# zbMATH — the first resource for mathematics

Background independent action for double field theory. (English) Zbl 1290.81069
Summary: Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.

##### MSC:
 81T13 Yang-Mills and other gauge theories in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81R05 Finite-dimensional groups and algebras motivated by physics and their representations
Full Text:
##### References:
 [1] Kugo, T.; Zwiebach, B., Target space duality as a symmetry of string field theory, Prog. Theor. Phys., 87, 801, (1992) [2] Hull, C.; Zwiebach, B., Double field theory, JHEP, 09, 099, (2009) [3] Hull, C.; Zwiebach, B., The gauge algebra of double field theory and Courant brackets, JHEP, 09, 090, (2009) [4] Tseytlin, AA, Duality symmetric formulation of string world sheet dynamics, Phys. Lett., B 242, 163, (1990) [5] Tseytlin, AA, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys., B 350, 395, (1991) [6] Siegel, W., Superspace duality in low-energy superstrings, Phys. Rev., D 48, 2826, (1993) [7] Siegel, W., Two vierbein formalism for string inspired axionic gravity, Phys. Rev., D 47, 5453, (1993) [8] Zwiebach, B., Closed string field theory: quantum action and the B-V master equation, Nucl. Phys., B 390, 33, (1993) [9] Courant, T., Dirac manifolds, Trans. Amer. Math. Soc., 319, 631, (1990) [10] Hitchin, N., Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser., 54, 281, (2003) [11] M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Oxford Univeristy, Oxford U.K. (2004), math/0401221. [12] Liu, Z-J; Weinstein, A.; Xu, P., Manin triples for Lie bialgebroids, J. Diff. Geom., 45, 547, (1997) [13] M. Gualtieri, Branes on Poisson varieties, arXiv:0710.2719. [14] Giveon, A.; Rabinovici, E.; Veneziano, G., Duality in string background space, Nucl. Phys., B 322, 167, (1989) [15] Shapere, AD; Wilczek, F., Selfdual models with theta terms, Nucl. Phys., B 320, 669, (1989) [16] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Phys. Rept., 244, 77, (1994) [17] Michishita, Y., Field redefinitions, T-duality and solutions in closed string field theories, JHEP, 09, 001, (2006) [18] Damour, T.; Deser, S.; McCarthy, JG, Nonsymmetric gravity theories: inconsistencies and a cure, Phys. Rev., D 47, 1541, (1993) [19] Tseytlin, AA, Σ-model approach to string theory, Int. J. Mod. Phys., A 4, 1257, (1989) [20] J. Polchinski, String theory. Vol. 1: an introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998). [21] Hull, CM; Reid-Edwards, RA, Gauge symmetry, T-duality and doubled geometry, JHEP, 08, 043, (2008) [22] Hull, CM; Reid-Edwards, RA, Non-geometric backgrounds, doubled geometry and generalised T-duality, JHEP, 09, 014, (2009) [23] Hull, CM, A geometry for non-geometric string backgrounds, JHEP, 10, 065, (2005) [24] Hull, CM, Doubled geometry and T-folds, JHEP, 07, 080, (2007) [25] Hull, CM, Generalised geometry for M-theory, JHEP, 07, 079, (2007) [26] Pacheco, PP; Waldram, D., M-theory, exceptional generalised geometry and superpotentials, JHEP, 09, 123, (2008) [27] Maharana, J.; Schwarz, JH, Noncompact symmetries in string theory, Nucl. Phys., B 390, 3, (1993) [28] Cremmer, E.; Julia, B., The SO(8) supergravity, Nucl. Phys., B 159, 141, (1979) [29] Wit, B.; Nicolai, H., Hidden symmetries, central charges and all that, Class. Quant. Grav., 18, 3095, (2001) [30] C.C. Chevalley, The algebraic theory of spinors, Columbia University Press, U.S.A. (1954). [31] E. Artin, Geometric algebra, Interscience Publishers Inc., U.S.A. (1957). [32] Buscher, TH, A symmetry of the string background field equations, Phys. Lett., B 194, 59, (1987) [33] Buscher, TH, Path integral derivation of quantum duality in nonlinear sigma models, Phys. Lett., B 201, 466, (1988) [34] Giveon, A.; Roček, M., Generalized duality in curved string backgrounds, Nucl. Phys., B 380, 128, (1992) [35] Hull, CM; Townsend, PK, Unity of superstring dualities, Nucl. Phys., B 438, 109, (1995) [36] Hillmann, C., Generalized $$E$$(7(7)) coset dynamics and D = 11 supergravity, JHEP, 03, 135, (2009)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.