# zbMATH — the first resource for mathematics

Generalized metric formulation of double field theory. (English) Zbl 1291.81255
Summary: The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

##### 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 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 81R15 Operator algebra methods applied to problems in quantum theory
Full Text:
##### References:
 [1] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Phys. Rept., 244, 77, (1994) [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] Hohm, O.; Hull, C.; Zwiebach, B., Background independent action for double field theory, JHEP, 07, 016, (2010) [5] Kugo, T.; Zwiebach, B., Target space duality as a symmetry of string field theory, Prog. Theor. Phys., 87, 801, (1992) [6] Zwiebach, B., Closed string field theory: quantum action and the B-V master equation, Nucl. Phys., B 390, 33, (1993) [7] Tseytlin, AA, Duality symmetric formulation of string world sheet dynamics, Phys. Lett., B 242, 163, (1990) [8] Tseytlin, AA, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys., B 350, 395, (1991) [9] Siegel, W., Superspace duality in low-energy superstrings, Phys. Rev., D 48, 2826, (1993) [10] Siegel, W., Two vierbein formalism for string inspired axionic gravity, Phys. Rev., D 47, 5453, (1993) [11] Giveon, A.; Rabinovici, E.; Veneziano, G., Duality in string background space, Nucl. Phys., B 322, 167, (1989) [12] Duff, MJ, Duality rotations in string theory, Nucl. Phys., B 335, 610, (1990) [13] Maharana, J.; Schwarz, JH, Noncompact symmetries in string theory, Nucl. Phys., B 390, 3, (1993) [14] Meissner, KA; Veneziano, G., Symmetries of cosmological superstring vacua, Phys. Lett., B 267, 33, (1991) [15] Meissner, KA; Veneziano, G., Manifestly $$O$$($$d$$, $$d$$) invariant approach to space-time dependent string vacua, Mod. Phys. Lett., A 6, 3397, (1991) [16] Kleinschmidt, A.; Nicolai, H., $$E$$_{10} and SO(9, 9) invariant supergravity, JHEP, 07, 041, (2004) [17] Hitchin, N., Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser., 54, 281, (2003) [18] N. Hitchin, Brackets, forms and invariant functionals, math/0508618. [19] M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Oxford University, Oxford, U.K. (2004), math/0401221. [20] Courant, T., Dirac manifolds, Trans. Amer. Math. Soc., 319, 631, (1990) [21] Hull, CM, A geometry for non-geometric string backgrounds, JHEP, 10, 065, (2005) [22] Graña, M.; Minasian, R.; Petrini, M.; Waldram, D., T-duality, generalized geometry and non-geometric backgrounds, JHEP, 04, 075, (2009) [23] Hillmann, C., Generalized $$E$$(7(7)) coset dynamics and D = 11 supergravity, JHEP, 03, 135, (2009) [24] Borisov, AB; Ogievetsky, VI, Theory of dynamical affine and conformal symmetries as gravity theory of the gravitational field, Theor. Math. Phys., 21, 1179, (1975) [25] West, PC, Hidden superconformal symmetry in M-theory, JHEP, 08, 007, (2000) [26] West, PC, $$E$$_{11}, SL(32) and central charges, Phys. Lett., B 575, 333, (2003)
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.