Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
Abstract
Under reasonable assumptions about the complex structure of the set of singularities on the Coulomb branch of N=2 superconformal field theories, we present a relatively simple and elementary argument showing that the scaling dimension, , of a Coulomb branch operator of a rank r theory is allowed to take values in a finite set of rational numbers∈ [nm|n,m∈ N, 0<m n, gcd(n,m)=1,\ (n)2r] where (n) is the Euler totient function. The maximal dimension grows superlinearly with rank as max r r. This agrees with the recent result of Caorsi and Cecotti.
0