  We characterize the multifractal behavior of Brownian motion in the vicinity
of an absorbing star polymer. We map the problem to an O(M)-symmetric
phi^4-field theory relating higher moments of the Laplacian field of Brownian
motion to corresponding composite operators. The resulting spectra of scaling
dimensions of these operators display the convexity properties which are
necessarily found for multifractal scaling but unusual for power of field
operators in field theory. Using a field-theoretic renormalization group
approach we obtain the multifractal spectrum for absorbtion at the core of a
polymer star as an asymptotic series. We evaluate these series using
resummation techniques.
