Nonassociative Star Product Deformations for D-Brane World-Volumes in Curved Backgrounds
By L. Cornalba, R. Schiappa. 2001
192 citations recorded by the source corpus.
Abstract: We investigate the deformation of D-brane world-volumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain the world-volume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture that unfolds is the following: when the gauge invariant combination ω=B+F is constant one obtains the standard Moyal deformation of the brane world-volume. Similarly, when dω= 0 one obtains the noncommutative Kontsevich deformation, physically corresponding to a curved brane in a flat background. When the background is curved, H=dω≠ 0, we find that the relevant algebraic structure is still based on the Kontsevich expansion, which now defines a nonassociative star product with an A∞ homotopy associative algebraic structure. We then recover, within this formalism, some known results of Matrix theory in curved backgrounds. In particular, we show how the effective action obtained in this framework describes, as expected, the dielectric effect of D-branes. The polarized branes are interpreted as a soliton, associated to the condensation of the brane gauge field.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/81bfb7e19d8cdb9bdaec70a178cd216f6bafd719
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Citations in the corpus
- T-duality and closed string non-commutative (doubled) geometry (2010, methodology): “• Studying the SU(2) WZW model with a quantized H-field, the authors of [46] (see also [ 47 ]) give some evidence that the corresponding closed string geometry is not only non-commutative, but is even non-associative.”
- Quasi-Lie Bialgebroids and Twisted Poisson Manifolds (2001, background): “The latter appeared recently in works of Park [14], Cornalba-Schiappa [ 2 ] and Klimycik-Strobl [5] on string theory, and were studied by y”
- Nonassociative gravity in string theory? (2010, background): “However, due to a background H-flux in this case, it turns out that the obtained structure is not only noncommutative but also nonassociative [15, 16, 17].”
- On spherical harmonics for fuzzy spheres in diverse dimensions (2001, background): “eloping quantum mechanics on these fuzzy spheres. 26 There have been a number of recent discussions of non-associative algebras emerging from considering background NS-sector H-fields in string theory [40][41]. Since spherical branes appearing in polarization effects or Matrix theory, which motivated ”
- Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, background): “In [22] it is shown that correlators of open string”
- Non‐geometric fluxes in supergravity and double field theory (2012, background): “Noncommutative and non-associative algebras have been found both for open strings ending on D-branes [8, 81–86] as well for closed strings moving on non-geometric backgrounds [87–91].”
- Non(anti)commutative superspace (2001, background): “al to a super three–form field strength which, in a complete covariant formalism, has the interpretation of the contorsion of the non(anti)commutative superspace. For the bosonic case, it was shown in [19] that the deformation of D–brane world-volumes in curved backgrounds, with H = d(B+ F) 6= 0, is ”
- Nonassociative Tori and Applications to T-Duality (2004, background): “((xy)z), so that φ(x,y,z)U(x)[U(y)U(z)] = [U(x)U(y)]U(z). (3.5) In fact, H3(G) was already interpreted as defining a nonassociative structure in [16], and this has resurfaced in the physics literature [22, 13]. 4. GeneralisedPacker–Raeburnstabilisation For a given antisymmetric tricharacter φon G the”