T-duality and closed string non-commutative (doubled) geometry
By D. Lust. 2010
192 citations recorded by the source corpus.
We provide some evidence that closed string coordinates will become non-commutative turning on geometrical fluxes and/or H-field flux background in closed string compactifications. This is in analogy to open string non-commutativity on the world volume of D-branes with B- and F-field background. The class of 3-dimensional backgrounds we are studying are twisted tori (fibrations of a 2-torus over a circle) and the their T-dual H-field, 3-form flux backgrounds (T-folds). The spatial non-commutativity arises due to the non-trivial monodromies of the toroidal Kähler resp. complex structure moduli fields, when going around the closed string along the circle direction. In addition we study closed string non-commutativity in the context of doubled geometry, where we argue that in general a non-commutative closed string background is T-dual to a commutative closed string background and vice versa. We also discuss the corresponding spatial uncertainty relations. Finally, in analogy to open string boundary conditions, we also argue that closed string momentum and winding modes define in some sense D-branes in closed string doubled geometry.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/58ffd2b0dd2d2ce2522f207405f28cb316919780
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Citations in the corpus
- Large gauge transformations in double field theory (2012, background): “In this respect we note that recently there have been proposals that in string theory there is a plausible role for string coordinates that are non-commutative or even non-associative [38–41], and it would be interesting to investigate if the unconventional group structure encountered here can be na”
- Nonassociative gravity in string theory? (2010, background): “(See [5] for a proposal of closed string NC geometry, and more recently [6].”
- Non‐geometric fluxes in supergravity and double field theory (2012, methodology): “5) by using the Heisenberg commutation relation rX, ps “ i in the kth direction [88].”
- Duality Symmetric String and M-Theory (2013, background): “Space limitations prevent us discussing in any detail a number of developments related to the contents of this chapter including21: the structure of large (finite) DFT gauge transformations [194, 195], the the matrix theory perspective of non-geometric fluxes [196, 197]; further perspectives on non-”
- Frame-like geometry of double field theory (2010, background): “(For recent papers related to this theory see [10, 11, 12, 13, 14].”
- The spacetime of double field theory: Review, remarks, and outlook (2013, unknown): “[38, 49–52]).”
- A ten-dimensional action for non-geometric fluxes (2011, background): “Furthermore, an interesting relation between non-geometrical fluxes and noncommutative and non-associative closed string geometry was discovered recently [9, 10, 11], see also [12] and references therein.”
- Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory (2012, background): “This structure was nicely illustrated in [5], where a three-torus with so-called elliptic Z4-monodromy was investigated: the coordinates of the geometric ω-background are clearly commuting, whereas the T-dual torus coordinates of the non-geometric Q-backgrounds are non-commuting, with the dual momen”