Multifractality of Brownian motion near absorbing polymers

characterize the multifractal behavior of Brownian motion in the vicinity o f 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 mo tion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties that are ne cessarily found for multifractal scaling but unusual for power of field ope rators in field theory. Using a field-theoretic renormalization group appro ach we obtain the multifractal spectrum for absorption at the core of a pol ymer star as an asymptotic series. We evaluate these series using resummati on techniques.