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10
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 ..."
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Cited by 794 (8 self)
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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
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 396 (26 self)
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A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
Witten’s open string field theory in constant Bfield background
 JHEP 0003 (2000) 017 [hepth/9912254
"... In this paper we consider Witten’s bosonic open string field theory in the presence of a constant background of the secondrank antisymmetric tensor field Bij. We extend the operator formulation of Gross and Jevicki in this situation and construct the overlap vertices explicitly. As a result we find ..."
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Cited by 17 (0 self)
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In this paper we consider Witten’s bosonic open string field theory in the presence of a constant background of the secondrank antisymmetric tensor field Bij. We extend the operator formulation of Gross and Jevicki in this situation and construct the overlap vertices explicitly. As a result we find a noncommutative structure of the Moyal type only in the zeromode sector, which is consistent with the result of the correlation functions among vertex operators in the world sheet formulation. Furthermore we find out a certain unitary transformation of the string field which absorbs the Moyal type noncommutative structure. It can be regarded as a microscopic origin of the transformation between the gauge fields in commutative and noncommutative gauge theories discussed by Seiberg and Witten. 1
Energymomentum tensors in matrix theory and in noncommutative gauge theories
, 2001
"... The energymomentum tensor of Matrix Theory is derived by computing disk amplitudes with one closed string and an arbitrary number of open strings and by taking the DKPS limit. We clarify its relation to the energymomentum tensor of the noncommutative gauge theory derived in our previous paper. ..."
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Cited by 15 (1 self)
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The energymomentum tensor of Matrix Theory is derived by computing disk amplitudes with one closed string and an arbitrary number of open strings and by taking the DKPS limit. We clarify its relation to the energymomentum tensor of the noncommutative gauge theory derived in our previous paper.
Noncommutativities of Dbranes and θchanging Degrees of Freedom in Dbrane Matrix Models
, 2000
"... It is known that when there are several Dbranes, their spacetime coordinates in general become noncommutative. From the point of view of noncommutative geometry, it reflects noncommutativity of the world volume of the Dbranes. On the other hand, as we showed in the previous work, in the presence ..."
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It is known that when there are several Dbranes, their spacetime coordinates in general become noncommutative. From the point of view of noncommutative geometry, it reflects noncommutativity of the world volume of the Dbranes. On the other hand, as we showed in the previous work, in the presence of the constant antisymmetric tensor field the momentum operators of the Dbranes have noncommutative structure. In the present paper, we investigate a relation between these noncommutativities and the description of Dbranes in terms of the noncommutative YangMills theory recently proposed by Seiberg and Witten. It is shown that the noncommutativity of the YangMills theory, which implies that of the world volume coordinates, originates from both noncommutativities of the transverse coordinates and momenta from the viewpoint of the lowerdimensional Dbranes. Moreover, we show that this noncommutativity is transformed by coordinate transformations on the world volume and thereby can be chosen in an arbitrary fixed value. We also make a brief comment on a relation between this fact and a hidden symmetry of the IIB matrix models.
Relations between NonCommutative and Commutative Spacetime 1
, 2001
"... Spacetime noncommutativity appears in string theory. In this paper, the noncommutativity in string theory is reviewed. At first we review that a Dpbrane is equivalent to a configuration of infinitely many D(p − 2)branes. If we consider the worldvolume as that of the Dpbrane, coordinates of the ..."
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Spacetime noncommutativity appears in string theory. In this paper, the noncommutativity in string theory is reviewed. At first we review that a Dpbrane is equivalent to a configuration of infinitely many D(p − 2)branes. If we consider the worldvolume as that of the Dpbrane, coordinates of the Dpbrane is commutative. On the other hand if we deal with the worldvolume as that of the D(p −2)branes, since coordinates of many Dbranes are promoted to matrices the worldvolume theory is noncommutative one. Next we see that using a point splitting reguralization gives a noncommutative Dbrane, and a noncommutative gauge field can be rewritten in terms of an ordinary gauge field. The transformation is called the SeibergWitten map. And we introduce second class constraints as boundary conditions of an open string. Since Neumann and Dirichlet boundary conditions are mixed in the constraints when the open string is coupled to a NS B field, the end points of the open string is noncommutative. 1
hepth/0101211 UT922 Formation of Spherical D2brane from Multiple D0branes
, 2001
"... We study Dbranes in SU(2) WZW model by means of the boundary state techniques. We realize the “fuzzy sphere ” configuration of multiple D0branes as the boundary state with the insertion of suitable Wilson line. By making use of the pathintegral representation we show that this boundary state pres ..."
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We study Dbranes in SU(2) WZW model by means of the boundary state techniques. We realize the “fuzzy sphere ” configuration of multiple D0branes as the boundary state with the insertion of suitable Wilson line. By making use of the pathintegral representation we show that this boundary state preserves the appropriate boundary conditions and leads to the Cardy state describing a spherical D2brane under the semiclassical approximation. This result directly implies that the spherical D2brane in SU(2) WZW model can be well described as the bound state of D0branes. After presenting the supersymmetric extension, we also investigate the BPS and the nonBPS configurations of Dbranes in the NS5 background. We demonstrate that the nonBPS configurations are actually unstable, since they always possess the open string tachyons. We further notice that the stable BPS bound state constructed by the tachyon Toward thorough understanding of Dbrane dynamics, the studies on the flat Dbranes with constant Bfield have recently received a great deal of interests [1, 2, 3]. One of the important
SNUST000601 hepth/0007055 TimeDelay at Higher Genus in HighEnergy Open String Scattering ∗
, 2000
"... We explore some aspects of causal timedelay in open string scattering studied recently by Seiberg, Susskind and Toumbas. By examining highenergy scattering amplitudes in fixed order perturbation theory, we argue that causal timedelay at Gth order is 1/(G + 1) times smaller than the timedelay at ..."
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We explore some aspects of causal timedelay in open string scattering studied recently by Seiberg, Susskind and Toumbas. By examining highenergy scattering amplitudes in fixed order perturbation theory, we argue that causal timedelay at Gth order is 1/(G + 1) times smaller than the timedelay at tree level. We give a spacetime interpretation of the result by utilizing the spacetime picture of highenergy open string scattering suggested by Gross and Mañes. We find that essential role is played by universal feature of string spacetime trajectory at high energy that each open string is fragmented into at most two open and O(G/2) closed little strings at the scattering point and by the absence of causal timedelay for closed strings. We also discuss a relation to the spacetime uncertainty principle and make brief comments on causal timedelay behavior in space/time noncommutative field theory as well as in heterotic string and its TypeI dual.
KEKTH715 hepth/0009215 Boundary States in BField Background
, 2001
"... We consider the boundary states which describe Dbranes in a constant Bfield background. We show that the twoform field Φ, which interpolates commutative and noncommutative descriptions of Dbranes, can be interpreted as the invariant field strength in the Tdual picture. We also show that the ext ..."
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We consider the boundary states which describe Dbranes in a constant Bfield background. We show that the twoform field Φ, which interpolates commutative and noncommutative descriptions of Dbranes, can be interpreted as the invariant field strength in the Tdual picture. We also show that the extended algebra parametrized by θ and Φ naturally appears as the commutation relations of the original and the Tdual coordinates. September