A Path Integral Approach¶to the Kontsevich Quantization Formula

Cattaneo, Alberto S.; Felder, Giovanni

doi:10.1007/s002200000229

Cited by 456 publications

(890 citation statements)

References 15 publications

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“…Here we unify the approaches using Cattaneo-Felder-Kontsevich's stringy reformulation of phase-space quantum mechanics [54,55] -leading to (1.1) -refined further by an algebraic treatment of embedding-field branch points where the boundary-singleton worldline breaks to form an asymptotic two-singleton composite in turn described by a bi-local operator reducing to a local operator only at the linearized level. This provides a natural geometric realization of Vasiliev's algebraic structures and indeed facilitates the construction of a deformation potentially giving rise to the full Vasiliev equation.…”

Section: Higher-spin Gauge Theory and Singleton Stringsmentioning

confidence: 99%

Brane partons and singleton strings

2006

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We examine p-branes in AdS D in two limits where they exhibit partonic behavior: rotating branes with energy concentrated to cusp-like solitons; tensionless branes with energy distributed over singletonic partons on the Dirac hypercone. Evidence for a smooth transition from cusps to partons is found. First, each cusp yields D − 2 normal-coordinate bound states with protected frequencies (for p > 2 there are additional bound states); and can moreover be related to a short open p-brane whose tension diverges at the AdS boundary leading to a decoupled singular CFT at the "brane at the end-of-the-universe". Second, discretizing the closed p-brane and keeping the number N of discrete partons finite yields an sp(2N )-gauged phase-space sigma model giving rise to symmetrized Ntupletons of the minimal higher-spin algebra ho 0 (D − 1, 2) ⊃ so(D − 1, 2). The continuum limit leads to a 2d chiral sp(2)-gauged sigma model which is critical in D = 7; equivalentá la Bars-Vasiliev to an su(2)-gauged spinor string; and furthermore dual to a WZW model in turn containing a topological so(6, 2) −2 /( so(6) ⊕ so(2)) −2 coset model with a chiral ring generated by singleton-valued weight-0 spin fields. Moreover, the two-parton truncation can be linked via a reformulationá la Cattaneo-Felder-Kontsevich to a topological open string on the phase space of the D-dimensional Dirac hypercone. We present evidence that a suitable deformation of the open string leads to the Vasiliev equations based on vector oscillators and weak sp(2)-projection. Geometrically, the bi-locality reflects broken boundary-singleton worldlines, while Vasiliev's intertwiner κ can be seen to relate T and R-ordered deformations of the boundary and the bulk of the worldsheet, respectively.

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Section: Higher-spin Gauge Theory and Singleton Stringsmentioning

confidence: 99%

Brane partons and singleton strings

2006

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“…This conclusion calls to mind the papers [39], [40], [41] within the Deformation Quantization approach [42], but we prefer here to not define the full character of this dot product.…”

Section: Quantum Extensionmentioning

confidence: 99%

Noncommutative coordinates on Riemann surfaces

Bandelloni

Lazzarini²

2004

Nuclear Physics B

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“…and that the above is nothing but the Cattaneo-Felder model [7] 1 Ar, b in the special case of invertible Poisson structure a a , with a = B + F. In this case, one can integrate out the one-forms %, which appear quadratically, and recover (23). We recall that the perturbation theory of the Cattaneo-Felder model generates the Kontsevich graphs, which are the basis of the product *B+F' One then expects (in an undoubtedly vague way) to obtain effective actions based on the full Kontsevich product.…”

Section: Back To the Matrix Actionmentioning

confidence: 98%

“…The product ^ is, on the other hand, the full product of Kontsevich, which is expressed in terms of a complicated diagrammatic expression involving derivatives of the Poisson structure a;" 1 , and for which there is an elegant path-integral expression, by Cattaneo and Felder [7]. In what follows, we will not need the explicit form for ^ On the other hand, since K and UJ are related by diffeomorphism, it is a general result of Kontsevich that the two products *# and ^ are equivalent.…”

Section: The Seiberg-witten Map Following Jurco and Schuppmentioning

confidence: 99%

On the general structure of the non-abelian Born–Infeld action

Cornalba¹

2000

Advances in Theoretical and Mathematical Physics

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We discuss the general structure of the non-abelian Born-Infeld action, together with all of the a' derivative corrections, in flat Ddimensional space-time. More specifically, we show how the connection between open strings propagating in background magnetic fields and gauge theories on non-commutative spaces can be used to constrain the form of the effective action for the massless modes of open strings at weak coupling. In particular, we exploit the invariance in form of the effective action under a change of non-commutativity scale of spacetime to derive algebraic equations relating the various terms in the a' expansion. Moreover, we explicitly solve these equations in the simple case D -2, and we show, in particular, how to construct the minimal invariant derivative extension of the NBI action.

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A Path Integral Approach¶to the Kontsevich Quantization Formula

Cited by 456 publications

References 15 publications

Brane partons and singleton strings

Brane partons and singleton strings

Noncommutative coordinates on Riemann surfaces

On the general structure of the non-abelian Born–Infeld action

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