Non-commutative Weitzenbock geometry, gerbe modules and WZW branes

TY - JOUR

T1 - Non-commutative Weitzenbock geometry, gerbe modules and WZW branes

AU - Recknagel, A

AU - Suszek, R R

PY - 2008

Y1 - 2008

N2 - We study the non-commutative matrix model which arises as the low-energy effective action of open strings in WZW models. We re-derive this fuzzy effective gauge dynamics in two different ways, without recourse to conformal field theory: The first method starts from a linearised version of the WZW sigma-model, which is classically equivalent to an action of the Schild type, which in turn can be quantised in a natural way to yield the matrix model. The second method relies on purely geometric symmetry principles-albeit within the non-commutative spectral geometry that is provided by the boundary CFT data: we show that imposing invariance under extended gauge transformations singles out the string-theoretic action up to the relevant order in the gauge field. The extension of ordinary gauge transformations by tangential shifts is motivated by the gerbe structure underlying the classical WZW model and standard within Weitzenbock geometry-which is a natural reformulation of geometry to use when describing strings in targets with torsion

AB - We study the non-commutative matrix model which arises as the low-energy effective action of open strings in WZW models. We re-derive this fuzzy effective gauge dynamics in two different ways, without recourse to conformal field theory: The first method starts from a linearised version of the WZW sigma-model, which is classically equivalent to an action of the Schild type, which in turn can be quantised in a natural way to yield the matrix model. The second method relies on purely geometric symmetry principles-albeit within the non-commutative spectral geometry that is provided by the boundary CFT data: we show that imposing invariance under extended gauge transformations singles out the string-theoretic action up to the relevant order in the gauge field. The extension of ordinary gauge transformations by tangential shifts is motivated by the gerbe structure underlying the classical WZW model and standard within Weitzenbock geometry-which is a natural reformulation of geometry to use when describing strings in targets with torsion

U2 - ARTN 089

DO - ARTN 089

M3 - Article

SN - 1029-8479

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 089

ER -