Abstract
Supersymmetric Yang--Mills theory is formulated in six dimensions, without the use of anticommuting variables. This is achieved using a new Nicolai map, to third order in the coupling constant. This is the second such map in six dimensions and highlights a potential ambiguity in the formalism.
Highlights
AND NOTATIONSupersymmetric theories may be formulated without the use of anticommuting variables [1,2]
Supersymmetric gauge theories are characterized by a Nicolai map—a transformation of the bosonic fields such that the Jacobian determinant of the transformation exactly cancels against the product of the Matthews-Salam-Seiler (MSS) [3,4] and Faddeev-Popov (FP) determinants [5,6]
This formalism offers an alternate perspective on the physics of supersymmetric gauge theories
Summary
Supersymmetric theories may be formulated without the use of anticommuting variables [1,2] In this approach, supersymmetric gauge theories are characterized by a Nicolai map—a transformation of the bosonic fields such that the Jacobian determinant of the transformation exactly cancels against the product of the Matthews-Salam-Seiler (MSS) [3,4] and Faddeev-Popov (FP) determinants [5,6]. For N 1⁄4 1 Yang Mills theories, alternate Nicolai maps are known to exist in four and six dimensions [15,16] These maps in light cone gauge, not constructed from a R prescription, work to all orders in perturbation theory. In a gauge-field dependent background γμðDμSÞabðxÞ ≡ γμ1⁄2δac∂μ − gfacdAdμðxÞScbðxÞ 1⁄4 δabδðxÞ: ð7Þ
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