Causality and supersymmetry in the superstring theory

doi:10.1088/0264-9381/20/13/301

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Classical and Quantum Gravity

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Classical and Quantum Gravity Volume 20 Number 13 Create an alert RSS this journal

M D Pollock 2003 Class. Quantum Grav. 20 2467 doi:10.1088/0264-9381/20/13/301

Causality and supersymmetry in the superstring theory

M D Pollock

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Reduction of the ten-dimensional, heterotic-superstring effective action hat S , including quartic higher-derivative terms $\hat{\calR}^4$ , yields a physical four-action S which is tachyon-free up to quadratic order Script R ²—the masses M₀ and M₂ of the spin-0 and spin-2 particles are both real—when the internal six-space is a Calabi–Yau metric bar g _μν and N = 1 supersymmetry is preserved via the equation d bar H ≡ tr( bar R wedge bar R ) − Tr( bar F wedge bar F )/30 = 0, where bar H _μνξ is the totally antisymmetric three-index field (while the bosonic string and type-II superstring may contain a spin-2 tachyon and a spin-0 tachyon, respectively). Here, we show that this crucial feature is independent of imposing supersymmetry, for if d bar H ≠ 0, there is an additional contribution to Script R ² which, however, produces no tachyons. Thus, the requirement of a stable, causal theory singles out the heterotic superstring irrespective of the requirement of N = 1 supersymmetry, which is essential at high energies rather for its roles in the vanishing of the cosmological constant and the maintenance of the gauge hierarchy.