Compact Orbifolds Research Articles

The spacetime life of a non-BPS D-particle

We investigate the classical geometry generated by a stable non-BPS D-particle. We consider the boundary state of a stable non-BPS D-particle in the covariant formalism in the type IIB theory orbifolded by (-1)^{F_L} I_4. We calculate the scattering amplitude between two D-particles in the non-compact and compact orbifold and analyse the short and long distance behaviour. At short distances we find no force at order $v^2$ for any radius, and at the critical radius we find a BPS-like behaviour up to $v^4$ corrections for long and short distances. Projecting the boundary state on the massless states of the orbifold closed string spectrum we obtain the large distance behaviour of the classical solution describing this non-BPS D-particle in the non-compact and compact cases. By using the non-BPS D-particle as a probe of the background geometry of another non-BPS D-particle, we recover the no-force condition at the critical radius and the $v^2$ behaviour of the probe. Moreover, assuming that the no-force persists for the complete geometry we derive part of the classical solution for the non-BPS D-particle.

Eigenvalues and suspension structure of compact Riemannian orbifolds with positive Ricci curvature

Let M be a compact n-dimensional Riemannian orbifold of Ricci curvature ≥n−1. We prove that for 1 ≤k≤n, the kth nonzero eigenvalue of the Laplacian on M is equal to the dimension n if and only if M is isometric to the k-times spherical suspension over the quotient Sn−k}Γ of the unit (n−k)-sphere by a finite group Γ⊂O(n−k+1) acting isometrically on Sn−k⊂ℝn−k+.

Zero branes on a compact orbifold

The non-commutative algebra which defines the theory of zero-branes on $T^4/Z_2$ allows a unified description of moduli spaces associated with zero-branes, two-branes and four-branes on the orbifold space. Bundles on a dual space $\hat T^4/Z_2$ play an important role in this description. We discuss these moduli spaces in the context of dualities of K3 compactifications, and in terms of properties of instantons on $T^4$. Zero-branes on the degenerate limits of the compact orbifold lead to fixed points with six-dimensional scale but not conformal invariance. We identify some of these in terms of the ADS dual of the $(0,2)$ theory at large $N$, giving evidence for an interesting picture of "where the branes live" in ADS.