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Selberg supertrace formula for super Riemann surfaces

III. Bordered super Riemann surfaces

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This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.

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  1. International School for Advanced Studies (ISAS), Via Beirut 4, I-34014, Trieste, Italy

    Christian Grosche

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Communicated by R. H. Dijkgraaf

Address from August 1993: II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany

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Grosche, C. Selberg supertrace formula for super Riemann surfaces. Commun.Math. Phys. 162, 591–631 (1994). https://doi.org/10.1007/BF02101748

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