Coleman mandula theorem and its avatar no higher spin

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Unformatted text preview: atar: No higher-spin conserved charges The Coleman-Mandula theorem (Coleman and Mandula, 1967) and its generalization to the case of supersymmetric theories with or without massless particles given by Haag, Lopuszanski, and Sohnius (1975) strongly restrict the symmetries of the S matrix of an interacting relativistic field theory in four-dimensional Minkowski spacetime.11 More precisely, (i) if the elastic two-body scattering amplitudes are generically nonvanishing (at almost all energies and angles), and (ii) if there is only a finite number of particle 11 For an extended pedagogical review, see Weinberg (2000), Chapter 24. 992 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . species on and below any given mass shell, then the maximal ´ possible extension of the Poincare algebra is the (semi)direct sum of a superalgebra (a superconformal algebra in the massless case) and an internal symmetry algebra spanned by elements that commute with the generators of the ´ Poincare algebra. In particular, this theorem rules out higher symmetry generators (equivalently, conserved charges) that could have come from higher-spin symmetries surviving at large distances. The argument goes as follows: the gauge symmetries associated with massless particles may survive at spatial infinity as nontrivial rigid symmetries. In turn, such symmetries should lead to the conservation of some asymptotic charges. Under the hypotheses of the generalized ColemanMandula theorem, nontrivial conserved charges associated with asymptotic higher-spin symmetries cannot exist. This corollary of the generalized Coleman-Mandula theorem partially overlaps with the Weinberg low-energy theorem because the conservation law (1) precisely corresponds to the existence of a conserved charge Q1 ÁÁÁsÀ1 which is a symmetric tensor of rank s À 1 that commutes with the translations, but does not commute with the Lorentz generators. D. Generalized Weinberg-Witten theorem The Weinberg-Witten theorem (Weinberg and Witten, 1980) states that a massless particle of spin strictly greater than 1 cannot possess an energy-momentum tensor T which is both Lorentz covariant and gauge invariant.12 Of course, this no-go theorem does not preclude gravitational interactions. In the spin-two case, it implies that there cannot exist any gauge-invariant energy-momentum tensor for the graviton. This proves that the energy of the gravitational field cannot be localized, but it obviously does not prevent the graviton from interacting with matter or with itself. Recently, a refinement of the Weinberg-Witten theorem was presented (Porrati, 2008) that genuinely prevents massless particles of spin strictly greater than 2 from coupling minimally to the graviton in flat background. The minimality condition is stated according to the Weinberg equivalence principle, namely, it refers to Lorentz minimal spin-two coupling (see Sec. II.B.2). In the Lagrangian appr...
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This document was uploaded on 09/28/2013.

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