N=4 super Yang-Mills correlators without anti-commuting variables

Abstract

Quantum correlators of pure supersymmetric Yang-Mills theories in D=3,4,6 and 10 dimensions can be reformulated via the non-linear and non-local transformation (`Nicolai map') that maps the full functional measure of the interacting theory to that of a free bosonic theory. As a special application we show that for the maximally extended N=4 theory in four dimensions, and up to order O(g^2), all known results for scalar correlators can be recovered in this way without any use of anti-commuting variables, in terms of a purely bosonic and ghost free functional measure for the gauge fields. This includes in particular the dilatation operator yielding the anomalous dimensions of composite operators. The formalism is thus competitive with more standard perturbative techniques.

18 pages, 7 figures. v2: typos corrected

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Cited by in corpus (13)

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• Construction method for the Nicolai map in supersymmetric Yang-Mills theories
• Universal form of the Nicolai map
• A perturbative expansion scheme for supermembrane and matrix theory
• Perturbative linearization of supersymmetric Yang-Mills theory
• Supersymmetric Yang-Mills theory in D=6 without anti-commuting variables
• Two Loop Ghost free Quantisation of Wilson Loops in $\mathcal{N}=4$ supersymmetric Yang-Mills
• An improved Nicolai map for super Yang-Mills theory
• Is the Nicolai map unique?
• Nicolai maps for super Yang-Mills on the light cone
• Supersymmetric large-order perturbation with the Nicolai map
• The coupling flow of $\mathcal{N}=4$ super Yang-Mills theory
• Nicolai maps and uniqueness in the light-cone gauge