Physics:Double field theory

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Short description: Framework in theoretical physics

In theoretical physics, double field theory refers to formalisms that capture the T-duality property of string theory as a manifest symmetry of a field theory.[1][2][3][4]


In double field theory, the T-duality transformation of exchanging momentum and winding modes of closed strings on toroidal backgrounds translates to a generalized coordinate transformation on a doubled spacetime, where one set of its coordinates is dual to momentum modes and the second set of coordinates is interpreted as dual to winding modes of the closed string. Whether the second set of coordinates has physical meaning depends on how the level-matching condition of closed strings is implemented in the theory: either through the weak constraint or the strong constraint.[5][1]

In strongly constrained double field theory, which was introduced by Warren Siegel in 1993, the strong constraint ensures the dependency of the fields on only one set of the doubled coordinates;[6][7] it describes the massless fields of closed string theory, i.e. the graviton, Kalb Ramond B-field, and dilaton, but does not include any winding modes, and serves as a T-duality invariant reformulation of supergravity.

Weakly constrained double field theory, introduced by Chris Hull and Barton Zwiebach in 2009, allows for the fields to depend on the whole doubled spacetime and encodes genuine momentum and winding modes of the string.[8]

Double field theory has been a setting for studying various string theoretical properties such as: consistent Kaluza-Klein truncations of higher-dimensional supergravity to lower-dimensional theories,[9][10] generalized fluxes,[11] and alpha-prime corrections of string theory in the context of cosmology and black holes.[12]


  1. 1.0 1.1 Aldazabal, Gerardo; Marqués, Diego; Núñez, Carmen (21 August 2013). "Double field theory: a pedagogical review". Classical and Quantum Gravity 30 (16): 163001. doi:10.1088/0264-9381/30/16/163001. 
  2. Berman, David S.; Thompson, Daniel C. (March 2015). "Duality symmetric string and M-theory". Physics Reports 566: 1–60. doi:10.1016/j.physrep.2014.11.007. 
  3. Hohm, Olaf; Hull, Chris; Zwiebach, Barton (August 2010). "Generalized metric formulation of double field theory". Journal of High Energy Physics 2010 (8). doi:10.1007/JHEP08(2010)008. 
  4. Hohm, O.; Lüst, D.; Zwiebach, B. (October 2013). "The spacetime of double field theory: Review, remarks, and outlook". Fortschritte der Physik 61 (10): 926–966. doi:10.1002/prop.201300024. 
  5. Zwiebach, Barton (2012). "Doubled Field Theory, T-Duality and Courant-Brackets" (in en). Strings and Fundamental Physics. Springer. pp. 265–291. ISBN 978-3-642-25947-0. Retrieved 18 January 2024. 
  6. Siegel, W. (15 June 1993). "Two-vierbein formalism for string-inspired axionic gravity". Physical Review D 47 (12): 5453–5459. doi:10.1103/PhysRevD.47.5453. 
  7. Siegel, W. (15 September 1993). "Superspace duality in low-energy superstrings". Physical Review D 48 (6): 2826–2837. doi:10.1103/PhysRevD.48.2826. 
  8. Hull, Chris; Zwiebach, Barton (23 September 2009). "Double field theory". Journal of High Energy Physics 2009 (09): 099–099. doi:10.1088/1126-6708/2009/09/099. 
  9. Baguet, A.; Pope, C.N.; Samtleben, H. (January 2016). "Consistent Pauli reduction on group manifolds". Physics Letters B 752: 278–284. doi:10.1016/j.physletb.2015.11.062. 
  10. Butter, Daniel; Hassler, Falk; Pope, Christopher N.; Zhang, Haoyu (3 April 2023). "Consistent truncations and dualities" (in en). Journal of High Energy Physics 2023 (4): 7. doi:10.1007/JHEP04(2023)007. ISSN 1029-8479. 
  11. Geissbühler, David; Marqués, Diego; Núñez, Carmen; Penas, Victor (June 2013). "Exploring double field theory". Journal of High Energy Physics 2013 (6). doi:10.1007/JHEP06(2013)101. 
  12. Hohm, Olaf; Siegel, Warren; Zwiebach, Barton (February 2014). "Doubled α ′-geometry". Journal of High Energy Physics 2014 (2). doi:10.1007/JHEP02(2014)065.