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- Title
SUPERSYMMETRY AND DIMENSIONALITY IN THE SUPERSTRING THEORY.
- Authors
POLLOCK, M. D.
- Abstract
The realization of non-linear global supersymmetry in the superstring theory requires the quadratic fermionic Lagrangian ${\mathcal T}^2_D \equiv T^2-T_{mn}T^{mn}$, defined from the D-dimensional, Minkowski-space energy–momentum tensor Tmn, to have the same form as the quadratic gravitational contribution ${\mathcal R}^2_D$ to the superstring Lagrangian. Here, we prove that this condition is only satisfied for the heterotic string theory after reduction to D = 4, irrespective of whether the original source of ${\mathcal R}^2_D$ in ten or twenty-six dimensions is the quadratic term $\hat{\mathcal R}^2$ or the quartic term $\hat{\mathcal R}^4$. If ${\mathcal R}^2_D$ derives from $\hat{\mathcal R}^4$, the solution is D = 4 (or the unphysical value D = 1), while if we suppose that D≠4 and $\hat{\mathcal R}^2_{\rm E}$ dominates, we obtain the (singular) solution (D-2)3 = 0. The world sheet is also discussed. The bosonic string and type-II superstring, on the other hand, yield solutions for D which are complex, non-integral, or at the singular point D = 2, where the Einstein equations hold identically.
- Subjects
STRING models (Physics); NUCLEAR reactions; THEORY of everything (Physics); PARTICLES (Nuclear physics); SYMMETRY (Physics)
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2009, Vol 24, Issue 23, p4373
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X09045832