Closed superstring moduli tree-level two-point scattering amplitudes in type IIB orientifold on \(T^6/(Z_2 \times Z_2)\). (English) Zbl 1472.81189
Summary: We reconsider the two-point string scattering amplitudes of massless Neveu-Schwarz-Neveu-Schwarz states of Type IIB orientifold superstring theory on the disk and projective plane in ten dimensions and analyse its \(\alpha^\prime\) expansion. We also discuss the unoriented Type IIB theory on \(T^6 / \mathbb{Z}_2 \times \mathbb{Z}_2\) where two-point string scattering amplitudes of the complex Kähler moduli and complex structures of the untwisted sector are computed on the disk and projective plane. New results are obtained together with known ones. Finally, we compare string scattering amplitudes results at \({\alpha^{\prime}}^2\)-order with the (curvature)\(^2\) terms in the low energy effective action of D-branes and \(\Omega \)-planes in both cases.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 32G13 | Complex-analytic moduli problems |
| 14N05 | Projective techniques in algebraic geometry |
| 81T12 | Effective quantum field theories |
References:
| [1] | Polchinski, J., Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett., 75, 4724 (1995) · Zbl 1020.81797 |
| [2] | Sagnotti, A., Open strings and their symmetry groups, (Mack, G.; etal., Cargese ’87, Non-Perturbative Quantum Field Theory (1988), Pergamon Press), 521 |
| [3] | Horava, P., Strings on world sheet orbifolds, Nucl. Phys. B, 327, 461 (1989) |
| [4] | Bianchi, M.; Sagnotti, A., On the systematics of open string theories, Phys. Lett. B, 247, 517 (1990) |
| [5] | Pradisi, G.; Sagnotti, A., Open string orbifolds, Phys. Lett. B, 216, 59 (1989) |
| [6] | Gimon, E. G.; Polchinski, J., Consistency conditions for orientifolds and d manifolds, Phys. Rev. D, 54, 1667-1676 (1996) |
| [7] | Bianchi, M.; Sagnotti, A., Twist symmetry and open string Wilson lines, Nucl. Phys. B, 361, 519 (1991) |
| [8] | Bianchi, M., Type I superstrings without D-branes |
| [9] | Bianchi, M.; Pradisi, G.; Sagnotti, A., Toroidal compactification and symmetry breaking in open string theories, Nucl. Phys. B, 376, 365 (1992) |
| [10] | Pradisi, G.; Sagnotti, A.; Stanev, Y. S., Planar duality in SU(2) WZW models, Phys. Lett. B, 354, 279 (1995) |
| [11] | Pradisi, G.; Sagnotti, A.; Stanev, Y. S., Completeness conditions for boundary operators in 2-D conformal field theory, Phys. Lett. B, 381, 97 (1996) · Zbl 0979.81585 |
| [12] | Angelantonj, C.; Sagnotti, A., Open strings, Phys. Rep.. Phys. Rep., Phys. Rep., 376, 6, 407 (2003), (Erratum) · Zbl 0999.83056 |
| [13] | Dudas, E., Theory and phenomenology of type I strings and M theory, Class. Quantum Gravity, 17, R41 (2000) · Zbl 1052.81582 |
| [14] | Blumenhagen, R.; Kors, B.; Lust, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rep., 445, 1 (2007) |
| [15] | Sagnotti, A.; Stanev, Y. S., Open descendants in conformal field theory, Fortschr. Phys.. Fortschr. Phys., Nucl. Phys. Proc. Suppl.. Fortschr. Phys.. Fortschr. Phys., Nucl. Phys. Proc. Suppl., Nucl. Phys. Proc. Suppl., 55, 200 (1997) · Zbl 0957.81682 |
| [16] | Dine, M.; Seiberg, N.; Wen, X.; Witten, E., Nonperturbative effects on the string world sheet, Nucl. Phys. B, 278, 769-789 (1986) |
| [17] | Dine, M.; Seiberg, N.; Wen, X.; Witten, E., Nonperturbative effects on the string world sheet. 2, Nucl. Phys. B, 289, 319-363 (1987) |
| [18] | Bianchi, M.; Samsonyan, M., Notes on unoriented D-brane instantons, Int. J. Mod. Phys. A, 24, 5737-5763 (2009) · Zbl 1179.81129 |
| [19] | Bianchi, M.; Inverso, G., Unoriented D-brane instantons, Fortschr. Phys., 60, 822 (2012) · Zbl 1253.81105 |
| [20] | Bianchi, M.; Kiritsis, E., Non-perturbative and flux superpotentials for Type I strings on the Z(3) orbifold, Nucl. Phys. B, 782, 26 (2007) · Zbl 1188.81139 |
| [21] | Johnson, C. V., On the orientifolding of type II NS-fivebranes, Phys. Rev. D, 56, 5160-5165 (1997) |
| [22] | Evans, N. J.; Johnson, C. V.; Shapere, A. D., Orientifolds, branes, and duality of 4-D gauge theories, Nucl. Phys. B, 505, 251-271 (1997) · Zbl 0925.81387 |
| [23] | Polchinski, J.; Chaudhuri, S.; Johnson, C. V., Notes on D-branes |
| [24] | Bianchi, M.; Stanev, Y. S., Open strings on the Neveu-Schwarz penta-brane, Nucl. Phys. B, 523, 193 (1998) · Zbl 1031.81590 |
| [25] | Kaluza, T., Zum Unitätsproblem der Physik, Int. J. Mod. Phys. D, 27, 14, Article 1870001 pp. (2018) |
| [26] | Klein, O., Quantum theory and five-dimensional theory of relativity, Z. Phys.. Z. Phys., Surv. High Energy Phys., 5, 241 (1986), (in German and English) |
| [27] | Candelas, P.; Horowitz, G. T.; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys. B, 258, 46 (1985) |
| [28] | Calabi, E., On Kaehler manifolds with vanishing canonical class, Princeton Math. Ser., 12, 78-89 (1957) · Zbl 0080.15002 |
| [29] | Yau, S. T., Calabi’s conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci., 74, 1798 (1977) · Zbl 0355.32028 |
| [30] | Ferrara, S.; Sabharwal, S., Quaternionic manifolds for type II superstring vacua of Calabi-Yau spaces, Nucl. Phys. B, 332, 317 (1990) |
| [31] | Blumenhagen, R.; Lust, D.; Theisen, S., Basic Concepts of String Theory (2013), Springer |
| [32] | Ferrara, S.; Van Proeyen, A., A theorem on N=2 special Kahler product manifolds, Class. Quantum Gravity, 6, L243 (1989) · Zbl 0681.53014 |
| [33] | Angelantonj, C.; Bianchi, M.; Pradisi, G.; Sagnotti, A.; Stanev, Y. S., Comments on Gepner models and type I vacua in string theory, Phys. Lett. B, 387, 743 (1996) |
| [34] | Kachru, S.; Kallosh, R.; Linde, A. D.; Trivedi, S. P., De Sitter vacua in string theory, Phys. Rev. D, 68, Article 046005 pp. (2003) · Zbl 1244.83036 |
| [35] | Balasubramanian, V.; Berglund, P.; Conlon, J. P.; Quevedo, F., Systematics of moduli stabilisation in Calabi-Yau flux compactifications, J. High Energy Phys., 0503, Article 007 pp. (2005) |
| [36] | Baumann, D.; McAllister, L., Inflation and string theory · Zbl 1339.83003 |
| [37] | Garousi, M. R.; Myers, R. C., Superstring scattering from D-branes, Nucl. Phys. B, 475, 193 (1996) · Zbl 0925.81178 |
| [38] | Hashimoto, A.; Klebanov, I. R., Decay of excited D-branes, Phys. Lett. B, 381, 437 (1996) |
| [39] | Hashimoto, A.; Klebanov, I. R., Scattering of strings from D-branes, Nucl. Phys. Proc. Suppl., 55, 118 (1997) · Zbl 0957.81628 |
| [40] | Bachas, C. P.; Bain, P.; Green, M. B., Curvature terms in D-brane actions and their M theory origin, J. High Energy Phys., 9905, Article 011 pp. (1999) · Zbl 1056.81059 |
| [41] | Garousi, M. R., Superstring scattering from O-planes, Nucl. Phys. B, 765, 166 (2007) · Zbl 1116.81334 |
| [42] | Berg, M.; Haack, M.; Kors, B., String loop corrections to Kahler potentials in orientifolds, J. High Energy Phys., 0511, Article 030 pp. (2005) |
| [43] | Berg, M.; Haack, M.; Kang, J. U.; Sjörs, S., Towards the one-loop Kähler metric of Calabi-Yau orientifolds, J. High Energy Phys., 1412, Article 077 pp. (2014) · Zbl 1333.81310 |
| [44] | Fotopoulos, A., On (alpha-prime)**2 corrections to the D-brane action for nongeodesic world volume embeddings, J. High Energy Phys., 0109, Article 005 pp. (2001) |
| [45] | Fotopoulos, A.; Tseytlin, A. A., On gravitational couplings in D-brane action, J. High Energy Phys., 0212, Article 001 pp. (2002) |
| [46] | Aldi, A.; Firrotta, M., Appendix & details: closed superstring moduli tree-level two-point scattering amplitudes in Type IIB orientifold on \(T^6 /( Z_2 \times Z_2)\) |
| [47] | Tanii, Y., Introduction to Supergravity (2014), Springer Japan · Zbl 1309.83005 |
| [48] | Kitaev, A., Notes on \(\widetilde{\operatorname{SL}}(2, \mathbb{R})\) representations |
| [49] | Gilmore, R., Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists (2008), Univ. Pr.: Univ. Pr. Cambridge, UK, 319 pp. · Zbl 1157.00009 |
| [50] | Polchinski, J., String Theory. Vol. 1 and Vol. 2: Superstring Theory and Beyond (1998), Cambridge University Press · Zbl 1006.81522 |
| [51] | Green, M. B.; Schwarz, J. H.; Witten, E., Superstring Theory, Loop Amplitudes, Anomalies and Phenomenology, vol. 2 (1987), Cambridge University Press; Green, M. B.; Schwarz, J. H.; Witten, E., Superstring Theory, Introduction, vol. 1 (1987), Cambridge University Press · Zbl 0619.53002 |
| [52] | Grinstein, B.; Wise, M. B., Vacuum energy and dilaton tadpole for the unoriented closed bosonic string, Phys. Rev. D, 35, 655 (1987) |
| [53] | Garousi, M. R., Duality constraints on effective actions, Phys. Rep., 702, 1 (2017) · Zbl 1370.81142 |
| [54] | Vafa, C.; Witten, E., On orbifolds with discrete torsion, J. Geom. Phys., 15, 189 (1995) · Zbl 0816.53053 |
| [55] | Lust, D.; Reffert, S.; Schulgin, W.; Stieberger, S., Moduli stabilization in type IIB orientifolds (I): orbifold limits, Nucl. Phys. B, 766, 68 (2007) · Zbl 1117.81116 |
| [56] | Ibanez, L. E.; Uranga, A. M., String Theory and Particle Physics: An Introduction to String Phenomenology (2012), Cambridge University Press · Zbl 1260.81001 |
| [57] | Schwarz, J. H., Dilaton - axion symmetry |
| [58] | Berkooz, M.; Douglas, M. R.; Leigh, R. G., Branes intersecting at angles, Nucl. Phys. B, 480, 265 (1996) · Zbl 0925.81211 |
| [59] | Antoniadis, I.; Bachas, C.; Fabre, C.; Partouche, H.; Taylor, T. R., Aspects of type I - type II - heterotic triality in four-dimensions, Nucl. Phys. B, 489, 160 (1997) · Zbl 0925.81243 |
| [60] | Berkooz, M.; Leigh, R. G., A D = 4 N=1 orbifold of type I strings, Nucl. Phys. B, 483, 187 (1997) · Zbl 0925.81227 |
| [61] | Lust, D.; Mayr, P.; Richter, R.; Stieberger, S., Scattering of gauge, matter, and moduli fields from intersecting branes, Nucl. Phys. B, 696, 205 (2004) · Zbl 1236.81167 |
| [62] | Bertolini, M.; Billo, M.; Lerda, A.; Morales, J. F.; Russo, R., Brane world effective actions for D-branes with fluxes, Nucl. Phys. B, 743, 1 (2006) · Zbl 1214.81190 |
| [63] | Burgess, C. P.; Morris, T. R., Open and unoriented strings a La Polyakov, Nucl. Phys. B, 291, 256 (1987) |
| [64] | Polchinski, J.; Witten, E., Evidence for heterotic - type I string duality, Nucl. Phys. B, 460, 525 (1996) · Zbl 1004.81526 |
| [65] | Tseytlin, A. A., Heterotic type I superstring duality and low-energy effective actions, Nucl. Phys. B, 467, 383 (1996) · Zbl 1002.81533 |
| [66] | Veltman, M. J.G., Quantum theory of gravitation, Conf. Proc. C, 7507281, 265 (1975) |
| [67] | Caron-Huot, S.; O’Connell, D., Spinor helicity and dual conformal symmetry in ten dimensions, J. High Energy Phys., 1108, Article 014 pp. (2011) · Zbl 1298.81163 |
| [68] | Stieberger, S., Open & closed vs. pure open string disk amplitudes |
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