Rational conformal field theory with matrix level and strings on a torus

Study of the matrix-level affine algebra $U_{m,K}$ is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of $U_{m,K}$ modular-invariant partition functions. Here we connect the algebra $U_{2,K}$ to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra $U_{m,K}$. This connection makes obvious that the rational theories are dense in the moduli space of strings on $T^m$, and may prove useful in other ways.Comment: 13 page

Fluoride Release from Two High-Viscosity Glass Ionomers after Exposure to Fluoride Slurry and Varnish

The effect of brushing with different fluoride slurries on the fluoride release (FR) of different high-viscosity glass ionomer cements (GICs) was investigated. Fifty-eight discs were fabricated from two high-viscosity GICs (GC Fuji IX (F9) and 3M ESPE Ketac-fil (KF)). Five specimens from each brand were used to measure Vickers microhardness and the remaining were randomly assigned to one of four groups (n = 6) based on two-factor combinations: (1) fluoride concentration in the abrasive slurry (275 or 1250 ppm fluoride as NaF) and (2) immersion in a 22,500 ppm fluoride-containing solution. Specimens were brushed for a total of 20,000 strokes over 4 days with daily FR measurement. Data were analyzed using analysis of variance and Bonferroni tests (α = 0.05). Baseline FR and microhardness values were different between the two tested material brands. Exposure to a 22,500 ppm solution was associated with higher FR but not the exposure to 1250 ppm slurries. Brushing and immersion of glass ionomer cements in a 22,500 ppm F solution led to higher FR that was more sustained for KF. Type of the glass ionomer, progressive brushing, and fluoride varnish affected FR but not the fluoride content in the abrasive slurry