Tomoki Nosaka

Exact instanton expansion of superconformal Chern-Simons theories from topological strings

A bstractIt was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model. The expression consists of a universal function constructed from the free energy of the refined topological string theory with an overall topological invariant characterizing the CalabiYau manifold. In this paper we explore two other superconformal Chern-Simons theories of the circular quiver type. We find that the partition function of one theory enjoys the same expression from the refined topological string theory as the ABJM matrix model with different topological invariants while that of the other is more general. We also observe an unexpected relation between these two theories.

Supersymmetric gauge theories on a squashed four-sphere

A bstractWe define a squashed four-sphere by a dimensional reduction of a twisted S4 × S1, and construct explicitly a supersymmetric Yang-Mills action on it. The action includes a non-trivial dilaton factor and a theta term with a non-constant theta. The partition function of this theory is calculated using the localization technique. The resulting partition function can be written in the form consistent with the AGT relation due to the non-constant theta term. The parameter b which characterizes the partition function in this form is not restricted to be real for the squashed four-sphere.

ABJM membrane instanton from a pole cancellation mechanism

The coefficients of the membrane instantons in the ABJM theory are known to be quadratic polynomials of the chemical potential. For better insight into this nonconstantness, we consider more general superconformal Chern\char21{}Simons theories labelled by two parameters

Superconformal Chern-Simons partition functions of affine D-type quiver from Fermi gas

(q,p)

Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons

. In these theories, we show that the membrane instantons split into three types of nonperturbative effects, one more type compared with the previous observation. We also determine their explicit coefficients which are independent of the chemical potential. We find that, although these constants contain poles at certain values of

Large N behavior of mass deformed ABJM theory

q

Instanton effects in ABJM theory with general R-charge assignments

and

Mass deformed ABJM theory on three sphere in large N limit

p

Complete factorization in minimal \( \mathcal{N}=4 \) Chern-Simons-matter theory

including the ABJM case, all of the poles cancel among themselves, and the finite quadratic polynomial coefficients are reproduced at these values. This is similar to what happens between the membrane instantons and the worldsheet instantons in the ABJM theory.

Instanton effects in rank deformed superconformal Chern-Simons theories from topological strings

A bstractWe consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact expression of the overall constant, which corresponds to the constant map in the topological string theory.