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.
Highlights
As a special application we show that for the maximally extended N 1⁄4 4 theory in four dimensions, and up to order Oðg2Þ, all known results for scalar correlators can be recovered in this way without any use of anticommuting variables, in terms of a purely bosonic and ghost-free functional measure for the gauge fields
Pure supersymmetric Yang-Mills theories exist in D 1⁄4 3, 4, 6 and 10 dimensions [1]
Only very recently that these constructions were extended to other dimensions, and in particular to the maximally extended D 1⁄4 10 and N 1⁄4 4; D 1⁄4 4 theories [8]
Summary
Pure supersymmetric Yang-Mills theories exist in D 1⁄4 3, 4, 6 and 10 dimensions [1]. In this paper we want to take a new and different look at this theory, exploiting the existence of a nonlocal and nonlinear transformation Tg (“Nicolai map”) that maps the full functional measure of the interacting Yang-Mills theory to the one of a theory of dim G-free (Maxwell) vector fields, where G is the gauge group in question [usually G 1⁄4 SUðNÞ]. The existence of the map Tg opens very different perspectives on the quantization of supersymmetric Yang-Mills theories, in terms of a ghost- and fermion-free formalism and with a purely bosonic functional measure This concerns especially the computation of quantum correlators. It would be interesting to find a link with the conformal bootstrap program (see e.g., [19] for a review), where again the N 1⁄4 4 theory appears to play a distinguished role [20] (see [21] and references therein for more recent work) and to elucidate the role of the conformal and dual-conformal symmetries in this context
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