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Brane Dynamics in Background Fluxes and Non-commutative Geometry

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TLDR
In this article, the boundary conformal field theory approach is used to study branes in a curved background with non-vanishing Neveu-Schwarz 3-form field strength.
Abstract
Branes in non-trivial backgrounds are expected to exhibit interesting dynamical properties. We use the boundary conformal field theory approach to study branes in a curved background with non-vanishing Neveu-Schwarz 3-form field strength. For branes on an $S^3$, the low-energy effective action is computed to leading order in the string tension. It turns out to be a field theory on a non-commutative `fuzzy 2-sphere' which consists of a Yang-Mills and a Chern-Simons term. We find a certain set of classical solutions that have no analogue for flat branes in Euclidean space. These solutions show, in particular, how a spherical brane can arise as bound state from a stack of D0-branes.

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Liouville Field Theory — A decade after the revolution

TL;DR: In this paper, a review of the recent developments of the Liouville field theory and its matrix model dual is presented, which includes some original material such as the derivation of the conjectured dual action for the N = 2 LiOUville theory from other known dualities and the comparison of the cross-cap state with the c = 0 unoriented matrix model.
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D branes on group manifolds and fusion rings

TL;DR: In this paper, the charge group for symmetry preserving D-branes on group manifolds for simple, simply-connected, connected compact Lie groups G has been computed, where G is a Lie group.
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Emergent geometry and gravity from matrix models: an introduction

TL;DR: In this paper, a review of non-commutative gravity within Yang-Mills matrix models is presented, where spacetime is described as a noncommutive brane solution of the matrix model, i.e. as a submanifold of.
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Noncommutative gauge theory on fuzzy sphere from matrix model

TL;DR: A noncommutative U(1) and U(n) gauge theory on the fuzzy sphere is derived from a three-dimensional matrix model by expanding the model around a classical solution of the fuzzy spheres.
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Nonassociative star product deformations for D-brane world-volumes in curved backgrounds

TL;DR: In this article, the deformation of D-brane world volumes in curved backgrounds is investigated, and the correlation functions of the resulting system are analyzed and the results of Matrix theory in this framework are shown.
References
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Journal ArticleDOI

String theory and noncommutative geometry

TL;DR: In this article, a non-zero B-field is introduced for string theory and the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and the corrections away from this limit are discussed.
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Noncommutative Geometry and Matrix Theory: Compactification on Tori

TL;DR: In this paper, the authors studied toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry, and argued that they correspond in supergravity to tori with constant background three-form tensor field.
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Bound states of strings and p-branes

TL;DR: In this paper, it was shown that the Type IIB superstring in ten dimensions has a family of soliton and bound state strings permuted by SL(2, Z ) and the space-time coordinates enter tantalizingly in the formalism as noncommuting matrices.
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Boundary conditions, fusion rules and the Verlinde formula

TL;DR: In this article, the Verlinde formula is derived from the partition function of a conformal field theory in an annulus, and a simple derivation of the vertex formula is given.
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Universal noninteger "ground-state degeneracy" in critical quantum systems.

TL;DR: G is argued to decrease under renormalization from a less stable to a more stable critical point and plays a role in boundary critical phenomena quite analogous to that played by c, the conformal anomaly, in the bulk case.