On Perturbation theory improved by Strong coupling expansion

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function consistent with the both expansions, which includes the standard Pad\'e approximant and fractional power of polynomial method constructed by Sen as special cases. We point out that we can construct enormous number of such interpolating functions in principle while the "best" approximation for the exact answer of the physical quantity should be unique among the interpolating functions. We propose a criterion to determine the "best" interpolating function, which is applicable except some situations even if we do not know the exact answer. It turns out that our criterion works for various examples including specific heat in two-dimensional Ising model, average plaquette in four-dimensional SU(3) pure Yang-Mills theory on lattice and free energy in c=1 string theory at self-dual radius. We also mention possible applications of the interpolating functions to system with phase transition.Comment: 31+11 pages, 15 figures, 9 tables, 1 Mathematica file; v3: minor correction

Instanton Effects in Orbifold ABJM Theory

We study the partition function of the orbifold ABJM theory on $S^3$, which is the $\mathcal{N}=4$ necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.Comment: 23 pages, 2 eps figures; v2: minor improvement