Results 1  10
of
22
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
Abstract

Cited by 794 (8 self)
 Add to MetaCart
We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary DiracBornInfeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its Tduality, and Morita equivalence. We also discuss the D0/D4 system, the relation to Mtheory in DLCQ, and a possible noncommutative version of the sixdimensional (2, 0) theory. 8/99
2001c, How noncommutative gauge theories couple to gravity, Nucl
 Phys. B599
"... We study coupling of noncommutative gauge theories on branes to closed string in the bulk. We derive an expression for the gauge theory operator dual to the bulk graviton, both in bosonic string theory and superstring theory. In either case, we find that the coupling is different from what was expec ..."
Abstract

Cited by 42 (5 self)
 Add to MetaCart
We study coupling of noncommutative gauge theories on branes to closed string in the bulk. We derive an expression for the gauge theory operator dual to the bulk graviton, both in bosonic string theory and superstring theory. In either case, we find that the coupling is different from what was expected in the literature when the graviton is polarized in the noncommutative directions. In the case of superstring, the expression for the energymomentum tensor is consistent with the way the bulk metric appears in the action for the noncommutative gauge theory. We also clarify some aspects of the correspondence between operators in the gauge theory and boundary conditions in the Noncommutative gauge theories can be realized as the zero slope limit of open string theory on branes in a background of strong NSNS twoform field Bij [1 11]. It was pointed out in [12, 13] that, for each local observable in a gauge theory in commutative space, one can define an observable in the noncommutative version of the theory. The
Noncommutative string theory, the Rmatrix, and Hopf
, 2000
"... Motivated by the form of the noncommutative *product in a system of open strings and Dpbranes with constant nonzero NeveuSchwarz 2form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its Rmatrix, and comment on some of its properties. We show that th ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
Motivated by the form of the noncommutative *product in a system of open strings and Dpbranes with constant nonzero NeveuSchwarz 2form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its Rmatrix, and comment on some of its properties. We show that the noncommutative string theory *product is a particular example of this multiplication, and comment on other possible Hopf algebraic properties which may underlie the theory.
World Volume Noncommutativity versus Target Space Noncommutativity,” JHEP 9903
, 1999
"... It is known that the noncommutativity of Dbrane coordinate is responsible for describing the higherdimensional Dbranes in terms of more fundamental ones such as Dparticles or Dinstantons, while considering a noncommutative torus as a target space is conjectured to be equivalent to introducing t ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
It is known that the noncommutativity of Dbrane coordinate is responsible for describing the higherdimensional Dbranes in terms of more fundamental ones such as Dparticles or Dinstantons, while considering a noncommutative torus as a target space is conjectured to be equivalent to introducing the background antisymmetric tensor field in matrix models. In the present paper we clarify the dual nature of both descriptions. Namely the noncommutativity of conjugate momenta of the Dbrane coordinates realizes the target space structure, whereas noncommutativity of the coordinates themselves realizes world volume structure. We explicitly construct a boundary state for the Dirichlet boundary condition where the string boundary is adhered to the Dbrane on the noncommutative torus. There are nontrivial relations between the parameters appeared in the algebra of the coordinates and that of the momenta.
Derivatives and the role of the Drinfeld twist in Noncommutative string theory,” hepth/0003234
"... We consider the derivatives which appear in the context of noncommutative string theory. First, we identify the correct derivations to use when the underlying structure of the theory is a quasitriangular Hopf algebra. Then we show that this is a specific case of a more general structure utilising th ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
We consider the derivatives which appear in the context of noncommutative string theory. First, we identify the correct derivations to use when the underlying structure of the theory is a quasitriangular Hopf algebra. Then we show that this is a specific case of a more general structure utilising the Drinfel’d twist. We go on to present reasons as to why we feel that the lowenergy effective action, when written in terms of the original commuting coordinates, should explicitly exhibit this twisting.
On the deformation quantization description of matrix compactifications
 Nucl. Phys. B541 651
, 1999
"... Matrix theory compactifications on tori have associated YangMills theories on the dual tori with sixteen supercharges. A noncommutative description of these YangMills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the ‘ ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Matrix theory compactifications on tori have associated YangMills theories on the dual tori with sixteen supercharges. A noncommutative description of these YangMills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the ‘Moyal Bdeformation ’ of the YangMills theories to nonconstant background Bfields on curved spaces. This generalization is described through Fedosov’s geometry of deformation quantization.
D0branes in a Hfield background and noncommutative geometry, Nucl. Phys. B569
, 2000
"... It is known that if we compactify D0branes on a torus with constant Bfield, the resulting theory becomes SYM theory on a noncommutative dual torus. We discuss the extension to the case of a Hfield background. In the case of a constant Hfield on a threetorus, we derive the constraints to realize ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
It is known that if we compactify D0branes on a torus with constant Bfield, the resulting theory becomes SYM theory on a noncommutative dual torus. We discuss the extension to the case of a Hfield background. In the case of a constant Hfield on a threetorus, we derive the constraints to realize this compactification by considering the correspondence to string theory. We carry out this work as a first step to examine the possibility to describe transverse M5branes in Matrix theory. PACS: 11.25.w; 11.25.Sq; 11.15.q Since the proposal of Matrix theory [1] as a nonperturbative formulation of Mtheory in the infinite momentum frame or DLCQ of Mtheory [2], it has passed various kinds of consistency tests [3]. Because the action of Matrix theory is equivalent to a regularized action of supermembrane in the light cone gauge [4], the relation of membranes to Matrix
Noncommutative Gauge Fields on Poisson Manifolds ∗
, 1999
"... It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of Mtheory to tori with constant background threeform field. This indicates that noncommutative gauge theories on more general manifolds also can be useful in string theory. We discuss ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of Mtheory to tori with constant background threeform field. This indicates that noncommutative gauge theories on more general manifolds also can be useful in string theory. We discuss a framework to noncommutative quantum gauge theory on Poisson manifolds by using the deformation quantization. The Kontsevich formula for the star product was given originally in terms of the perturbation expansion and it leads to a nonrenormalizable quantum field theory. We discuss the nonperturbative path integral formulation of Cattaneo and Felder as a possible approach to construction of noncommutative quantum gauge theory on Poisson manifolds. Some other aspects of classical and quantum noncommutative field theory are also discussed. ∗Invited lecture given by I.V. Volovich at the Madeira workshop on Noncommutative Infinite
hepth/0101145 Dbrane Solutions in NonCommutative Gauge Theory on Fuzzy Sphere
, 2001
"... Noncommutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2brane in S3 with the background bfield. We identify a subset of solutions of this theory which are analogs of “unstable ” solitons on a noncommutative flat D2brane ..."
Abstract
 Add to MetaCart
(Show Context)
Noncommutative gauge theory on fuzzy sphere was obtained by Alekseev et al. as describing the low energy dynamics of a spherical D2brane in S3 with the background bfield. We identify a subset of solutions of this theory which are analogs of “unstable ” solitons on a noncommutative flat D2brane found by Gopakumar et al. Analogously to the flat case, these solutions have the interpretation as describing D0branes “not yet dissolved ” by the D2brane. We confirm this interpretation by showing the precise agreement of the binding energy computed in the noncommutative and ordinary BornInfeld descriptions. We then study stability of the solution describing a single D0brane off a D2brane. Similarly to the flat case, we find an instability when the D0brane is located close to the D2brane. We furthermore obtain the complete mass spectrum of 02 fluctuations, which thus gives a prediction for the low energy spectrum of the 02 CFT in S3. We also discuss in detail how the instability to a formation of the fuzzy sphere modifies the usual Higgs mechanism for small separation between the branes.
from Twisted (2,0) and Little String Theories
, 1998
"... We show that the moduli space of the (2, 0) and littlestring theories compactified on T 3 with Rsymmetry twists is equal to the moduli space of U(1) instantons on a noncommutative T 4. The moduli space of U(q) instantons on a noncommutative T 4 is obtained from littlestring theories of NS5brane ..."
Abstract
 Add to MetaCart
We show that the moduli space of the (2, 0) and littlestring theories compactified on T 3 with Rsymmetry twists is equal to the moduli space of U(1) instantons on a noncommutative T 4. The moduli space of U(q) instantons on a noncommutative T 4 is obtained from littlestring theories of NS5branes at Aq−1 singularities with twists. A large class of gauge theories with N = 4 SUSY in 2+1D and N = 2 SUSY in 3+1D are limiting cases of these theories. Hence, the moduli spaces of these gauge theories can be read off from the moduli spaces of instantons on noncommutative tori. We study the phase transitions in these theories and the action of Tduality. On the purely mathematical side, we give a prediction for the moduli space of 2 U(1) instantons on a noncommutative T 4.