Strong-Weak Coupling Duality in Scalar Lattice QFT with Application to Strong Coupling Decompositions

Abstract: Dualities between quantum field theories have proven to be a powerful tool in various areas of physics. In this paper, we introduce a new perspective for obtaining strong coupling expansions based on a well-known technique -- the Field-space Fourier transform. We discuss the advantages of this approach for a class of Euclidean quantum field theories on a general lattice, with a focus on a self-interacting $\phi^4$ scalar field theory defined on a cubic lattice of arbitrary dimension. We establish a duality between the strong coupling regime of this theory and the weak coupling regime of a corresponding dual theory. Without loss of generality, we choose the original theory to be local and show that its dual action becomes nonlocal. Using standard diagrammatic techniques, we derive expansions for the two-point correlator and the free energy per site in the regime of large and intermediate coupling constants $g$. The obtained expansions remain regular in the limit $g \to 0$ and exhibit rapid numerical convergence in the considered regions. Numerical analysis in dimensions $d = 2$ and $d = 3$ demonstrates good agreement between our analytical results and Monte Carlo simulations. Furthermore, we show that the strong coupling expansions are consistent with traditional weak coupling expansions.