Sanefumi Moriyama

Non-perturbative effects and the refined topological string

A bstractThe partition function of ABJM theory on the three-sphere has nonperturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local ℙ1 × ℙ1, in the NekrasovShatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

Instanton effects in ABJM theory from Fermi gas approach

A bstractWe study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k = 1, 2, 3, 4, 6 up to N = 44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.

Summing up all genus free energy of ABJM matrix model

The localization technique allows us to compute the free energy of the U(N)k × U(N)−k Chern-Simons-matter theory dual to type IIA strings on AdS4 × CP3 from weak to strong ’t Hooft coupling λ = N/k at finite N, as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large ’t Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up allthe1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form — the Airy function,

Exact results on the ABJM Fermi gas

{\text{Ai}}\left( {{{\left( {{{{\pi {k^2}}} \left/ {{\sqrt {2} }} \right.}} \right)}^{{{2} \left/ {3} \right.}}}{\lambda_{\text{ren}}}} \right)

Observables as Twist Anomaly in Vacuum String Field Theory

, with the renormalized ’t Hooft coupling λren.

ABJ fractional brane from ABJM Wilson loop

A bstractWe study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z(N) up to N = 9 with the Chern-Simons level k = 1. We find that the eigenvalue problem of this quantum mechanical system is reduced to the diagonalization of a certain Hankel matrix. In reducing the number of integrations by commuting coordinates and momenta, we find an exact relation concerning the grand partition function, which is interesting on its own right and very helpful for determining the partition function. We also study the TBA-type integral equations that allow us to compute the grand partition function numerically. Surprisingly, all of our exact partition functions are written in terms of polynomials of π−1 with rational coefficients.

ABJM Wilson Loops in Arbitrary Representations

We reveal a novel mathematical structure in physical observables, the mass of tachyon fluctuation mode and the energy density, associated with a classical solution of vacuum string field theory constructed previously [hep-th/0108150]. We find that they are expressed in terms of quantities which apparently vanish identically due to twist even-odd degeneracy of eigenvalues of a Neumann coefficient matrix defining the three-string interactions. However, they can give non-vanishing values because of the breakdown of the degeneracy at the edge of the eigenvalue distribution. We also present a general prescription of correctly simplifying the expressions of these observables. Numerical calculation of the energy density following our prescription indicates that the present classical solution represents the configuration of two D25-branes.

Cubic interactions in pp-wave light-cone string field theory

A bstractWe present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

Brane Configuration from Monopole Solution in Non-Commutative Super Yang-Mills Theory

A bstractWe study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

Exact Results on Twist Anomaly

We use the supergravity modes to clarify the role of the prefactor in the light-cone superstring field theory on a pp-wave background. We verify some of the proposals of Constable and give further evidence for the correspondence between N=4 Super Yang-Mills gauge theory and string theory on a pp-wave. We also consider energy-preserving processes and find that they give a vanishing cubic interaction Hamiltonian matrix.