Narrow Results

Equations of motion for M2- and M5-branes are written down in the $E_{11}$ current algebra formulation of M-theory. These branes correspond to currents of the second and the fifth rank antisymmetric tensors in the $E_{11}$ representation, whereas the electric and magnetic fields (coupled to M2- and M5-branes) correspond to currents of the third and the sixth rank antisymmetric tensors, respectively. We show that these equations of motion have solutions in terms of the coordinates on M2- and M5-branes. We also discuss the geometric equations, and show that there are static solutions when M2- or M5-brane exists alone and also when M5-brane wraps around M2-brane. This situation is realized because our Einstein-like equation contains an extra term which can be interpreted as gravitational energy contributing to the curvature, thus avoiding the usual intersection rule.

We discuss the gravity duals of SO/USp superconformal quiver gauge theories on M5-branes which are localized on top of ℝ⁵/ℤ₂ and wrapping on a Riemann surface of genus g. We concentrate on Riemann surfaces with no punctures and show that the gravity solutions are classified by the genus g of the Riemann surface and the torsion part of the four-form flux.

We find that, apart from the instanton contributions, the all genus partition function of the ABJM matrix model sums up to the Airy function. We present the result, discuss its implication and also summarize some further progress.

We show that the ABJM theory, which is an superconformal U(N) × U(N) Chern-Simons matter theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model derived by using the localization method. Here we calculate the free energy, and show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion.

We discuss thermodynamical stability of the type IIB background of and its local M-theory uplift, evaluation of electrical conductivity, charge susceptibility, diffusion constant, the Einstein relation relating the three, obtaining the QCD deconfinement temperature compatible with lattice data and speed of sound, in the ‘MQGP’ limit of involving g_s ≲ 1, which we expect will shed light on strongly coupled thermal systems (such as the sQGP).