Exact solutions of closed string theory

Abstract

Theoretical Physics Group, Blackett LaboratoryImperial College, London SW7 2BZ, U.K. AbstractWe review explicitly known exact D = 4 solutions with Minkowski signature in closed bosonic string theory. Classical string solutions with space-time interpretation are represented by conformal sigma models. Two large (intersecting) classes of solutions are described by gauged WZW models and 'chiral null models' (models with conserved chiral null current). The latter class includes plane-wave type backgrounds (admitting a covariantly constant null Killing vector) and backgrounds with two null Killing vectors (e.g., fundamental string solution). D > 4 chiral null models describe some exact D = 4 solutions with electromagnetic fields, for example, extreme electric black holes, charged fundamental strings and their generalisations. In addition, there exists a class of conformal models representing axially symmetric stationary magnetic flux tube backgrounds (including, in particular, the dilatonic Melvin solution). In contrast to spherically symmetric chiral null models for which the corresponding conformal field theory is not known explicitly, the magnetic flux tube models (together with some non-semisimple WZW models) are among the first examples of solvable unitary conformal string models with non-trivial D = 4 curved space-time interpretation. For these models one is able to express the quantum hamiltonian in terms of free fields and to find explicitly the physical spectrum and string partition function. To appear as a review in Classical and Quantum GravityMay 1995 ⋆ e-mail address: tseytlin@ic.ac.uk † On leave from Lebedev Physics Institute, Moscow, Russia. IntroductionString theory is a remarkable extension of General Relativity which is consistent at the quantum level. One of the important problems is to study the set of exact classical solutions to string equations of motion. This may clarify its formal aspects but also may be relevant for understanding the implications of string theory for cosmology and black holes (assuming that in certain regions, e.g., at small times/scales, the effective string coupling is small so that perturbative and non-perturbative corrections to string equations of motion can be ignored). To be able to address issues of singularities and strong field behavior one should determine not just solutions of the leading-order low-energy string effective equations derived under the assumption of small field gradients (|α ′ R| ≪ 1, etc.) but solutions that are exact to all orders in α ′ (i.e., the corresponding exact conformal σ-models), and, ultimately, how first-quantized string modes propagate in a given background (i.e., the underlying conformal field theories).

Erratum: Solitonic strings and BPS saturated dyonic black holes [Phys. Rev. D53, 5619 (1996)]

“…The chiral null models [6,3] are a class of twodimensional (2d) σ-models which generalize both plane wave type and fundamental string type models and are defined by the following string Lagrangian:…”

“…To embed an effective field theory solution into string theory one is to find the corresponding world-sheet conformal σ-model whose couplings reduce to the given background fields at scales larger than the compactification and string scales (see, e.g., [3] and references therein). Thus, four-dimensional effective field theory backgrounds generically appear to be only large-distance approximations to higher-dimensional string solutions.…”

“…For example, a higher-dimensional string 'oscillating' in a compact internal direction reduces to a family of black holes with the same asymptotic charges but different non-vanishing massive Kaluza-Klein fields which are invisible at scales larger than the compactification scale. 3 In order to make this qualitative picture quantitative, i.e. to compute the black hole entropy directly from string theory, one has to address the question of string loop and α ′ corrections.…”

String theory: exact solutions, marginal deformations and hyperbolic spaces

“…This amounts, at first order in α ′ , to the following equations of motion for the metric g, the Kalb-Ramond field B and the dilaton Φ [CMPF85,Tse95]:…”

Cosmological theories from

“…Recently constructing exact string solutions on gravitational backgrounds [1] has interested many string theorists, the main motivation of which has been that these backgrounds can shed light on different areas of gravitation such as the nature of singularities and black hole physics. Most of the found solutions are constructed as the product of two theories.…”