Chiral multi-loops

Honerkamp, Josef

doi:10.1016/0550-3213(72)90299-4

Cited by 289 publications

(201 citation statements)

References 6 publications

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“…The recognition of the role of σ-models in string theory was prompted by the covariant path integral representation for the string-theory scattering amplitudes [2] and by studies of σ-models as geometrical 2-dimensional quantum field theories [3,4]. It was observed [5] that the generating functional for the string scattering amplitudes can be interpreted as a partition function Z of a σ-model with couplings being the string space-time fields.…”

Section: Sigma Model Approachmentioning

confidence: 99%

“…3 In addition, there are special exact solutions of superstring theory only (corresponding to σ-models with extended (4, n) world-sheet and partial space-time supersymmetry). Even having in mind superstring applications, it is still important to understand mechanisms leading to exactness of particular solutions which may not be directly based on extended supersymmetry (some physically interesting solutions may have broken space-time supersymmetry).…”

Section: Classes Of Exact Solutionsmentioning

confidence: 99%

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Exact solutions of closed string theory

Tseytlin

1995

Class. Quantum Grav.

109

222

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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).

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Section: Sigma Model Approachmentioning

confidence: 99%

Section: Classes Of Exact Solutionsmentioning

confidence: 99%

Exact solutions of closed string theory

Tseytlin

1995

Class. Quantum Grav.

109

222

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“…The covariant calculation includes the expansion in Riemann normal coordinates [105,147,114]), and the coefficients of the expansion for b µν depend only on H µνλ and its derivatives, but not directly on the b µν components. After all, the geometry of the D-dimensional space is characterized by three kinds of fields: metric g µν , dilaton Φ and completely antisymmetric field H µνλ , which satisfies the constraint ε µναβ ∂ α H ναβ = 0 coming from (6.2).…”

Section: What Is the Difference With Metric?mentioning

confidence: 99%

Physical aspects of the space–time torsion

2002

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Abstract. We review many quantum aspects of torsion theory and discuss the possibility of the space-time torsion to exist and to be detected. The paper starts, in Chapter 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Chapter 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Chapter 4 is devoted to the action of spinning and spinless particles in a space-time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Chapter 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion-torsion interaction implies that torsion itself has a huge mass, and can not be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Chapter 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.

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“…Being tangent vectors, ξ α transform linearly under the BFM symmetry. In a more geometrical language, the implementation of the BFM is equivalent to the transition to the set of normal coordinates [37,38] in a neighborhood U of the point P .…”

Section: Introductionmentioning

confidence: 99%

The background field method and the linearization problem for Poisson manifolds

Grassi

Quadri

2005

Nuclear Physics B

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The background field method (BFM) for the Poisson Sigma Model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg-Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.

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Chiral multi-loops

Cited by 289 publications

References 6 publications

Exact solutions of closed string theory

Exact solutions of closed string theory

Physical aspects of the space–time torsion

The background field method and the linearization problem for Poisson manifolds

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