Related papers: The coupling flow of ${\cal N}=4$ super Yang-Mills…
Recently, a universal formula for the Nicolai map in terms of a coupling flow functional differential operator was found. We present the full perturbative expansion of this operator in Yang-Mills theories where supersymmetry is realized…
The nonlocal bosonic theory obtained from integrating out all anticommuting and auxiliary variables in a globally supersymmetric theory is characterized by the Nicolai map. We present a universal formula for the latter in terms of an…
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…
The nonlocal bosonic theory obtained from integrating out all anticommuting and auxiliary variables in a globally supersymmetric theory is characterized by the Nicolai map. The latter is generated by a coupling flow functional differential…
Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the Matthews-Salam-Seiler and…
We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1)…
In rigidly supersymmetric quantum theories, the Nicolai map allows one to turn on a coupling constant (from zero to a finite value) by keeping the (free) functional integration measure but subjecting the fields to a particular nonlocal and…
We consider the $4d$ $\mathcal{N}=2$ superconformal quiver gauge theory obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two…
In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog.\ Theor.\ Exp.\ Phys.\ \textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) $\mathcal{N}=1$ super Yang--Mills theory (SYM) that works within…
We consider two four-dimensional gauge theories with gauge group $SU(N)$: the $\mathcal{N}=4$ Super Yang-Mills (SYM) theory and the $\mathcal{N}=2$ quiver gauge theory obtained as a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In this…
We construct Nicolai maps for supersymmetric Yang-Mills theory in four and ten spacetime dimensions in the light-cone gauge, where the elimination of non-propagating degrees of freedom causes nonlocal and four-fermi interactions in the…
We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in terms of…
In 1980 Hermann Nicolai proposed a characterization of supersymmetric theories that became known as the Nicolai map. This is a particular nonlocal and nonlinear field transformation, whose perturbative expansion is given by fermion-line…
In this thesis, we study the Nicolai maps of the 2-dimensional Wess-Zumino model, $\mathcal{N}=1$ super Yang-Mills and $\mathcal{N}=4$ super Yang-Mills. We compute the Nicolai map of the 2-dimensional Wess-Zumino model up to the fifth order…
The Nicolai map is a field transformation that relates supersymmetric theories at finite couplings $g$ with the free theory at $g=0$. It is obtained via an ordered exponential of the coupling flow operator integrated from $0$ to $g$.…
We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite…
We compute the Nicolai map for the supersymmetric Yang-Mills theory, in the light-cone gauge, to the second order in the coupling constant for all critical dimensions (d=3,4,6,10). The process of integrating out unphysical degrees of…
We study the four-dimensional $\mathcal{N}=4$ super-Yang-Mills (SYM) theory on the unorientable spacetime manifold $\mathbb{RP}^4$. Using supersymmetric localization, we find that for a large class of local and extended SYM observables…
Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant…
We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…