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We review some aspects of the cutting and gluing law in local quantum field theory. In particular, we emphasize the description of gluing by a path integral over a space of polarized boundary conditions, which are given by leaves of some Lagrangian foliation in the phase space. We think of this path integral as a non-local $(d-1)$-dimensional gluing theory associated to the parent local $d$-dimensional theory. We describe various properties of this procedure and spell out conditions under which symmetries of the parent theory lead to symmetries of the gluing theory. The purpose of this paper is to set up a playground for the companion paper where these techniques are applied to obtain new results in supersymmetric theories.
We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $text{QFT}_d$ quantized on a $(d-1)$-manifold
In this paper we consider a conformal invariant chain of $L$ sites in the unitary irreducible representations of the group $SO(1,5)$. The $k$-th site of the chain is defined by a scaling dimension $Delta_k$ and spin numbers $frac{ell_k}{2}$, $frac{do
We solve, for finite $N$, the matrix model of supersymmetric $U(N)$ Chern-Simons theory coupled to $N_{f}$ massive hypermultiplets of $R$-charge $frac{1}{2}$, together with a Fayet-Iliopoulos term. We compute the partition function by identifying it
We investigate certain $Z_3$-graded associative algebras with cubic $Z_3$-invariant constitutive relations. The invariant forms on finite algebras of this type are given in the low dimensional cases with two or three generators. We show how the Lor
We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomegeneous conformal Hopf algebras $mathcal{U}_{theta }(su(2,2)ltimes T^{4}$) and $mathcal{U}_{bar{theta}}(su(2,2)