31,762 research outputs found
Non-associative Deformations of Geometry in Double Field Theory
Non-geometric string backgrounds were proposed to be related to a
non-associative deformation of the space-time geometry. In the flux formulation
of double field theory (DFT), the structure of mathematically possible
non-associative deformations is analyzed in detail. It is argued that on-shell
there should not be any violation of associativity in the effective DFT action.
For imposing either the strong or the weaker closure constraint we discuss two
possible non-associative deformations of DFT featuring two different ways how
on-shell associativity can still be kept.Comment: 29 pages, 1 figure, v2: major revision of section 4, discussion of
closure constraint change
Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
We use a T-duality invariant action to investigate the behaviour of a string
in non-geometric backgrounds, where there is a non-trivial global
patching or monodromy. This action leads to a set of Dirac brackets describing
the dynamics of the doubled string, with these brackets determined only by the
monodromy. This allows for a simple derivation of non-commutativity and
non-associativity in backgrounds which are (even locally) non-geometric. We
focus here on the example of the three-torus with H-flux, finding
non-commutativity but not non-associativity, and also comment on the relation
to the exotic brane, which shares the same monodromy.Comment: 31 pages, v2: refs added, corrections to sec 5, results updated, v3:
published version with additional discussion in sec
Open-String Non-Associativity in an R-flux Background
We derive the commutation relations for open-string coordinates on D-branes
in non-geometric background spaces. Starting from D0-branes on a
three-dimensional torus with H-flux, we show that open strings with end points
on D3-branes in a three-dimensional R-flux background exhibit a non-associative
phase-space algebra, which is similar to the non-associative R-flux algebra of
closed strings. Therefore, the effective open-string gauge theory on the
D3-branes is expected to be a non-associative gauge theory. We also point out
differences between the non-associative phase space structure of open and
closed strings in non-geometric backgrounds, which are related to the different
structure of the world-sheet commutators of open and closed strings.Comment: 29 pages; v2: added section 3.5, minor changes; v3: published
version, clarifications added in sections 3 and 4, added appendix B.
On some algebraic examples of Frobenius manifolds
We construct some explicit quasihomogeneous algebraic solutions to the
associativity (WDVV) equations by using analytical methods of the finite gap
integration theory. These solutions are expanded in the uniform way to
non-semisimple Frobenius manifolds.Comment: 14 page
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