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## String theory and noncommutative geometry (1999)

Venue: | JHEP |

Citations: | 791 - 8 self |

### Citations

2956 | Non–commutative Geometry,
- Connes
- 1994
(Show Context)
Citation Context ...t has been studied by many authors both from a mathematical and a physical perspective. The theory of operator algebras has been suggested as a framework for physics in noncommutative spacetime – see =-=[2]-=- for an exposition of the philosophy – and Yang-Mills theory on a noncommutative torus has been proposed as an example [3]. Though this example at first sight appears to be neither covariant nor causa... |

650 |
Noncommutative Geometry And String Field Theory,” Nucl. Phys. B268
- Witten
- 1986
(Show Context)
Citation Context ...rly work relating membranes to large matrices [7], has motivated in [8,9] constructions somewhat similar to [3]. Noncommutative geometry has also been used as a framework for open string field theory =-=[10]-=-. Part of the beauty of the analysis in [4] was that T-duality acts within the noncommutative Yang-Mills framework, rather than, as one might expect, mixing the modes of noncommutative Yang-Mills theo... |

367 |
Noncommutative Geometry and Matrix Theory: Compactification on Tori.
- Connes, Douglas, et al.
- 1998
(Show Context)
Citation Context ... a noncommutative torus has been proposed as an example [3]. Though this example at first sight appears to be neither covariant nor causal, it has proved to arise in string theory in a definite limit =-=[4]-=-, with the noncovariance arising from the expectation value of a background field. This analysis involved toroidal compactification, in the limit of small volume, with fixed and generic values of the ... |

307 | Tachyon condensation on the brane antibrane system,”
- Sen
- 1998
(Show Context)
Citation Context ...on projects out one of these pairs. Which pair is being projected out depends on whether we study D0-branes or anti-D0-branes. (This is a general feature of D-brane physics, exploited for instance in =-=[60]-=-: strings ending on D0-branes or D0-branes have the same boundary condition but opposite GSO projection.) We use the conventions that for D0-branes we keep the states with energies E + ± and for anti-... |

306 | A path integral approach to the Kontsevich quantization formula,
- Cattaneo, Felder
- 2000
(Show Context)
Citation Context ...model with only such a boundary interaction, plus gauge fixing terms, is a special case of the theory used by Kontsevich in studying deformation quantization [46], as has been subsequently elucidated =-=[47]-=-.) If one regards (2.17) as a one-dimensional action (ignoring the fact that x i (τ) is the boundary value of a string), then it describes the motion of electrons in the presence of a large magnetic f... |

209 |
Born-Infeld action, supersymmetry and string theory, in The many faces of the superworld. Yuri Golfand memorial volume
- Tseytlin
(Show Context)
Citation Context ... For this, we examine the constant term in the effective Lagrangian. For slowly varying fields, the effective Lagrangian is the Dirac-Born-Infeld Lagrangian (for a recent review of the DBI theory see =-=[48]-=- and references therein) LDBI = 1 gs(2π) p (α′) p+1 2 √ det(g + 2πα ′ (B + F)). (2.39) The coefficient is determined by the Dp-brane tension which for B = 0 is Tp(B = 0) = 1 gs(2π) p (α′) p+1 2 . (2.4... |

201 |
Non-linear electrodynamics from quantized strings,”
- Fradkin, Tseytlin
- 1985
(Show Context)
Citation Context ...ldsheet treatment that makes the computations particularly simple [14]. In the latter paper, it was suggested that rather classical features of the propagation of strings in a constant magnetic field =-=[41,42]-=- can be reinterpreted in terms of noncommutativity of spacetime. In the present paper, we will build upon these suggestions and reexamine the quantization of open strings ending on D-branes in the pre... |

168 |
C∗ algèbres et géométrie différentielle.
- Connes
- 1980
(Show Context)
Citation Context ...lgebra A of functions on a noncommutative torus. Mathematically, representations of a ring are usually called modules. We will aim to understand in physical terms the usual mathematical constructions =-=[62,63,4,16]-=- of projective modules over a noncommutative torus, and the “Morita equivalences” between them, which [4,16-19] are intimately related to T-duality. For simplicity, we will discuss bosonic strings. (I... |

152 | D-branes and the noncommutative torus
- Douglas, Hull
- 1998
(Show Context)
Citation Context ...ematic and efficient description of the physics in terms of noncommutative Yang-Mills theory when B is large. The limit of a torus of small volume with fixed theta angle (that is, fixed periods of B) =-=[4,11]-=- is an example with large B, but it is also possible to have large B on Rn and thereby make contact with the application of noncommutative Yang-Mills to instantons on R4 . An important element in our ... |

140 | D-branes and deformation quantization
- Schomerus
- 1999
(Show Context)
Citation Context ...ses arguing for noncommutativity of string coordinates in the presence of a B-field, in a Hamiltonian treatment [13] and also in a worldsheet treatment that makes the computations particularly simple =-=[14]-=-. In the latter paper, it was suggested that rather classical features of the propagation of strings in a constant magnetic field [41,42] can be reinterpreted in terms of noncommutativity of spacetime... |

136 |
Why is the Matrix Model Correct?,” Phys
- Seiberg
- 1997
(Show Context)
Citation Context ...ive. 85The compactification on a null circle needs a careful definition. Here we will define it as a limit of a compactification on a space-like circle in the (x 0 , x 1 ) plane which is almost null =-=[66,67]-=-. Its invariant radius ǫR will eventually be taken to zero. In order to study this system we follow the following steps: (1) We boost the system to bring the space-like circle to be along x 1 . (2) We... |

133 |
Noncommutative open string and D-brane,” Nucl. Phys. B550
- Chu, Ho
- 1999
(Show Context)
Citation Context ...ysics on noncommuting spacetime. A suggestion in this direction is given by recent analyses arguing for noncommutativity of string coordinates in the presence of a B-field, in a Hamiltonian treatment =-=[13]-=- and also in a worldsheet treatment that makes the computations particularly simple [14]. In the latter paper, it was suggested that rather classical features of the propagation of strings in a consta... |

130 |
M-Theory as a matrix model: A conjecture, Phys. Rev. D55
- Banks, Fischler, et al.
- 1997
(Show Context)
Citation Context ...his sequence of steps we find a system which typically has a smooth limit as ǫ is taken to zero. This limit was first discussed in [68] and later in the context of this definition of the Matrix Model =-=[5]-=- in [69,67]. We will now follow these steps for the case of compactification on a null circle with constant nonzero C±ij. We consider M-theory compactified on the null circle (7.1). We assume that the... |

79 |
Rieffel, “Yang-Mills for noncommutative two-tori
- Connes, A
- 1987
(Show Context)
Citation Context ...s been suggested as a framework for physics in noncommutative spacetime – see [2] for an exposition of the philosophy – and Yang-Mills theory on a noncommutative torus has been proposed as an example =-=[3]-=-. Though this example at first sight appears to be neither covariant nor causal, it has proved to arise in string theory in a definite limit [4], with the noncovariance arising from the expectation va... |

79 |
String Loop Corrections To Beta Functions”, Nucl. Phys. B288
- Callan, Lovelace, et al.
- 1987
(Show Context)
Citation Context ...ldsheet treatment that makes the computations particularly simple [14]. In the latter paper, it was suggested that rather classical features of the propagation of strings in a constant magnetic field =-=[41,42]-=- can be reinterpreted in terms of noncommutativity of spacetime. In the present paper, we will build upon these suggestions and reexamine the quantization of open strings ending on D-branes in the pre... |

78 |
Covariant field equations of the M-theory fivebrane,” Phys
- Howe, Sezgin, et al.
- 1997
(Show Context)
Citation Context ...in R6 . There is no completely satisfactory covariant Lagrangian describing the dynamical twoform B on the M5-brane. We can use either a non-covariant Lagrangian [72] or covariant equations of motion =-=[73]-=-. Here we will follow the latter approach. The background H field transforms as 10 ⊕ 10 ′ under the six-dimensional Lorentz group. It can be written as H = H + + H− , where H + is selfdual (10 of the ... |

71 | A New Goldstone multiplet for partially broken supersymmetry, Phys.Rev. D55
- Bagger, Galperin
- 1997
(Show Context)
Citation Context ...mply by δ ∗ λα = ǫ2 4πα ′η∗ α, δ ∗ λ ˙α = ǫ2 4πα ′η∗ ˙α. (4.31) Here η and η are constants, and we have chosen a convenient normalization. One of the many special properties of the DBI theory is that =-=[52]-=- it has in four dimensions a supersymmetric extension that preserves not only the linearly realized supersymmetry – many bosonic theories have such a supersymmetric version – but also, what is much mo... |

71 | Perturbative quantum gauge fields on the noncommutative torus - Krajewski, Wulkenhaar - 2000 |

65 |
Interacting Chiral Gauge Fields in Six-Dimensions and BornÄInfeld Theory //
- Perry, Schwarz
- 1997
(Show Context)
Citation Context ...constraints on H on a single M5-brane in R6 . There is no completely satisfactory covariant Lagrangian describing the dynamical twoform B on the M5-brane. We can use either a non-covariant Lagrangian =-=[72]-=- or covariant equations of motion [73]. Here we will follow the latter approach. The background H field transforms as 10 ⊕ 10 ′ under the six-dimensional Lorentz group. It can be written as H = H + + ... |

59 | Quantum field theory on noncommutative space-times and the persistence of ultraviolet divergences - Chaichian, Demichev, et al. - 2000 |

58 | D0 Branes on T n and Matrix Theory
- Sen
- 1998
(Show Context)
Citation Context ...uence of steps we find a system which typically has a smooth limit as ǫ is taken to zero. This limit was first discussed in [68] and later in the context of this definition of the Matrix Model [5] in =-=[69,67]-=-. We will now follow these steps for the case of compactification on a null circle with constant nonzero C±ij. We consider M-theory compactified on the null circle (7.1). We assume that the metric is ... |

49 |
on the Antifield-BRST Formalism for Gauge Theories, Nucl.Phys.B (Proc.Suppl.) 18A
- Henneaux
- 1990
(Show Context)
Citation Context ...tions. Note that the situation that we are considering here is the opposite of a gauge theory in which the gauge group has field-dependent structure constants or only closes on shell. This means (see =-=[50]-=- for a fuller explanation) that one has a well-defined gauge equivalence 7 Fadde’ev-Popov quantization of gauge theories is formulated in terms of the gauge group, but in the more general Batalin-Vilk... |

49 |
Partially Broken Global Supersymmetry and the Superstring
- Hughes, Polchinski
- 1986
(Show Context)
Citation Context ...nalyze supersymmetric configurations, the stringy instantons. We recall first that, in general, a Dp-brane preserves only half of the supersymmetry of Type II superstring theory. In an interpretation =-=[51]-=- that actually predates the D-brane era, this means the theory along the brane has spontaneously broken (or “nonlinearly realized”) supersymmetry along with its unbroken (or “linearly realized”) super... |

47 |
Trigonometric structure constants for new infinite-dimensional algebras,
- Fairlie, Fletcher, et al.
- 1989
(Show Context)
Citation Context ...airly natural in the context of the matrix model of M-theory [5,6], and the original discussion was made in this context. Indeed, early work relating membranes to large matrices [7], has motivated in =-=[8,9]-=- constructions somewhat similar to [3]. Noncommutative geometry has also been used as a framework for open string field theory [10]. Part of the beauty of the analysis in [4] was that T-duality acts w... |

41 |
U-duality of Born-Infeld on the noncommutative twotorus,” JHEP 9812
- Hofman, Verlinde
- 1998
(Show Context)
Citation Context ...en understood more fully [16,17]. The modules and their T-dualities have been reconsidered in a more elementary language [18-20], and the relation to the DiracBorn-Infeld Lagrangian has been explored =-=[19,20]-=-. The BPS spectrum has been more fully understood [18,19,21]. Various related aspects of noncommutative gauge theories have been discussed in [22-31]. Finally, the authors of [32] suggested interestin... |

37 | Non-local Field Theories and the Non-commutative Torus,” Phys - Berkooz - 1998 |

36 | Renormalizability of the supersymmetric Yang–Mills theories on the noncommutative torus - Sheikh-Jabbari - 1999 |

33 | Comments on supersymmetric Yang-Mills theory on a noncommutative torus - Li - 1998 |

30 | Finite Field Theory on Noncommutative Geometries - Cho, Hinterding, et al. |

29 | Mixed branes and M(atrix) theory on noncommutative torus, [hep-th/9803067 - Ardalan, Arfaei, et al. - 1999 |

28 | Noncommutative Geometry and D-Branes - Ho, Wu |

28 |
Deformation quantization of Poisson manifolds I,” q-alg/9709040
- Kontsevich
- 1997
(Show Context)
Citation Context ...− i 2 ∫ Bijx ∂Σ i ∂tx j . (2.17) (A sigma model with only such a boundary interaction, plus gauge fixing terms, is a special case of the theory used by Kontsevich in studying deformation quantization =-=[46]-=-, as has been subsequently elucidated [47].) If one regards (2.17) as a one-dimensional action (ignoring the fact that x i (τ) is the boundary value of a string), then it describes the motion of elect... |

27 | Nonrelativistic fermions, coadjoint orbits of W(infinity) and string field theory at c = 1 - Dhar, Mandal, et al. - 1992 |

22 | Matrix theory on noncommutative torus - Kawano - 1998 |

21 |
Light cone description of (2,0) superconformal theories in six-dimensions
- Aharony, Berkooz, et al.
- 1998
(Show Context)
Citation Context ...g a constant (a Fayet-Iliopoulos term) to the ADHM equations. This constant had been argued, following [35], to arise in the 1description of instantons on D-branes upon turning on a constant B-field =-=[36]-=-, 1 so putting the two facts together it was proposed that instantons on branes with a B-field should be described by noncommutative Yang-Mills theory [34,37]. Another very cogent argument for this is... |

18 | Gauge theories on the noncommutative sphere - Klimcik - 1998 |

17 |
BPS states on noncommutative tori and duality”, Nucl. Phys. B550
- Konechny, Schwarz
- 1999
(Show Context)
Citation Context ...-dualities have been reconsidered in a more elementary language [18-20], and the relation to the DiracBorn-Infeld Lagrangian has been explored [19,20]. The BPS spectrum has been more fully understood =-=[18,19,21]-=-. Various related aspects of noncommutative gauge theories have been discussed in [22-31]. Finally, the authors of [32] suggested interesting relations between noncommutative gauge theory and the litt... |

13 |
Morita equivalence and duality,” Nucl. Phys. B534
- Schwarz
- 1998
(Show Context)
Citation Context ...ing noncommutative Yang-Mills theory more directly from open strings without recourse to matrix theory [11-15]. The role of Morita equivalence in establishing T-duality has been understood more fully =-=[16,17]-=-. The modules and their T-dualities have been reconsidered in a more elementary language [18-20], and the relation to the DiracBorn-Infeld Lagrangian has been explored [19,20]. The BPS spectrum has be... |

12 | Algebraic Treatment of Compactification on Noncommutative - Casalbuoni - 1998 |

12 | Large N limit of noncommutative gauge theories,” hep-th/9908134 - Maldacena, Russo |

11 |
Super Yang-Mills on the noncommutative torus,” hepth/9807198
- Morariu, Zumino
(Show Context)
Citation Context ...-dualities have been reconsidered in a more elementary language [18-20], and the relation to the DiracBorn-Infeld Lagrangian has been explored [19,20]. The BPS spectrum has been more fully understood =-=[18,19,21]-=-. Various related aspects of noncommutative gauge theories have been discussed in [22-31]. Finally, the authors of [32] suggested interesting relations between noncommutative gauge theory and the litt... |

11 | Divergencies in a Field Theory on - Filk - 1996 |

10 |
Lectures on Integrable Systems
- Hoppe
- 1992
(Show Context)
Citation Context ...airly natural in the context of the matrix model of M-theory [5,6], and the original discussion was made in this context. Indeed, early work relating membranes to large matrices [7], has motivated in =-=[8,9]-=- constructions somewhat similar to [3]. Noncommutative geometry has also been used as a framework for open string field theory [10]. Part of the beauty of the analysis in [4] was that T-duality acts w... |

10 | Noncommutative geometry and spacetime gauge symmetries of string theory - Lizzi, Szabo - 1999 |

10 | World volume noncommutativity versus target space noncommutativity,” JHEP9903 - Kato, Kuroki - 1999 |

10 | Zachos, “Integrable symplectic trilinear interaction terms for matrix membranes,” Phys - Curtright, Fairlie, et al. - 1997 |

10 | Noncommutative Regularization for the Practical Man,” hep-th/9908052 - Hawkins |

7 |
Resolutions of Moduli Spaces of
- Nakajima
- 1994
(Show Context)
Citation Context ...e. The instanton moduli space must therefore be modified, for nonzero B, to eliminate the small instanton singularity. Adding a constant to the ADHM equations resolves the small instanton singularity =-=[40]-=-, and since going to noncommutative R 4 does add this constant [34], this strongly encourages us to believe that instantons with the B-field should be described as instantons on a noncommutative space... |

6 |
38; “The Electromagnetic Field
- Rev
- 1947
(Show Context)
Citation Context ... the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2, 0) theory. 8/991. Introduction The idea that the spacetime coordinates do not commute is quite old =-=[1]-=-. It has been studied by many authors both from a mathematical and a physical perspective. The theory of operator algebras has been suggested as a framework for physics in noncommutative spacetime – s... |

6 | On noncommutative Nahm transform, hep-th/ 9810147 - Astashkevich, Nekrasov, et al. |

5 |
Noncommutative Geometry From 0-Branes
- Cheung, Krogh
- 1998
(Show Context)
Citation Context ...gs that wind on a geodesic around the torus, starting and ending at the origin. That these open strings in the small volume limit generate the algebra of a noncommutative torus was the starting point =-=[4,11,12]-=- in applications of noncommutative Yang-Mills theory to string theory. From the point of view of the present paper, the statement can be justified by computing the OPE’s of the 0-0 open strings, which... |

5 |
Instantons on Noncommutative R 4 and (2,0
- Nekrasov, Schwarz
- 1998
(Show Context)
Citation Context ...ittle string theory [33]. Large Instantons And The α ′ Expansion Our work has been particularly influenced by certain further developments, including the analysis of instantons on a noncommutative R4 =-=[34]-=-. It was shown that instantons on a noncommutative R4 can be described by adding a constant (a Fayet-Iliopoulos term) to the ADHM equations. This constant had been argued, following [35], to arise in ... |

4 |
Morita equivalence and T-duality (or B versus Θ),” hepth/9908019
- Pioline, Schwarz
(Show Context)
Citation Context ...en understood more fully [16,17]. The modules and their T-dualities have been reconsidered in a more elementary language [18-20], and the relation to the DiracBorn-Infeld Lagrangian has been explored =-=[19,20]-=-. The BPS spectrum has been more fully understood [18,19,21]. Various related aspects of noncommutative gauge theories have been discussed in [22-31]. Finally, the authors of [32] suggested interestin... |

4 |
Instantons on a noncommutative T 4 from twisted (2,0) and little-string theories,” Nucl
- Cheung, Ganor, et al.
(Show Context)
Citation Context ...has been explored [19,20]. The BPS spectrum has been more fully understood [18,19,21]. Various related aspects of noncommutative gauge theories have been discussed in [22-31]. Finally, the authors of =-=[32]-=- suggested interesting relations between noncommutative gauge theory and the little string theory [33]. Large Instantons And The α ′ Expansion Our work has been particularly influenced by certain furt... |

4 |
D-branes and K theory,” JHEP 9812, 019
- Witten
- 1998
(Show Context)
Citation Context ...heory (in an arbitrary closed string background) the D-brane charge takes values in this K-theory – generalizing the relation of D-brane charge to ordinary complex K-theory in the long distance limit =-=[64,65]-=-. 7. Relation To M-Theory In DLCQ Motivated by the spectrum of BPS states, Connes, Douglas and Schwarz [4] proposed that M-theory compactified on a null circle (DLCQ) x − = 1 2 (x0 − x 1 ) ∼ x − + 2πR... |

1 | The One Loop UV Divergent Structure of U(1 - Martin, Sanchez-Ruiz - 1999 |

1 |
Some Elements of Connes’ NC Geometry, and Space-Time Geometry,” in: Chen Ning Yang, a Great Physicist of the Twentieth
- Chamseddine, Froehlich
- 1995
(Show Context)
Citation Context ...arly work relating membranes to large matrices [7], has motivated in [8,9] constructions somewhat similar to [3]. For other thoughts about applications of noncommutative geometry in physics, see e.g. =-=[10]-=-. Noncommutative geometry has also been used as a framework for open string field theory [11]. Part of the beauty of the analysis in [4] was that T-duality acts within the noncommutative Yang-Mills fr... |