Coloumb gas boundary CFT and surface multifractality in higher dimensions

Multifractals appear in various natural phenomena and they are characterized by a continuous spectrum of multifractal exponents. Previously, using conformal invariance and the Abelian nature of the Operator Product Expansion (OPE), it was shown that the multifractal spectrum of critical wavefunctions at Anderson transitions (ATs) must be parabolic in d greater than or equal to 2. For the critical wavefunctions, the multifractal exponents measured at the surface are in general different from their bulk counterparts. In this work, we study the boundary conditions for the simplest conformal field theory that has an Abelian OPE, i.e. the higher-dimensional generalization of the Coulomb gas theory. We obtain closed form expressions for scaling dimensions and the boundary OPE coefficients of vertex operators, which characterize the theory in arbitrary even dimensions. Finally, we establish the connections to surface multifractality at ATs, wherein our results serve as probes of conformal symmetry.