He is a professor at the Independent University of Moscow and is researcher at the Landau Institute for Theoretical Physics. He is also a member of the editorial board of the Moscow Mathematical Journal.
Belavin forestood the discovery of the BPST instanton (1975) which aided the understanding of the chiral anomaly and gave new directions within quantum field theory. With G. Avdeeva he showed evidence of new coupling regimes for gauge field theory (1973). He also developed the Belavin S-matrices, exactly solvable models in two-dimensional relativistic theories in (1981). He co-authored the BPZ paper (1984) with Alexander Polyakov and Alexander Zamolodchikov on two-dimensional conformal field theory, which became important for string theory. With Vadim Knizhnik he made the Belavin-Knizhnik theorem on dual amplitudes in string theory (1986).