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Super-Liouville theory with boundary. (English) Zbl 0996.81095
Summary: We study $$N=1$$ super-Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states are classified by using the modular transformation property of annulus partition functions, but there are some of those whose wave functions cannot be obtained from the analysis of modular property. There are two ways of putting boundary condition on supercurrent, and it turns out that the two choices lead to different boundary states in quality. Some properties of boundary vertex operators are also presented. The boundary degenerate operators are shown to connect two boundary states in a way slightly more complicated than the bosonic case.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics
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##### References:
 [1] Fateev, V.; Zamolodchikov, A.; Zamolodchikov, Al., Boundary Liouville field theory I. boundary state and boundary two-point function · Zbl 0946.81070 [2] Zamolodchikov, A.; Zamolodchikov, Al., Liouville field theory on a pseudosphere · Zbl 0946.81070 [3] Hosomichi, K., Bulk-boundary propagator in Liouville theory on a disc, Jhep, 0111, 044, (2001) [4] Ponsot, B.; Teschner, J., Boundary Liouville field theory: boundary three point function, Nucl. phys. B, 622, 309, (2002) · Zbl 0988.81068 [5] Giveon, A.; Kutasov, D.; Schwimmer, A., Comments on D-branes in AdS3, Nucl. phys. B, 615, 133, (2001) · Zbl 0988.81088 [6] Parnachev, A.; Sahakyan, D.A., Some remarks on D-branes in AdS3, Jhep, 0110, 022, (2001) [7] Lee, P.; Ooguri, H.; Park, J.W., Boundary states for AdS2 branes in ads3 [8] Ponsot, B.; Schomerus, V.; Teschner, J., Branes in the Euclidean AdS3 [9] Arvis, J.F.; Arvis, J.F., Spectrum of the supersymmetric Liouville theory, Nucl. phys. B, Nucl. phys. B, 218, 309, (1983) [10] D’Hoker, E., Classical and quantal supersymmetric Liouville theory, Phys. rev. D, 28, 1346, (1983) [11] Babelon, O.; Babelon, O., Construction of the quantum supersymmetric Liouville theory for string models, Phys. lett. B, Nucl. phys. B, 258, 680, (1985) [12] Zamolodchikov, A.B.; Pogosian, R.G., Operator algebra in two-dimensional superconformal field theory, Sov. J. nucl. phys., 47, 929, (1988) [13] Abdalla, E.; Abdalla, M.C.; Dalmazi, D.; Harada, K., Correlation functions in super-Liouville theory, Phys. rev. lett., 68, 1641, (1992) · Zbl 0969.81626 [14] Di Francesco, P.; Kutasov, D., World-sheet and space – time physics in two-dimensional (super)string theory, Nucl. phys. B, 375, 119, (1992) [15] Aoki, K.I.; D’Hoker, E.; Aoki, K.I.; D’Hoker, E., Correlation functions of minimal models coupled to two-dimensional quantum supergravity, Mod. phys. lett. A, Mod. phys. lett. A, 7, 333, (1992) · Zbl 1021.81781 [16] Dalmazi, D.; Abdalla, E., Correlators in noncritical superstrings including the spinor emission vertex, Phys. lett. B, 312, 398, (1993) [17] Poghosian, R.H., Structure constants in the N=1 super-Liouville field theory, Nucl. phys. B, 496, 451, (1997) · Zbl 0935.81063 [18] Rashkov, R.C.; Stanishkov, M., Three-point correlation functions in N=1 super-Liouville theory, Phys. lett. B, 380, 49, (1996) [19] Ahn, C.; Rim, C.; Stanishkov, M., Exact one-point function of N=1 super-Liouville theory with boundary · Zbl 0996.81045 [20] Polyakov, A.M., Quantum geometry of fermionic strings, Phys. lett. B, 103, 211, (1981) [21] Distler, J.; Hlousek, Z.; Kawai, H., Super-Liouville theory as a two-dimensional, superconformal supergravity theory, Int. J. mod. phys. A, 5, 391, (1990) [22] Chaudhuri, S.; Kawai, H.; Tye, S.H., Path integral formulation of closed strings, Phys. rev. D, 36, 1148, (1987) [23] Green, M.B.; Seiberg, N., Contact interactions in superstring theory, Nucl. phys. B, 299, 559, (1988) [24] Dine, M.; Seiberg, N., Microscopic knowledge from macroscopic physics in string theory, Nucl. phys. B, 301, 357, (1988) [25] Goulian, M.; Li, M., Correlation functions in Liouville theory, Phys. rev. lett., 66, 2051, (1991) [26] Bershadsky, M.A.; Knizhnik, V.G.; Teitelman, M.G., Superconformal symmetry in two dimensions, Phys. lett. B, 151, 31, (1985) [27] Friedan, D.; Qiu, Z.A.; Shenker, S.H., Superconformal invariance in two-dimensions and the tricritical Ising model, Phys. lett. B, 151, 37, (1985) [28] Nam, S.K., The Kac formula for the N=1 and the N=2 superconformal algebras, Phys. lett. B, 172, 323, (1986) [29] Teschner, J., On the Liouville three point function, Phys. lett. B, 363, 65, (1995) [30] Dorn, H.; Otto, H.J., Two and three point functions in Liouville theory, Nucl. phys. B, 429, 375, (1994) · Zbl 1020.81770 [31] Zamolodchikov, A.; Zamolodchikov, Al., Structure constants and conformal bootstrap in Liouville field theory, Nucl. phys. B, 477, 577, (1996) · Zbl 0925.81301 [32] Belavin, A.A.; Polyakov, A.M.; Zamolodchikov, A.B., Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. phys. B, 241, 333, (1984) · Zbl 0661.17013 [33] Ghoshal, S.; Zamolodchikov, A.B.; Ghoshal, S.; Zamolodchikov, A.B., Boundary S matrix and boundary state in two-dimensional integrable quantum field theory, Int. J. mod. phys. A, Int. J. mod. phys. A, 9, 4353, (1994), Erratum · Zbl 0985.81714 [34] Nepomechie, R.I., The boundary supersymmetric sine-Gordon model revisited, Phys. lett. B, 509, 183, (2001) · Zbl 0977.81151
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