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## Penrose limits, supergravity and brane dynamics (2002)

Citations: | 104 - 7 self |

### Citations

536 | Exact solutions of Einstein’s field equations - Stephani, Kramer, et al. - 2003 |

473 | Type IIB Green-Schwarz superstring in plane wave RamondRamond background,” Nucl. Phys. B625
- Metsaev
- 2002
(Show Context)
Citation Context ... the AdS5 ×S 5 solution of IIB superstring theory. The other known maximally supersymmetric pp-wave solutions in four [5] and five and six dimensions [6] can also be obtained in this way. As shown in =-=[7]-=-, the (Green–Schwarz) IIB superstring on the maximally supersymmetric Hpp-wave solution is a free theory after gauge-fixing, and can therefore be quantised exactly. This fact together with the above r... |

403 | A new maximally supersymmetric background of IIB superstring theory
- Blau, Figueroa-O’Farrill, et al.
- 2002
(Show Context)
Citation Context ...3] it was also shown that the limits of the corresponding (D − p − 2)-form field strengths agree with those of the Hpp-waves [3]. We conclude that the maximally supersymmetric Hpp-waves of [2, 1] and =-=[4]-=- appear as Penrose limits along generic null geodesics of the near horizon geometries of the M2/5 and D3 branes, respectively [3]. Likewise, the maximally supersymmetric Hpp-waves in four [5] and five... |

221 |
Black strings and p-branes
- Horowitz, Strominger
- 1991
(Show Context)
Citation Context ...o they can easily be adapted to any choice of frame. Next we shall investigate the D-branes, NS-branes and M-branes separately. 5.3.2. D-branes. The spacetime metric of a Dp-brane in the string frame =-=[22, 23, 24, 25]-=- is where ds 2 = H −1 2ds 2 1 (�1,p ) + H 2ds 2 (�9−p ) Fp+2 = dvol(�1,p ) ∧ dH −1 e 2φ = H 3−p 2 H = 1 + Qp r7−p (5.21) (5.22) is a harmonic function on the transverse space�9−p , r is the radial coo... |

194 |
Any space-time has a plane wave as a limit,” in Differential geometryand relativity
- Penrose
- 1976
(Show Context)
Citation Context ...used in [8] to propose a novel derivation of the spectrum of IIB superstrings on both Minkowski and maximally supersymmetric Hpp-wave spacetimes from gauge theory using the AdS/CFT correspondence. In =-=[9]-=- Penrose showed that any spacetime (i.e., any solution of the Einstein field equations) has a limiting spacetime which is a plane wave. This limit can be thought of as a “first order approximation” to... |

124 |
Covariant action for the super-five-brane of M-theory, Phys
- Bandos, Lechner, et al.
- 1997
(Show Context)
Citation Context ...his has already been done [7] and some of the consequences have subsequently been explored in [8]. Next we turn to investigate the Penrose limit of a M5-brane probe in an eleven-dimensional spacetime =-=[47, 48, 49, 50, 51]-=-. To describe the field equations of the M5-brane in a general supergravity background as given in [49], we begin with some definitions. We denote with γµν = e a µ eb ν nab the induced metric on the w... |

123 |
Black Holes and Membranes in Higher Dimensional Theories with Dilaton Fields
- Gibbons, Maeda
- 1988
(Show Context)
Citation Context ...o they can easily be adapted to any choice of frame. Next we shall investigate the D-branes, NS-branes and M-branes separately. 5.3.2. D-branes. The spacetime metric of a Dp-brane in the string frame =-=[22, 23, 24, 25]-=- is where ds 2 = H −1 2ds 2 1 (�1,p ) + H 2ds 2 (�9−p ) Fp+2 = dvol(�1,p ) ∧ dH −1 e 2φ = H 3−p 2 H = 1 + Qp r7−p (5.21) (5.22) is a harmonic function on the transverse space�9−p , r is the radial coo... |

123 |
D-brane actions with local kappa symmetry
- Aganagic, Popescu, et al.
(Show Context)
Citation Context ...s string units as a function of p is Tp = 1 kp(α ′) p+1 2 for some constant kp which depends of the string coupling constant. The bosonic part of a typical action of a Dp-brane in a curved background =-=[43, 44, 45, 46]-=- is (∫ Ip[g, B, C] = Tp d p+1 σe −Φ√ ∫ g + F + e F ) ∧ C , (10.1) with F = α ′ F + B and C = ∑ k Ck, where F is the Born–Infeld two-form field strength, B is the NSNS two-form gauge potential and Ck a... |

119 |
Supermembranes and eleven-dimensional supergravity,” Phys
- Bergshoeff, Sezgin, et al.
- 1987
(Show Context)
Citation Context .... Worldvolume dynamics and Penrose limits The effect of the Penrose limit on the dynamics of brane probes with worldvolume and Wess-Zumino couplings, like the fundamental string [41] and the M2-brane =-=[42]-=-, has been investigated in [3]. It was found that thePENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 63 Penrose limit is a large tension limit for the probe. Here we shall extend this analysis for br... |

111 |
Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory
- Figueroa-O’Farrill, Papadopoulos
- 2001
(Show Context)
Citation Context ...re related by a limiting procedure, known as the Penrose limit. In particular, it has been found that elevendimensional Minkowski spacetime and the maximally supersymmetric Hppwave 1 of [2] (see also =-=[1]-=-) can arise as Penrose limits of the AdS4 ×S 7 and AdS7 ×S 4 solutions of M-theory [3]. In addition, ten-dimensional Minkowski spacetime and the maximally supersymmetric Hpp-wave of [4] are Penrose li... |

91 | Overlapping Branes
- Gauntlett, Kastor, et al.
- 1996
(Show Context)
Citation Context ...[17]. 6. Penrose limits of intersecting branes The methods developed to investigate the Penrose limits of branes can be easily adapted to investigate the Penrose limit of intersecting brane solutions =-=[30, 31, 32]-=-. Since the solutions for intersecting branes localised at the same point in the overall transverse space are of cohomogeneity one, the same symmetry considerations that have been employed for branes ... |

88 |
Lorentzian symmetric spaces
- Cahen, Wallach
- 1970
(Show Context)
Citation Context ...ric (2.8) metric takes the form ¯g = 2dx + dx − ( ) ∑ + (dx − ) 2 + ∑ dx i dx i . (2.13) i,j Aij(x − )x i x j When Aij is constant this metric describes a lorentzian symmetric or Cahen– Wallach space =-=[18]-=-. Such spaces include the maximally supersymmetric iPENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 9 Hpp-waves of eleven-dimensional [2, 1] and IIB supergravity [4], namely ( 3∑ 9∑ ) 9∑ g11 = 2dx + ... |

86 |
Algèbres de Lie et produit scalaire invariant
- Medina, Revoy
- 1985
(Show Context)
Citation Context ...h a bi-invariant metric. This is essentially the construction in [13], which, as shown in [39], is an example of a more general construction of Lie groups with bi-invariant metrics first discussed in =-=[40]-=-. 10. Worldvolume dynamics and Penrose limits The effect of the Penrose limit on the dynamics of brane probes with worldvolume and Wess-Zumino couplings, like the fundamental string [41] and the M2-br... |

83 | Vacuum states in supersymmetric Kaluza-Klein theory - Kowalski-Glikman - 1984 |

80 |
Strings in flat space and pp waves from N=4 super Yang
- Berenstein, Maldacena, et al.
(Show Context)
Citation Context ... name Hpp-wave was coined in [1] to denote pp-waves with a homogeneous geometry, say G/H, and homogeneous (that is, G-invariant) fluxes.PENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 3 were used in =-=[8]-=- to propose a novel derivation of the spectrum of IIB superstrings on both Minkowski and maximally supersymmetric Hpp-wave spacetimes from gauge theory using the AdS/CFT correspondence. In [9] Penrose... |

78 |
Covariant field equations of the M-theory fivebrane,” Phys
- Howe, Sezgin, et al.
- 1997
(Show Context)
Citation Context ...his has already been done [7] and some of the consequences have subsequently been explored in [8]. Next we turn to investigate the Penrose limit of a M5-brane probe in an eleven-dimensional spacetime =-=[47, 48, 49, 50, 51]-=-. To describe the field equations of the M5-brane in a general supergravity background as given in [49], we begin with some definitions. We denote with γµν = e a µ eb ν nab the induced metric on the w... |

73 | Tseytlin, “Intersecting M-branes as four-dimensional black holes,” Nucl. Phys. B475
- Klebanov, A
- 1996
(Show Context)
Citation Context ...nal black holes that arise in toroidal compactifications of M- and string theories can be thought off as reduction to five-dimensions of intersecting brane configurations in ten and eleven dimensions =-=[30, 33]-=-. We shall use the form of such four- and five-dimensional black hole solutions as summarised in [34]. The relevant five-dimensional black hole metric can be written in the form ds 2 = −(H1H2H3) −2 3d... |

63 | Plane Wave Limits and T-Duality - Güven |

55 |
Black and super p-branes in diverse dimensions, Nucl.Phys. B416
- Duff, Lu
- 1994
(Show Context)
Citation Context ...Penrose limits of the AdS2 × S2 , AdS2 ×S3 or AdS3 ×S2, and AdS3 ×S3 solutions of the corresponding supergravity theories. The latter is the near-horizon limit of the six-dimensional self-dual string =-=[21]-=- whose Penrose limits we will discuss in Section 7.3. In the light of the results of section 3.6, this derivation also provides an alternative proof that these solutions are indeed maximally supersymm... |

49 |
Harmonic superpositions of M-branes,” Nucl
- Tseytlin
- 1996
(Show Context)
Citation Context ...[17]. 6. Penrose limits of intersecting branes The methods developed to investigate the Penrose limits of branes can be easily adapted to investigate the Penrose limit of intersecting brane solutions =-=[30, 31, 32]-=-. Since the solutions for intersecting branes localised at the same point in the overall transverse space are of cohomogeneity one, the same symmetry considerations that have been employed for branes ... |

46 |
World volume action of the M theory five-brane,” Nucl
- Aganagic, Park, et al.
- 1997
(Show Context)
Citation Context ...his has already been done [7] and some of the consequences have subsequently been explored in [8]. Next we turn to investigate the Penrose limit of a M5-brane probe in an eleven-dimensional spacetime =-=[47, 48, 49, 50, 51]-=-. To describe the field equations of the M5-brane in a general supergravity background as given in [49], we begin with some definitions. We denote with γµν = e a µ eb ν nab the induced metric on the w... |

45 |
Black p-brane solutions of D=11 supergravity theory
- Guven
- 1992
(Show Context)
Citation Context ... general result obtained in Section 4.4 that the Penrose limit of any AdS ×S space along a radial geodesic is flat. Turning now to investigate the M5-brane. The supergravity solution for the M5-brane =-=[29]-=- is ds 2 = H −1 3ds 2 2 (�1,5 ) + H 3ds 2 (�5 ) F7 = dvol(�1,5 ) ∧ dH −1 (5.47) Thus we have that (a+b)′ = H 1 6. This differential equation cannot be easily integrated. Nevertheless we can write the ... |

43 |
Limits of spacetimes
- Geroch
- 1969
(Show Context)
Citation Context ...ith those properties of a supergravity background which are inherited by its Penrose limits. By rephrasing the Penrose limit in the more general context of “limits of spacetimes” introduced by Geroch =-=[16]-=-, we shall show that the numbers both of symmetries and supersymmetries never decrease in a Penrose limit. We shall also show that the symmetry superalgebra of a supergravity background gets contracte... |

43 |
The Selfdual type IIB superthreebrane
- Duff, Lu
- 1991
(Show Context)
Citation Context ...o they can easily be adapted to any choice of frame. Next we shall investigate the D-branes, NS-branes and M-branes separately. 5.3.2. D-branes. The spacetime metric of a Dp-brane in the string frame =-=[22, 23, 24, 25]-=- is where ds 2 = H −1 2ds 2 1 (�1,p ) + H 2ds 2 (�9−p ) Fp+2 = dvol(�1,p ) ∧ dH −1 e 2φ = H 3−p 2 H = 1 + Qp r7−p (5.21) (5.22) is a harmonic function on the transverse space�9−p , r is the radial coo... |

29 | A Class of string backgrounds as a semiclassical limit of WZW models,” Phys
- Olive, Rabinovici, et al.
- 1994
(Show Context)
Citation Context ...be quantised exactly. String theory on ppwave NSR backgrounds has been considered before (see, for example, [11] and references therein). In fact, the various contractions of WZW models considered in =-=[12, 13, 14, 15]-=- are special cases of a Penrose limit. Since the Penrose limit relates in a precise way a general supergravity background to a pp-wave, it allows us to understand string theory on many backgrounds at ... |

25 |
The Dirichlet super p-branes
- Cederwall, Gussich, et al.
- 1997
(Show Context)
Citation Context ...s string units as a function of p is Tp = 1 kp(α ′) p+1 2 for some constant kp which depends of the string coupling constant. The bosonic part of a typical action of a Dp-brane in a curved background =-=[43, 44, 45, 46]-=- is (∫ Ip[g, B, C] = Tp d p+1 σe −Φ√ ∫ g + F + e F ) ∧ C , (10.1) with F = α ′ F + B and C = ∑ k Ck, where F is the Born–Infeld two-form field strength, B is the NSNS two-form gauge potential and Ck a... |

24 |
Multi-membrane solutions of D=11 supergravity
- Duff, Stelle
- 1991
(Show Context)
Citation Context ...try of the solution. This group does not act transitively on the spacetime. 5.3.4. M-branes. There are two cases to consider, the M2-brane and the M5-brane. The supergravity solution for the M2-brane =-=[28]-=- is Thus we have ds 2 = H −2 3ds 2 1 (�1,2 ) + H 3ds 2 (�8 ) F4 = dvol(�1,3 ) ∧ dH −1 (5.40) (a + b) ′ = H −1 6 . (5.41) This differential equation cannot be easily integrated. Nevertheless we can wri... |

22 |
Holonomy and the Lie algebra of infinitesimal motions of a Riemannian manifold
- Kostant
- 1955
(Show Context)
Citation Context ...o additional linear conditions. 3.5.2. Killing transport. We now describe a useful local characterisation of Killing vectors as parallel sections of a vector bundle with connection (see, for example, =-=[19, 16]-=-). Let X be any vector field on a connected n-dimensional spacetime (M, g) and let AX denote the map taking a vector field Y to ∇Y X. This map is tensorial (that is, C ∞ (M)-linear) and hence defines ... |

22 |
Covariant description of superstrings
- Green, Schwarz
- 1984
(Show Context)
Citation Context ... discussed in [40]. 10. Worldvolume dynamics and Penrose limits The effect of the Penrose limit on the dynamics of brane probes with worldvolume and Wess-Zumino couplings, like the fundamental string =-=[41]-=- and the M2-brane [42], has been investigated in [3]. It was found that thePENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 63 Penrose limit is a large tension limit for the probe. Here we shall exten... |

21 |
Exact solutions of closed string theory
- Tseytlin
(Show Context)
Citation Context ...fies dramatically due to the existence of a natural light-cone gauge, and in many cases can be quantised exactly. String theory on ppwave NSR backgrounds has been considered before (see, for example, =-=[11]-=- and references therein). In fact, the various contractions of WZW models considered in [12, 13, 14, 15] are special cases of a Penrose limit. Since the Penrose limit relates in a precise way a genera... |

20 |
A Small Note on PP-Wave Vacua
- Meessen
(Show Context)
Citation Context ...persymmetric Hpp-wave of [4] are Penrose limits of the AdS5 ×S 5 solution of IIB superstring theory. The other known maximally supersymmetric pp-wave solutions in four [5] and five and six dimensions =-=[6]-=- can also be obtained in this way. As shown in [7], the (Green–Schwarz) IIB superstring on the maximally supersymmetric Hpp-wave solution is a free theory after gauge-fixing, and can therefore be quan... |

17 |
Tseytlin, “Four-dimensional plane wave string solutions with coset CFT description
- Sfetsos, A
- 1994
(Show Context)
Citation Context ...be quantised exactly. String theory on ppwave NSR backgrounds has been considered before (see, for example, [11] and references therein). In fact, the various contractions of WZW models considered in =-=[12, 13, 14, 15]-=- are special cases of a Penrose limit. Since the Penrose limit relates in a precise way a general supergravity background to a pp-wave, it allows us to understand string theory on many backgrounds at ... |

16 |
Penrose limits and maximal supersymmetry,” arXiv:hep-th/0201081
- Blau, Figueroa-O’Farrill, et al.
(Show Context)
Citation Context ...been found that elevendimensional Minkowski spacetime and the maximally supersymmetric Hppwave 1 of [2] (see also [1]) can arise as Penrose limits of the AdS4 ×S 7 and AdS7 ×S 4 solutions of M-theory =-=[3]-=-. In addition, ten-dimensional Minkowski spacetime and the maximally supersymmetric Hpp-wave of [4] are Penrose limits of the AdS5 ×S 5 solution of IIB superstring theory. The other known maximally su... |

15 |
The Isometry group and Killing spinors for the pp-wave space-time
- Chrusciel, Kowalski-Glikman
- 1984
(Show Context)
Citation Context ...= dudv + ρ 2 sin(u/2ρ) 2 ds 2 (�p+1 ) + (sin(u/2)) 2 ds 2 (�D−p−3 ) , (4.15) which is, as we have seen in Section 2.2, the metric of a Cahen–Wallach symmetric space in Rosen coordinates (compare with =-=[20]-=- for the d = 11 solution). To determine the resulting Cahen–Wallach space more explicitly, let us introduce coordinates y a for a = 1, . . ., D − 2 in such a way that the metric (4.15) becomes where R... |

15 |
Embedding of various relativistic riemannian spaces in pseudo-euclidean spaces
- Rosen
- 1965
(Show Context)
Citation Context ...ing is stated in [18], but the suggested embedding in that paper does not seem to work. The isometric embedding of pp-waves is itself not new. It has been discussed in the four-dimensional context in =-=[36, 37]-=- and is reviewed in [35, §32].PENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 61 embedding space �2,4 �2,4 ↑ ⏐ AdS2 ×S 2 ↑ ⏐ Penrose limit −−−−−−−→ CW4 (9.15) where the vertical arrows are the isomet... |

13 |
Nonsemisimple Sugawara constructions
- Figueroa-O’Farrill, Stanciu
- 1994
(Show Context)
Citation Context ...pic. If we now perform the generalised Penrose limit of G × H along H we obtain a non-semisimple Lie group with a bi-invariant metric. This is essentially the construction in [13], which, as shown in =-=[39]-=-, is an example of a more general construction of Lie groups with bi-invariant metrics first discussed in [40]. 10. Worldvolume dynamics and Penrose limits The effect of the Penrose limit on the dynam... |

11 |
Lu: Elementary fivebrane solutions of D=10 supergravity
- Duff, X
- 1991
(Show Context)
Citation Context |

10 |
Positive energy theorem and vacuum states for the Einstein-Maxwell system, Phys
- Kowalski-Glikman
- 1985
(Show Context)
Citation Context ...i spacetime and the maximally supersymmetric Hpp-wave of [4] are Penrose limits of the AdS5 ×S 5 solution of IIB superstring theory. The other known maximally supersymmetric pp-wave solutions in four =-=[5]-=- and five and six dimensions [6] can also be obtained in this way. As shown in [7], the (Green–Schwarz) IIB superstring on the maximally supersymmetric Hpp-wave solution is a free theory after gauge-f... |

10 |
Gauge invariant and gauge fixed D-brane actions, Nucl.Phys. B495
- Aganagic, Popescu, et al.
- 1997
(Show Context)
Citation Context ...s string units as a function of p is Tp = 1 kp(α ′) p+1 2 for some constant kp which depends of the string coupling constant. The bosonic part of a typical action of a Dp-brane in a curved background =-=[43, 44, 45, 46]-=- is (∫ Ip[g, B, C] = Tp d p+1 σe −Φ√ ∫ g + F + e F ) ∧ C , (10.1) with F = α ′ F + B and C = ∑ k Ck, where F is the Born–Infeld two-form field strength, B is the NSNS two-form gauge potential and Ck a... |

7 |
Exact string solutions and duality
- Tseytlin
- 1994
(Show Context)
Citation Context ...be quantised exactly. String theory on ppwave NSR backgrounds has been considered before (see, for example, [11] and references therein). In fact, the various contractions of WZW models considered in =-=[12, 13, 14, 15]-=- are special cases of a Penrose limit. Since the Penrose limit relates in a precise way a general supergravity background to a pp-wave, it allows us to understand string theory on many backgrounds at ... |

7 |
Embeddings of the plane-fronted waves and other space-times
- Collinson
- 1968
(Show Context)
Citation Context ...ing is stated in [18], but the suggested embedding in that paper does not seem to work. The isometric embedding of pp-waves is itself not new. It has been discussed in the four-dimensional context in =-=[36, 37]-=- and is reviewed in [35, §32].PENROSE LIMITS, SUPERGRAVITY AND BRANE DYNAMICS 61 embedding space �2,4 �2,4 ↑ ⏐ AdS2 ×S 2 ↑ ⏐ Penrose limit −−−−−−−→ CW4 (9.15) where the vertical arrows are the isomet... |

4 |
Gauging a nonsemisimple WZW model
- Sfetsos
- 1994
(Show Context)
Citation Context |

4 | Composite black holes in string theory
- Tseytlin
(Show Context)
Citation Context ...reduction to five-dimensions of intersecting brane configurations in ten and eleven dimensions [30, 33]. We shall use the form of such four- and five-dimensional black hole solutions as summarised in =-=[34]-=-. The relevant five-dimensional black hole metric can be written in the form ds 2 = −(H1H2H3) −2 3dt 2 + (H1H2H3) 1 3ds 2 (�4 ) , (7.1) where Hi = 1 + Qi r 2 . The harmonic functions Hi are inherited ... |

3 |
Vacuum interpolation in supergravity via p-branes,” Phys
- Gibbons, Townsend
- 1993
(Show Context)
Citation Context ...culations reduce to those we have done for the Penrose limit along a generic null geodesic of the associated AdS ×S spaces. The near horizon geometries of the various branes have been investigated in =-=[17]-=-. 6. Penrose limits of intersecting branes The methods developed to investigate the Penrose limits of branes can be easily adapted to investigate the Penrose limit of intersecting brane solutions [30,... |

3 |
Supersymmetric string solitons,” arXiv:hep-th/9112030
- Jr, Harvey, et al.
(Show Context)
Citation Context ...r the general formulae given in the previous section, in particular (5.15) with (5.18), can be used to find the Penrose limit metric. 5.3.3. Fundamental strings and NS5-branes. The NS5-brane solution =-=[26]-=- is ds 2 = ds 2 (�1,5 ) + H(r)ds 2 (�4 ) F7 = dvol(�1,5 ) ∧ dH −1 e 2φ = H (5.29) where H = 1+ Q5 r2 is a harmonic function in�4 and Q5 is the charge of NS5brane. So in this case (a + b) ′ = ±H 1 2. U... |

3 |
Nonreductive WZW models and their CFTs,” Nuc. Phys. B458
- Figueroa-O’Farrill, Stanciu
- 1996
(Show Context)
Citation Context ...cial case of this generalised Penrose limit has appeared in [13] in the context of exact string backgrounds given by WZW models on nonsemisimple Lie groups admitting a bi-invariant metric (see, e.g., =-=[38]-=-). As shown in [13], the Lie algebras of some of these Lie groups can be obtained by a contraction of semisimple Lie algebras. This contraction is a special case of the generalised Penrose limit allud... |