford form and the Polyakov measure in string theory. Commun. Math. Phys.107, 359 (1986) · Zbl 0604.14016 · doi:10.1007/BF01220994
[3] Baranov, M.A., Schwarz, A.S.: On the multiloop contribution to the string theory. Int. J. Mod. Phys. A3, 28 (1987)
[4] Deligne, P.: Le determinant de la cohomologie. Contemp. Math.67, 93 (1987) · Zbl 0629.14008
[5] Rosly, A.A., Schwarz, A.S., Voronov, A.A.: Geometry of superconformal manifolds. Commun. Math. Phys.113, 129-152 (1988) · Zbl 0675.58010 · doi:10.1007/BF01218264
[6] Voronov, A.A.: A formula for the Mumford measure in superstring theory. Funk. Anal. Prilozh.22, 67 (1988) · Zbl 0688.14025
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