Baranov, A. M.; Manin, Yu. I.; Frolov, I. V.; Schwarz, A. S. A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings. (English) Zbl 0624.58033 Commun. Math. Phys. 111, 373-392 (1987). An analogue of the classical Selberg trace formula is given for discrete groups, acting on the upper complex half-superplane. Applications to the fermionic string measure on the moduli superspace are discussed. Cited in 26 Documents MSC: 58Z05 Applications of global analysis to the sciences 81S40 Path integrals in quantum mechanics Keywords:Selberg trace formula; fermionic string measure; moduli superspace × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Polyakov, A.M.: Phys. Lett.103 B, 207, 211 (1981) [2] Alvarez, O.: Nucl. Phys. B216, 125 (1983) · doi:10.1016/0550-3213(83)90490-X [3] Baranov, M.A., Schwarz, A.S.: Pisma ?ETP42, 340 (1985) [4] Hajhal, D.: The Selberg trace formula forPSL(2, ?). Lecture Notes in Mathematics, Vol. 548. Berlin, Heidelberg, New York: Springer 1976 [5] D’Hoker, E., Phong, D.H.: Columbia Univ. preprint CU-TP-323 [6] Baranov, M.A., Frolov, I.V., Schwarz, A.S.: Theor. Math. Phys.16, 202 (1985) [7] Alessandrini, A.: Nuovo Cimento2 A, 321 (1971) [8] Restuccia, A., Taylor, J.G.: Kings College Preprint, 1985 [9] Mandelstam, S.: Seminar presented at Workshop on Strings at Santa Barbara, August 1985 [10] Gilbert, G.: Univ. of Texas Preprint UTTG-23-85 [11] Belavin, A., Knizhnik, V., Morozov, A., Perelomov, A.: ITEP preprint ITEP-59, 1986 [12] Manin, Yu.I.: Pisma ?ETP43, 161 (1986) [13] Wolpert, S.A.: Bull. AMS11, 189 (1984); Ann. Math.117, 207 (1983) · Zbl 0565.32011 · doi:10.1090/S0273-0979-1984-15264-9 [14] Abikoff, W.: The real analytic theory of Teichm?ller space. Berlin, Heidelberg, New York: Springer 1980 · Zbl 0452.32015 [15] Baranov, M.A., Schwarz, A.S.: Int. J. Mod. Phys. (submitted) [16] Volkov, D.V., Zeltukhin, A.A., Pashnev, A.I.: In: Nonlocal, nonlinear, nonrenormalizable field theories. Moscow: Dubna 1976, p. 272 [17] Schwarz, A.S.: Commun. Math. Phys.87, 37 (1982) · Zbl 0503.53048 · doi:10.1007/BF01211055 [18] Schwarz, A.S.: Theor. Math. Phys.60, 37 (1984) [19] Berezin, F.A.: Introduction to algebra and calculus with anticommuting variables. Moscow University 1983 · Zbl 0527.15020 [20] Shander, V.I.: Funkt. Anal. Prilozh.14, 89 (1980) · Zbl 0473.35075 · doi:10.1007/BF01086549 [21] Howe, P.: J. Phys. A12, 393 (1979) · doi:10.1088/0305-4470/12/3/015 [22] Martinec, E.: Phys. Rev. D28, 2604 (1983) · doi:10.1103/PhysRevD.28.2604 [23] Moore, G., Nelson, P., Polchinski, J.: Harvard Univ. preprint, HUTP-85/A90; Univ. of Texas Preprint UTTG-38-85 [24] Baranov, M.A., Manin, Yu.I., Frolov, I.V., Schwarz, A.S.: Yad. Fiz.43, 1053 (1986) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.