Two-loop finiteness of Chern–Simons theory in background field method

We perform two-loop calculation of Chern–Simons in background field method using the hybrid regularization of higher-covariant derivative and dimensional regularization. It is explicitly shown that Chern–Simons field theory is finite at the two-loop level. This finiteness plays an important role in the relation of Chern–Simons theory with two-dimensional conformal field theory and the description of a link invariant.