### Citations

307 | Tachyon condensation on the brane antibrane system,”
- Sen
- 1998
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Citation Context ... in string theory have been investigated recently [9-14]. It has been shown that in many instances these are naturally understood as bound states of a brane-antibrane system with tachyon condensation =-=[10,11,13]-=-, and more concretely as novel stable but nonsupersymmetric D-branes [12,14]. Brane anti-brane annihilation in the special case of ninebranes – which will be important in the present paper – has been ... |

307 |
Noncommutative geometry and matrix theory:
- Connes, Douglas, et al.
- 1998
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Citation Context ...ndidate. Perhaps there is an approach via noncommutative geometry; so far, noncommutative geometry has been used to describe D-branes coupled to flat but irrational and topologically trivial B-fields =-=[36]-=-. Orbifolds With Discrete Torsion D-branes on an orbifold with discrete torsion will lead, in view of the analysis in [37], to a mixture of two of the constructions that we have considered. In this ca... |

250 |
Consistency conditions for orientifolds and D–manifolds
- Gimon, Polchinski
- 1996
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Citation Context ...ccording to which KSp(S 5 ) = Z2, KSp(S 1 ) = KSp(S 3 ) = KSp(S 7 ) = KSp(S 9 ) = 0. Comparison To Gimon-Polchinski One might wonder whether we instead could use the arguments of Gimon and Polchinski =-=[38]-=- to learn how Ω acts on the 0-0 strings. Their approach would entail examining the operator product of 0-9 and 9-0 vertex operators. These vertex operators require some novelty, since spin fields for ... |

249 | Brane dynamics from the Born-Infeld action,” Nucl
- Callan, Maldacena
- 1998
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Citation Context ...suitable expectation value, one would return to the vacuum state without this pair. 1 This has been argued [11] using techniques in [26]. Brane-antibrane annihilation can also be seen semiclassically =-=[27,28]-=-. The fact that the p-p and p-p strings have a reversed GSO projection can be formalized as follows. Consider the p-p brane system to have a two-valued Chan-Paton label i, where i = 1 for an open stri... |

224 |
Dirichlet Branes And Ramond-Ramond Charges,” Phys
- Polchinski
- 1995
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Citation Context ...s a −1-brane in Type I superstring theory. October, 19981. Introduction One of the most important insights about nonperturbative behavior of string theory is that D-branes carry Ramond-Ramond charge =-=[1]-=-. Massless Ramond-Ramond fields are differential forms, and therefore the Ramond-Ramond charges would appear to be cohomology classes – measured by integrating the differential forms over suitable cyc... |

128 |
Superconnections and the Chern Character,” Topology 24
- Quillen
- 1985
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Citation Context ...). Because of the GSO projection, the off-diagonal fermionic gauge fields of U(1|1) are absent, and we get instead a structure whose lowest modes correspond to a “superconnection” (in the language of =-=[29]-=-), that is to a matrix of the form ( A T T A ′ ) , (3.2) where A and A ′ are the gauge fields and T is the p-p tachyon. If A and A ′ are connections on bundles E and F (E and F are the bundles of “bos... |

123 |
modules. Topology 3
- Atiyah, Bott, et al.
- 1964
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Citation Context ...⃗x = (x1, . . ., x2k) is an element of S2k−1 (that is, a 2k-vector with ⃗x 2 = 1), then we define the tachyon field by T(⃗x) = ⃗Γ · ⃗x. (4.1) It has winding number 1 and (according to section 2.13 of =-=[30]-=-) generates π2k−1(U(2k−1 )). That the p-brane charge of this configuration is 1 and all higher (and lower) charges vanish can be verified by using the formulas for brane charges induced by gauge field... |

77 | Light-cone supersymmetry and D-branes - Green, Gutperle - 1996 |

52 |
Baryons And Branes
- Witten
- 1998
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Citation Context ... identified with a standard construction in K-theory, involving the Thom isomorphism or Bott class. In concluding the argument, one also needs a topological condition that has been noticed previously =-=[16]-=- and can be understood as a worldsheet global anomaly [17] but which has hitherto seemed rather obscure. In section five, we generalize the discussion to orbifolds and orientifolds, and also to includ... |

43 |
On the Bound States of p
- Gava, Narain, et al.
- 1997
(Show Context)
Citation Context ...brane-antibrane pair. In other words, by giving the tachyon field a suitable expectation value, one would return to the vacuum state without this pair. 1 This has been argued [11] using techniques in =-=[26]-=-. Brane-antibrane annihilation can also be seen semiclassically [27,28]. The fact that the p-p and p-p strings have a reversed GSO projection can be formalized as follows. Consider the p-p brane syste... |

37 |
D-branes and discrete torsion,” hep-th/9807235
- Douglas
(Show Context)
Citation Context ...be D-branes coupled to flat but irrational and topologically trivial B-fields [36]. Orbifolds With Discrete Torsion D-branes on an orbifold with discrete torsion will lead, in view of the analysis in =-=[37]-=-, to a mixture of two of the constructions that we have considered. In this case, instead of the K-theory of pairs (E, F) of bundles with G action, one wants the K-theory of such pairs with a projecti... |

17 | D-Branes and Topological Field Theories,” hep-th 9511222, Nucl. Phys. B463 - Bershadsky, Sadov, et al. - 1996 |

15 | Stable non-BPS states - Sen, Zwiebach - 2000 |

13 | Brane - anti-brane forces,” hep-th/9511194 - Banks, Susskind |

11 | I-Brane Inflow And Anomalous Couplings On D-Branes,” hep-th/9605033 - Green, Harvey, et al. - 1997 |

11 |
Strings from five-branes
- Duff, Lu
- 1991
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Citation Context ... an SO(32) bundle on S 8 . This bundle has p1(V ) = 0 (since p1(V ) would take values in H 4 (S 8 ), which vanishes), and ∫ S 8 p2(V ) = 6k, (2.2) 1 This object has actually been first constructed in =-=[20]-=-, where the coupling to the B-field was computed. 3 R 8where k is an arbitrary integer. The factor of 6 arises as follows. As we remarked above, the topological charge of an SO(32) bundle V on S 8 is... |

8 |
K-Theory and Reality,” Quart
- Atiyah
- 1966
(Show Context)
Citation Context ...that has been called 15 If a bundle E is defined with transition functions gij relative to an open cover Ui of X, then the complex conjugate of E is a bundle E with transition functions gij. 28KR(X) =-=[32]-=-. KR(X) depends, of course, on the choice of τ, but this is not usually indicated explicitly in the notation. Now let us try to interpret case (ii). Since (−1) FL reverses the sign of D-brane charge, ... |

7 |
K-theory and Ramond-Ramond charge,” hep-th/9710230, JHEP 9711
- Minasian, Moore
- 1997
(Show Context)
Citation Context ...p and back to SO in adding four to the brane dimension; these facts are reminiscent of the periodicity formulas πi(U(N)) = πi+2(U(N)) and πi(SO(N)) = πi±4(Sp(N)).) Such arguments motivated a proposal =-=[6]-=- that D-brane charge takes value in K(X). (The proposal was accompanied by a remark that the torsion in KO(X) would provide simple and interesting examples.) Also, a possible relation of orientifolds ... |

7 | Point-Like States for Type - Green - 1994 |

6 | Lectures on K(X - Bott - 1969 |

4 |
Spin From Isospin In A Gauge Theory,” Phys
- Jackiw, Rebbi
- 1976
(Show Context)
Citation Context ...of SO(32) by showing that it is odd under a 2π 4rotation in H. We write V = U ⊕ W, with U a non-trivial SO(n) bundle and W a trivial H bundle. As in many such problems involving charge fractionation =-=[20]-=-, the essence of the matter is to look at the zero modes of the Dirac operator. In Type I superstring theory, the massless fermions that are not neutral under SO(32) are gluinos, which transform in th... |

3 |
The Mirror Transform Of Type I Vacua
- Sen, Sethi
- 1997
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Citation Context ...on of SO(n), or any other representation in which the central element −1 of SO(n) acts trivially.) So (5.7) asserts that the cohomology class H ∗ of the B-field equals ˜w2(V ). This statement is true =-=[35]-=-. Therefore, Type I Dbrane charge takes values in KO [H](X), giving strong encouragement to the expectation that the analogous statements are true for Type II. Comparison To Cohomology Theory One poin... |

2 | Comparing D-Branes To Black Branes,” Phys - Lifschytz - 1996 |

2 |
M.: Graded Brauer Groups and K-theory
- Donovan, Karoubi
- 1970
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Citation Context ...define a twisted K-group K [H](X) whose elements are pairs (E, F) of such twisted bundles subject to the usual equivalence relation, which says that (E, F) is equivalent to (E ⊕H, F ⊕H) for any H. In =-=[35]-=-, it is shown that (5.6) is the condition for a submanifold W to determine a class in this kind of K-theory. It is possible to describe twisted bundles more intrinsically, without talking about open c... |

1 |
Equivariant Topological Sigma Models,” hep-th/9309124
- Horava
(Show Context)
Citation Context .... (The proposal was accompanied by a remark that the torsion in KO(X) would provide simple and interesting examples.) Also, a possible relation of orientifolds with KR-theory was briefly mentioned in =-=[8]-=-. In another line of development, stable but nonsupersymmetric (that is, non-BPS) states in string theory have been investigated recently [9-14]. It has been shown that in many instances these are nat... |

1 |
reprinted with other useful references
- Atiyah, K-Theory
- 1967
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Citation Context ... I zerobrane that has been discussed before, and a new Type I −1-brane. For more background on K-theory and fuller explanations of some constructions that we will meet later, the reader might consult =-=[18,19]-=-. I have generally tried to make this paper self-contained and readable with no prior familiarity with K-theory, though certain assertions will be made without proof. 2. Some Questions About Type I Su... |

1 |
Le Groupe de Brauer,” section 1.6
- Grothendieck
- 1968
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Citation Context ...f E are valued in an ordinary vector bundle, whose sections make an algebra A(E). In the mathematical literature, K [H](X) is defined in terms of modules for the algebra A(E). One fundamental theorem =-=[33]-=- asserts that for any [H] of finite order n, there exists a twisted bundle E of some finite rank m (which is always a multiple of n). Given this theorem, one proves as follows that K(X) and K [H](X) a... |

1 | Brane-Anti-Brane Forces,” hep-th/9511194. 43 - Banks, Susskind |