Consistent boundary conditions for open strings. (English) Zbl 1027.83027

Lindström, Ulf; Roček, Martin; van Nieuwenhuizen, Peter

Nucl. Phys., B 662, No. 1-2, 147-169 (2003).

Summary: We study boundary conditions for the bosonic, spinning (NSR) and Green-Schwarz open string, as well as for (1+1)-dimensional supergravity. We consider boundary conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or \(\kappa\)(Siegel)-symmetry of the action, (3) closure of the set of boundary conditions under the symmetry transformations, and (4) the boundary limits of bulk Euler-Lagrange equations that are “conjugate” to other boundary conditions. We find corrections to Neumann boundary conditions in the presence of a bulk tachyon field. We discuss a boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of boundary conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neuman boundary conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.

MSC:

83E30	String and superstring theories in gravitational theory
83-02	Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E50	Supergravity
83C05	Einstein’s equations (general structure, canonical formalism, Cauchy problems)

Keywords:

Green-Schwarz open string; (1+1)-dimensional supergravity; path integral quantization; bulk Euler-Lagrange equations; Neuman boundary conditions

References:

[1]	van Nieuwenhuizen, P., The BRST formalism for the open spinning string, (Martinis, M.; Andrić, I., Superstrings, Anomalies and Unification. Superstrings, Anomalies and Unification, Proceedings, 5th Adriatic Meeting on Particle Physics, Dubrovnik, Yugoslavia, 16-28 June 1986 (1987), World Scientific: World Scientific Singapore)
[2]	Haggi-Mani, P.; Lindström, U.; Zabzine, M., Boundary conditions, supersymmetry and \(A\)-field coupling for an open string in a \(B\)-field background, Phys. Lett. B, 483, 443 (2000) · Zbl 1031.81610
[3]	Albertsson, C.; Lindström, U.; Zabzine, M., \(N=1\) supersymmetric sigma model with boundaries. I, Commun. Math. Phys., in press · Zbl 1028.81044
[4]	Albertsson, C.; Lindström, U.; Zabzine, M., \(N=1\) supersymmetric sigma model with boundaries. II · Zbl 1097.81548
[5]	Lindström, U.; Zabzine, M., \(N=2\) boundary conditions for non-linear sigma models and Landau-Ginzburg models
[6]	Hori, K.; Iqbal, A.; Vafa, C., D-branes and mirror symmetry
[7]	Warner, N. P., Supersymmetry in boundary integrable models, Nucl. Phys. B, 450, 663 (1995) · Zbl 0925.81346
[8]	Kokado, A.; Konisi, G.; Saito, T., NS open strings with \(B\) field and closed string tachyon vertex
[9]	Nakamura, S., Closed string tachyon condensation and on-shell effective action of open-string tachyons · Zbl 1055.81611
[10]	Chalmers, G., Open string decoupling and tachyon condensation, JHEP, 0106, 012 (2001)
[11]	Husain, T. Z.; Zabzine, M., Bosonic open strings in a tachyonic background field
[12]	Sagnotti, A., Open strings and their symmetry groups · Zbl 1302.81147
[13]	Pradisi, G.; Sagnotti, A., Open string orbifolds, Phys. Lett. B, 216, 59 (1989)
[14]	Angelantonj, C.; Sagnotti, A., Open strings, Phys. Rep., 371, 1 (2002) · Zbl 0999.83056
[15]	Gibbons, G. W., Cosmological evolution of the rolling tachyon, Phys. Lett. B, 537, 1 (2002) · Zbl 0995.83084
[16]	Chu, C. S.; Howe, P. S.; Sezgin, E., Strings and D-branes with boundaries, Phys. Lett. B, 428, 59 (1998) · Zbl 1355.81121
[17]	Berkovits, N.; Pershin, V., Supersymmetric Born-Infeld from the pure spinor formalism of the open superstring · Zbl 1226.81160
[18]	Grassi, P. A.; Policastro, G.; Porrati, M.; van Nieuwenhuizen, P., Covariant quantization of superstrings without pure spinor constraints, JHEP, 0210, 054 (2002)
[19]	Shifman, M. A.; Vainshtein, A. I.; Voloshin, M. B., Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry, Phys. Rev. D, 59, 045016 (1999)
[20]	Nastase, H.; Stephanov, M. A.; van Nieuwenhuizen, P.; Rebhan, A., Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons, Nucl. Phys. B, 542, 471 (1999) · Zbl 0942.81042
[21]	Goldhaber, A. S.; Litvintsev, A.; van Nieuwenhuizen, P., Local Casimir energy for solitons
[22]	Bordag, M.; Goldhaber, A. S.; van Nieuwenhuizen, P.; Vassilevich, D., Heat kernels and zeta-function regularization for the mass of the SUSY kink, Phys. Rev. D, in press
[23]	Hori, K., Linear models of supersymmetric D-branes · Zbl 1022.81045
[24]	Rothstein, M., Integration on noncompact supermanifolds, Trans. Am. Math. Soc., 299, 387 (1987) · Zbl 0611.58014
[25]	Vassilevich, D. V., QED on curved background and on manifolds with boundaries: unitarity vs. covariance, Phys. Rev. D, 52, 999 (1995)
[26]	Vassilevich, D. V., The Faddeev-Popov trick in the presence of boundaries, Phys. Lett. B, 421, 93 (1998)
[27]	M. Roček, P. van Nieuwenhuizen, An introduction to modern string theory, in preparation; M. Roček, P. van Nieuwenhuizen, An introduction to modern string theory, in preparation
[28]	Friedan, D.; Martinec, E. J.; Shenker, S. H., Conformal invariance, supersymmetry and string theory, Nucl. Phys. B, 271, 93 (1986)
[29]	Siegel, W., Hidden local supersymmetry in the supersymmetric particle action, Phys. Lett. B, 128, 397 (1983)
[30]	Siegel, W., Light cone analysis of covariant superstring, Nucl. Phys. B, 236, 311 (1984)
[31]	Green, M. B.; Schwarz, J. H., Covariant description of superstrings, Phys. Lett. B, 136, 367 (1984)