Submissions from Angel M. Garcia-Padilla

[1]  faKiv:2403.07616 [pdf]
M-Theory on the compact $S^3$ w=\frac{2\pi c }$ CFT
Comments: 12 pages, 2 figures

We study the formula for the WZW-theory on the compact $S^3$ $WZW$ w=\frac{2\pi c }$ CFT. In the case of the $S^5$ boundary condition, we find that the $S^3$ w=\frac{2\pi c }$ formula is equivalent to the $S^5$ formula in light of the spectral and gravitational energy of the two CFTs, but have no relation to the equivalence between $S^3$ and $S^5$ formulas, which is confirmed by the work of others. However we have a relation between the spectral and gravitational energy of the two CFTs based on an explicit Euler-Higgs formula.

[2]  faKiv:2403.08301 [pdf]
A family of $SU(N)$ superconformal global symmetries
Comments: 18 pages, 1 figure, v2 references updated

We study a family of $SU(N)$ superconformal global symmetry groups in the context of a $SU(N)$ superconformal field theory. These symmetries are the $SU(N)$ super-Yang-Mills monodromy groups and $SU(N)$ super-Riemann groups. Our work is focused on the three-loop Fourier transform of the standard $SU(N)$ K\"ahler-Petersson theory in $N=3$ superconformal field theories on a $SU(N)$-symmetric $N=2$ lattice. We show that the $SU(N)$ super-Riemann groups in $N=2$ superconformal field theories have a strong coupling to the $SU(N)$ super-Yang-Mills groups. We discuss the implications of the strong coupling on the structure of super-Riemann groups and the supersymmetry.