Gluing I: Integrals and Symmetries

Abstract

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.

arXiv comment47 pages, 3 figures; v2: references added

References in corpus (8)

• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Perturbative quantum gauge theories on manifolds with boundary
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Holomorphic blocks and the 5d AGT correspondence
• N=2 gauge theories on the hemisphere $H{S}^4$
• Boundary F-maximization
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• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing
• Computation of Kontsevich Weights of Connection and Curvature Graphs for Symplectic Poisson Structures