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String Tension and the Generation of the Conformal Anomaly
| Content Provider | Semantic Scholar |
|---|---|
| Author | Nicolaidis, A. Paschalis, J. E. Porfyriadis, P. I. |
| Copyright Year | 1997 |
| Abstract | The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension T0 as a small perturbation. The expansion parameter is the worldsheet speed of light c , which is proportional to T0 . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders c and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to c. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly. nicolaid@ccf.auth.gr paschali@ccf.auth.gr porfyriadis@physics.auth.gr The most striking feature of quantum string models is their prediction of a critical spacetime dimension outside of which the quantum theory is problematical. Clearly it is quite important to understand how conformal invariance is broken by quantum effects. The whole issue becomes even more interesting by noticing the similarities between the canonical formulations of the string model and of general relativity. In both cases the Hamiltonian is weakly vanishing and the existing constraints reflect the underlying reparametrization invariance ( in two or four dimensions ) [1]. It appears that we should address the problem within a framework which allows us to consider the string tension as a small perturbation. Such a formalism, the c expansion, has been proposed by De Vega and Nicolaidis in ref.[2]. The limit T0 → 0 corresponds to the high energy limit of the string theory and it is also the appropriate limit for a string in strong gravitational field. The zeroth term in the c expansion provides the null string. The null string is a tensionless string where each point of the string moves along a null geodesic [3]. The quantization of a null string in de Sitter spacetime was studied in ref.[4]. No anomaly was found and it was conjectured that the dimensionful string tension lies at the origin of the conformal anomaly. We examine carefully here the quantum generation of the conformal anomaly and trace its explicit dependence upon the string tension. Aspects of this problem were addressed also in [5]. The starting point is the reformulated string Lagrangian [2] L = 1 4λ [ẊẊGμν(X) − c X X Gμν(X)] (1) where c = 2λT0 is the world-sheet speed of light. The string equations of motion read Ẍ − cX ′′μ + Γμκλ(Ẋ Ẋ − cX X ) = 0 (2) supplemented by the constraints Φ = 1 2 (ẊẊGμν + c X X Gμν) = 0 (3) Ψ = cẊX Gμν = 0 (4) Now we proceed to a series expansion in powers of c [2]. Writing X(σ, τ) = A(σ, τ) + cB(σ, τ) + · · · (5) we obtain the equations of motion for the zeroth order term Ä + ΓμκνȦ Ȧ = 0 (6) |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9702185v2.pdf |
| Alternate Webpage(s) | http://cds.cern.ch/record/321339/files/9702185.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9702185v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Anomaly detection Dimensions Empty string Hamiltonian (quantum mechanics) Null Value Population Parameter Power (Psychology) Quantum Hall effect Quantum mechanics Semantics (computer science) Series expansion Sitter (BEAM) Software bug Tension orders - HL7PublishingDomain |
| Content Type | Text |
| Resource Type | Article |
