Two-loop N=4 super-Yang–Mills effective action and interaction between D3-branes Original Research Article

We compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of N=4 SYM theory in 4 dimensions, assuming that the gauge group SU(N+1) is broken to SU(N)×U(1) by a constant scalar background X. While the leading 1-loop correction is the familiar c1F4/|X|4 term, the 2-loop expression starts with c2F6/|X|8. The 1-loop constant c1 is known to be equal to the coefficient of the F4 term in the Born–Infeld action for a probe D3-brane separated by distance |X| from a large number N of coincident D3-branes. We show that the same is true also for the 2-loop constant c2: it matches the coefficient of the F6 term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the F6 term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the v6 term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the (1+0)-dimensional reduction of N=4 SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory—supergravity correspondence for higher order (F8, etc.) terms.