13 The equations of the saddle point are the following Assume that a smooth locus for the support of ˆ ρ is allowed. In that case, we can differ- entiate the equation 11 six times, with the Laplacian in 6 dimensions to the cubed power. We find then that as the first two terms obviously are cancelled. Notice that so that away from z 1 = 0 we have that because the function is harmonic: a sum of a holomorphic plus an antiholomorphic piece. Also, is is easy to show that ( ∇ $^{2}$)$^{2}$log( ⃗ a − ⃗ b ) ∝ δ $^{6}$( ⃗ a − ⃗ b ). With these, we would find that ˆ ρ = 0. This argument contradicts that ∫ ˆ ρ = 1, so the assumption that ˆ ρ is smooth does not work. This argument has been given before in [5, 23], and we are presenting it here for completeness. What this indicates is that the density distribution of particles is singular. Since for q = 0 the original probability distribution is spherically symmetric, it is natural to assume that the associated distribution is spherically symmetric. The radius was computed in [18]. This has also been checked numerically in [6, 7]. A generalization to all Calabi-Yau cone conformal field theory singularities for this result can be found in [23], where it was seen that this procedure matches various other supergravity calculations in the absence of symmetry. For q > 0 but very small, we expect that the distribution does not change much, except in the region z 1 ≃ 0. Thus we expect that the distribution gives a five dimensional manifold of R $^{6}$, possibly with a boundary, and that the region near z 1 = 0 has no density of eigenvalues present. After all, the effective potential repels all particles from the locus z 1 = 0. This where C is a Lagrange multiplier enforcing the constraint (9). These equations are valid on the support of ρ . We can prove that these equations lead to a singular support for ρ . We do this by contradiction. C − ⃗ a 2 + q log( a 2 1 + a 2 $_{2}$) + ∫ d $^{6}$b ˆ ρ ( b ) log | ⃗ a − ⃗ b | 2 = 0 (11) ( ∇ $^{2}$)$^{3}$q log( a 2 1 + a 2 $_{2}$) + ∫ db $^{6}$ˆ ρ ( b ) ∇ $^{2}$log | ⃗ a − ⃗ b | 2 = 0 (12) log( a 1 + a 2 $_{2}$) ≃ log( z $^{1}$) + log(¯ z $^{1}$) (13) ∇ $^{2}$log( a 1 + a 2 $_{2}$) = ∇ 2 ( log( z $^{1}$) + log(¯ z $^{1}$) ) = 0 (14)