Spacetime singularities in string theory

Horowitz, Gary T.; Steif, Alan R.

doi:10.1103/physrevlett.64.260

Cited by 374 publications

(553 citation statements)

References 16 publications

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“…It has been argued [29] that this leads to singular string propagation and therefore, naively, one might think that these solutions are unphysical. However, we believe that this is not the case.…”

Section: Discussionmentioning

confidence: 99%

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PP-waves from rotating and continuously distributed D3-branes

Brandhuber

Sfetsos

2002

J. High Energy Phys.

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We study families of PP-wave solutions of type-IIB supergravity that have (light-cone) time dependent metrics and RR five-form fluxes. They arise as Penrose limits of supergravity solutions that correspond to rotating or continuous distributions of D3-branes. In general, the solutions preserve sixteen supersymmetries. On the dual field theory side these backgrounds describe the BMN limit of N = 4 SYM when some scalars in the field theory have non-vanishing expectation values. We study the perturbative string spectrum and in several cases we are able to determine it exactly for the bosons as well as for the fermions. We find that there are special states for particular values of the light-cone constant P + .

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Section: Discussionmentioning

confidence: 99%

“…If the metric is of the form (1) the fluctuations of the eight transverse modes are governed by Schrödinger equations (see, for instance, [29])…”

Section: The Perturbative String Spectrummentioning

confidence: 99%

PP-waves from rotating and continuously distributed D3-branes

Brandhuber

Sfetsos

2002

J. High Energy Phys.

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“…are solutions to all orders in α ′ for the bosonic/fermionic string in D = 26/10 provided A ij satisfies the condition [4] 4 m 2 (n − k) = A ij A ij .…”

Section: The Background As the Penrose Limit Of Ds N × S Nmentioning

confidence: 99%

“…This observation led in the sixties and seventies to a detailed study of the geometric properties of planewave metrics and of matter fields defined on them [2]. Already within string theory, it soon became clear that higher-dimensional plane waves give exact solutions to string theory, provided the Kalb-Ramond and dilaton fields satisfy certain conditions [3] [4]. The generalization of the Penrose limiting procedure relating higher dimensional plane waves with more complicated solutions to string theory [5] further triggered the interest in such space-times.…”

Section: Introductionmentioning

confidence: 99%

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

Horcajada

Ruiz

2008

Nuclear Physics B

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The open string on the plane-wave limit of dS n × S n with constant B 2 and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form, and defining from its inverse the canonical commutation relations. Canonical quantization is proved to be perfectly suited for this task, since the symplectic form is unambiguously defined and non-singular. The string position and the string momentum operators are shown to satisfy equal-time canonical commutation relations. Noticeably the string position operators define non-commutative spaces for all values of the string worldsheet parameter σ, thus extending non-commutativity outside the branes on which the string endpoints may be assumed to move. The Minkowski spacetime limit is smooth and reproduces the results in the literature, in particular non-commutativity gets confined to the endpoints.

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“…As we will see, now the lack of global hyperbolicity can be well understood, but Ehlers-Kundt conjecture still remains open. The applications to string theory have highlights as: (a) gravitational pp-waves are relevant spacetimes with vanishing scalar invariants (VSI, see [19,42] for a classification), and such spacetimes yield exact backgrounds for string theory (vanishing of α ′ corrections, [2,30]), (b) Berenstein, Maldacena and Nastase [5] have recently proposed and influential solvable model for string theory by taking the Penrose limit in AdS 5 × S 5 spacetimes, or (c) after realizing that Gödel like universes can be supersimetrically embedded in string theory, it was realized and emphasized that these solutions were T -dual to compactified plane wave backgrounds [13,28,35].…”

Section: Introductionmentioning

confidence: 99%

On the Geometry of pp-Wave Type Spacetimes

Flores

Sánchez

Analytical and Numerical Approaches to Mathematical Relativity

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Abstract.Global geometric properties of product manifolds M = M × R 2 , endowed with a metric type ·, · = ·, · R + 2dudv + H(x, u)du 2 (where ·, · R is a Riemannian metric on M and H : M × R → R a function), which generalize classical plane waves, are revisited. Our study covers causality (causal ladder, inexistence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate points. Appropiate mathematical tools for each problem are emphasized and the necessity to improve several Riemannian (positive definite) results is claimed.The behaviour of H(x, u) for large spatial component x becomes essential, being a spatial quadratic behaviour critical for many geometrical properties. In particular, when M is complete, if −H(x, u) is spatially subquadratic, the spacetime becomes globally hyperbolic and geodesically connected. But if a quadratic behaviour is allowed (as happen in plane waves) then both global hyperbolicity and geodesic connectedness maybe lost.From the viewpoint of classical General Relativity, the properties which remain true under generic hypotheses on M (as subquadraticity for H) become meaningful. Natural assumptions on the wave -finiteness or asymptotic flatness of the front-imply the spatial subquadratic behaviour of |H(x, u)| and, thus, strong results for the geometry of the wave. These results not always hold for plane waves, which appear as an idealized non-generic limit case.

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Spacetime singularities in string theory

Cited by 374 publications

References 16 publications

PP-waves from rotating and continuously distributed D3-branes

PP-waves from rotating and continuously distributed D3-branes

Quantization of the open string on plane-wave limits of and non-commutativity outside branes

On the Geometry of pp-Wave Type Spacetimes

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