Abstract
We compute the one-instanton effective action of $$ \mathcal{N}=4 $$ super Yang-Mills theory with gauge group Sp(2N). The result can be written in a very compact and manifestly supersymmetric form involving an integral over the superspace of an irrational function of the $$ \mathcal{N}=4 $$ on-shell superfields. In the Coulomb branch, the instanton corrects both the MHV and next-to-next-MHV higher derivative terms D 4 F 2n+2 and F 2n+4. We confirm at the non-perturbative level the non-renormalization theorems for MHV F 2n+2 terms that are expected to receive perturbative corrections only at n-loops. We compute also the one and two-loop corrections to the D 4 F 4 term and show that its completion under $$ \mathrm{S}\mathrm{L}\left(2,\mathrm{\mathbb{Z}}\right) $$ duality is consistent with the one-instanton results of U(2) gauge group.
Highlights
Nothing was known before Maldacena’s conjecture [4]
As shown in [9], instanton corrections to correlation functions of chiral primary operators (CPO’s) in N = 4 SYM vanish in the pairwise light-like limit, which hints to the absence of such corrections to light-like Wilson loops if the so-called correlation/Wilson loop duality [10,11,12,13,14] still holds at the non-perturbative level
This observation motivated the recent proposal by Schwarz [16] socalled “Highly Effective Action” (HEA) of N = 4 SYM with gauge group U(2)
Summary
The N = 4 SYM in 4D can be realised in String Theory as the low energy theory describing the dynamics of open strings ending on a stack of D3-branes. For N D3-branes and oriented open strings one finds the gauge group U(N ). The lowest modes of open strings with at least one end on the D(−1)-branes exactly produce the moduli (positions, size, orientations) specifying the instanton solution and the D(−1)-D3 action describes the Yang-Mill action in the instanton background. One has an explicit prametrization of the instanton super-moduli space. By computing string amplitudes on disks with mixed boundary conditions (both D3 and D(−1)), one can derive the exact couplings of the super-moduli to the physical on-shell fields. Including unoriented projections that combine world-sheet parity Ω with space-time involutions one can analyse orthogonal and symplectic groups.
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