Hiroyuki Fuji

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,

The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings

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

A New N = 4 Membrane Action via Orbifold

, with the renormalized ’t Hooft coupling λren.

3d analogs of Argyres-Douglas theories and knot homologies

We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S1 with the monodromy L2R up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.

The Volume Conjecture and Topological Strings

M-theory remains to be a mysterious subject even after more than ten years of intensive research. Perhaps one of the clues of this difficult topic is to ask the question: what is the theory on multiple branes (M2-branes and M5-branes) in M-theory? Recently, Bagger, Lambert and Gustavsson (BLG) [1] proposed a Lagrangian description of the worldvolume theory on multiple M2-branes. The theory is three dimensional, has manifest N = 8 R-symmetry and is believed to be superconformal, and thus satisfies some of the important conditions imposed on the worldvolume theory of M2-branes. However, it should be stressed that we still do not have a proof that BLG theory is the theory on M2-branes. In my recent work in collaboration with Hiroyuki Fuji and Seiji Terashima [2], we thus studied a Z2-orbifold of BLG theory, obtaining a Lagrangian with N = 4 supersymmetry which should be realized again on M2-branes. This work serves as a non-trivial consistency check of the BLG theory as a candidate for theories on multiple M2-branes. First of all, even the fact that we can take orbifold of BLG theory is far from trivial since BLG theory have different matter contents as compared with worldvolume theories of D2-branes. Second, we have found that the classical vacuum moduli space of BLG theory exactly coincides with that of the strong coupling limit of worldvolume theory on a D2-branes. In fact, we found three branches in our vacuum moduli space, and the result is consistent in all three branches. Our analysis needs O(4) (rather than SO(4)) gauge theory on D2-brane side, which suggest a small correction to the works of [3]. As a byproduct of our analysis, we also proposed a new non-perturbative duality (O-duality) interchanging O2 − -branes with orbifold R 4 /Z2 and O2 − -branes with D6-branes.

Open string amplitudes in various gauges

A bstractWe study singularities of algebraic curves associated with 3d

A note on computations of the D-brane superpotential

\mathcal{N}=2

Gravitational corrections for supersymmetric gauge theories with flavors via matrix models

theories that have at least one global flavor symmetry. Of particular interest is a class of theories TK labeled by knots, whose partition functions package Poincaré polynomials of the Sr -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d

Causal dynamical triangulation with extended interactions in 1+1 dimensions

\mathcal{N}=2

QUANTUM FLUCTUATIONS OF ROTATING STRINGS IN AdS5 × S5

theories TK and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in Sr-colored HOMFLY homologies.