Abstract
We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to the general R-charge assignment to the matter fields. Though the deformation breaks the conformal symmetry, we find that the partition function shares various structures with the superconformal cases, such as the Airy function expression of the perturbative expansion in 1/N with the overall constant A(k) related to the constant map in the ABJM case through a simple rescaling of k. We also identify five kinds of the non-perturbative effects in 1/N which correspond to the membrane instantons. The instanton exponents and the singular structure of the coefficients depend on the continuous deformation parameters, in contrast to the superconformal case where all the parameters are integers associated with the orbifold action on the moduli space. This implies that the singularity of the instanton effects would be observable also in the gravity side.
Highlights
ABJM theory can be reduced to a matrix model with 2N integration variables [6]
We study the large N expansion of the partition function of the quiver superconformal Chern-Simons theories deformed by two continuous parameters which correspond to general R-charge assignment to the matter fields
Though the deformation breaks the conformal symmetry, we find that the partition function shares various structures with the superconformal cases, such as the Airy function expression of the perturbative expansion in 1/N with the overall constant A(k) related to the constant map in the ABJM case through a simple rescaling of k
Summary
We provide the Fermi gas formalism for general R-charge assignments (1.9). Compared with the superconformal case ζa = 0, the only difference is the shift in the arguments of the cosinehyperbolic factors which come from the 1-loop determinant of the bifundamental hypermultiplets This fact allows the straightforward application of the computational techniques in [9] to derive the Fermi gas formalism.. We show that the large μ expansion of the grand potential J(μ) takes the form of (1.3), with C, B and A given as (1.12), up to the non-perturbative corrections O(e−μ). Plugging these expressions into the inversion formula (1.1), we obtain the all order perturbative expansion of the partition function in 1/N , which sum up to an Airy function as (1.4). Substituting these results into δn (3.12), we obtain the expression of B in (1.12)
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