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位相的膜理論における対称性とフラックス背景の双対性

別所 泰輝 東北大学

2020.11.25

概要

本研究では,超弦理論の背景時空に非幾何学的フラックスが存在する場合のコンパクト化を議論すべく,Courant algebroid を用いて非幾何学的フラックスの微分幾何学的構造を解析する.そのために,Poisson 多様体上のCourant algebroid の構造を,QP 多様体上での超幾何学的構成方法を用いて再定式化する.その結果を用いて,非幾何学的フラックスが存在する場合の位相的膜理論とカレント代数を構成した.さらに,H フラックス, R フラックス間を変換するCourant algebroid の新しい双対性を提唱し,これらフラックス間の変換が次数付きシンプレクティック多様体上の正準変換と理解出来ることを示した [1].

参考文献

[1] Taiki Bessho, Marc A. Heller, Noriaki Ikeda, and Satoshi Watamura. Topological Mem- branes, Current Algebras and H-flux - R-flux Duality based on Courant Algebroids. JHEP, 04:170, 2016.

[2] Tamiaki Yoneya. Interacting Fermionic and Pomeronic Strings: Gravitational Interaction of the Ramond Fermion. Nuovo Cim. A, 27:440, 1975.

[3] Joseph Polchinski. String Theory, volume 1 of Cambridge Monographs on Mathematical Physics. Cambridge University Press, 1998.

[4] K.S. Narain, M.H. Sarmadi, and Edward Witten. A Note on Toroidal Compactification of Heterotic String Theory. Nucl. Phys. B, 279:369–379, 1987.

[5] Jeremy Michelson. Compactifications of type IIB strings to four-dimensions with non- trivial classical potential. Nucl. Phys. B, 495:127–148, 1997.

[6] J. Scherk and John H. Schwarz. Spontaneous breaking of supersymmetry through di- mensional reduction. Physics Letters B, 82(1):60 – 64, 1979.

[7] Jessie Shelton, Washington Taylor, and Brian Wecht. Nongeometric flux compactifica- tions. JHEP, 10:085, 2005.

[8] C M Hull. Doubled Geometry and T-Folds. JHEP, 07:080, 2007.

[9] C.M. Hull and R.A. Reid-Edwards. Non-geometric backgrounds, doubled geometry and generalised T-duality. JHEP, 09:014, 2009.

[10] Nigel Hitchin. Generalized Calabi-Yau manifolds. arXiv Mathematics e-prints, page math/0209099, September 2002.

[11] Marco Gualtieri. Generalized complex geometry. arXiv Mathematics e-prints, page math/0401221, January 2004.

[12] Gil R. Cavalcanti and Marco Gualtieri. Generalized complex geometry and T-duality. In A Celebration of the Mathematical Legacy of Raoul Bott (CRM Proceedings & Lec- ture Notes) American Mathematical Society (2010) 341-366. ISBN: 0821847775, page 0821847775, 2011.

[13] Albert S. Schwarz. Geometry of Batalin-Vilkovisky quantization. Commun. Math. Phys., 155:249–260, 1993.

[14] Albert S. Schwarz. Semiclassical approximation in Batalin-Vilkovisky formalism. Com- mun. Math. Phys., 158:373–396, 1993.

[15] N. Hitchin. Generalized calabi-yau manifolds. The Quarterly Journal of Mathematics, 54(3):281–308, Sep 2003.

[16] Marco Gualtieri. Generalized complex geometry. Annals of Mathematics, 174(1):75–123, Jul 2011.

[17] Zhang-Ju Liu, Alan Weinstein, and Ping Xu. Manin Triples for Lie Bialgebroids. J. Diff. Geom., 45(3):547–574, 1997.

[18] Yvette Kosmann-Schwarzbach. Quasi, twisted, and all that... in poisson geometry and lie algebroid theory. The Breadth of Symplectic and Poisson Geometry, page 363–389.

[19] Pavol Sˇevera. Poisson–Lie T-Duality and Courant Algebroids. Lett. Math. Phys., 105(12):1689–1701, 2015.

[20] L. Caston and R. Fioresi. Mathematical Foundations of Supersymmetry. arXiv e-prints, page arXiv:0710.5742, October 2007.

[21] V. S. Varadarajan. Super geometry, pages 93–120. Springer New York, New York, NY, 2011.

[22] Dmitry Roytenberg. Courant algebroids, derived brackets and even symplectic super- manifolds, 1999.

[23] Tsuguhiko Asakawa, Hisayoshi Muraki, Shuhei Sasa, and Satoshi Watamura. Poisson- generalized geometry and R-flux. Int. J. Mod. Phys., A30(17):1550097, 2015.

[24] Rui Loja Fernandes. Connections in poisson geometry. i. holonomy and invariants. Jour- nal of Differential Geometry, 54(2):303–365, 2000.

[25] Izu Vaisman. Reduction and submanifolds of generalized complex manifolds. Differential Geometry and Its Applications, 25:147–166, 2005.

[26] Dmitry Roytenberg. Quasi-lie bialgebroids and twisted poisson manifolds. Letters in Mathematical Physics, 61:123–137, 2002.

[27] Dmitry Roytenberg. On the structure of graded symplectic supermanifolds and Courant algebroids. In Workshop on Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics Manchester, England, July 7-13, 2001, 2002.

[28] Andreas Deser and Jim Stasheff. Even symplectic supermanifolds and double field theory. Commun. Math. Phys., 339(3):1003–1020, 2015.

[29] Ursula Carow-Watamura, Noriaki Ikeda, Tomokazu Kaneko, and Satoshi Watamura. DFT in supermanifold formulation and group manifold as background geometry. JHEP, 04:002, 2019.

[30] Zhang-Ju Liu, Alan Weinstein, and Ping Xu. Manin Triples for Lie Bialgebroids. eprint arXiv:dg-ga/9508013, pages dg–ga/9508013, August 1995.

[31] Yvette Kosmann-Schwarzbach. Quasi, twisted, and all that... in poisson geometry and lie algebroid theory. The Breadth of Symplectic and Poisson Geometry, page 363–389.

[32] Jae-Suk Park. Topological open p-branes. In Symplectic geometry and mirror symmetry. Proceedings, 4th KIAS Annual International Conference, Seoul, South Korea, August 14-18, 2000, pages 311–384, 2000.

[33] Noriaki Ikeda. Deformation of BF theories, topological open membrane and a general- ization of the star deformation. JHEP, 07:037, 2001.

[34] M. Alexandrov, A. Schwarz, O. Zaboronsky, and M. Kontsevich. The Geometry of the master equation and topological quantum field theory. Int. J. Mod. Phys., A12:1405– 1429, 1997.

[35] Alberto S. Cattaneo and Giovanni Felder. On the AKSZ formulation of the Poisson sigma model. Lett. Math. Phys., 56:163–179, 2001.

[36] Dmitry Roytenberg. AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories. Lett. Math. Phys., 79:143–159, 2007.

[37] I. A. Batalin and G. A. Vilkovisky. Gauge algebra and quantization. Physics Letters B, 102(1):27–31, June 1981.

[38] Glenn Barnich, Friedemann Brandt, and Marc Henneaux. General solution of the Wess- Zumino consistency condition for Einstein gravity. Phys. Rev. D, 51:1435–1439, 1995.

[39] I. A. Batalin and G. A. Vilkovisky. Quantization of gauge theories with linearly dependent generators. Phys. Rev. D, 28:2567–2582, Nov 1983.

[40] Noriaki Ikeda and K. I. Izawa. General form of dilaton gravity and nonlinear gauge theory. Prog. Theor. Phys., 90:237–246, 1993.

[41] Noriaki Ikeda. Two-dimensional gravity and nonlinear gauge theory. Annals Phys., 235:435–464, 1994.

[42] Peter Schaller and Thomas Strobl. Poisson structure induced (topological) field theories. Mod. Phys. Lett., A9:3129–3136, 1994.

[43] Ctirad Klimcik and Thomas Strobl. WZW - Poisson manifolds. J. Geom. Phys., 43:341– 344, 2002.

[44] Anton Alekseev and Thomas Strobl. Current algebras and differential geometry. JHEP, 03:035, 2005.

[45] Giulio Bonelli and Maxim Zabzine. From current algebras for p-branes to topological M-theory. JHEP, 09:015, 2005.

[46] Noriaki Ikeda and Kozo Koizumi. Current Algebras and QP Manifolds. Int. J. Geom. Meth. Mod. Phys., 10:1350024, 2013.

[47] Noriaki Ikeda and Xiaomeng Xu. Current Algebras from DG Symplectic Pairs in Super- geometry. 2013.

[48] J Grabowski and P Urbanski. Tangent lifts of poisson and related structures. Journal of Physics A: Mathematical and General, 28(23):6743–6777, Dec 1995.

[49] Yukio Kaneko, Hisayoshi Muraki, and Satoshi Watamura. Contravariant Gravity on Poisson Manifolds and Einstein Gravity. Class. Quant. Grav., 34(11):115002, 2017.

[50] Izu Vaisman. On the geometry of double field theory. J. Math. Phys., 53:033509, 2012.

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