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.

This is a review of exceptional field theory: a generalisation of Kaluza–Klein theory that unifies the metric and $p$-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates may be viewed as conjugate to brane winding modes. This unifies the maximal supergravities, treating their previously hidden exceptional Lie symmetries as a fundamental geometric symmetry. Duality orbits of solutions simplify into single objects, that in many cases have simple geometric interpretations, for instance as wave or monopole-type solutions. It also provides a route to explore exotic or nongeometric aspects of M-theory, such as exotic branes, $U$-folds, and more novel sorts of non-Riemannian spaces.

Our goal in this paper is to give a brief survey of recent developments in the study of M-theory on singular Calabi–Yau three-folds, topological strings in the presence of a flat but topologically nontrivial B-field and their relationship to hybrid phases of certain Gauged Linear Sigma Models (GLSM).

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.

This lecture consists of three parts. In part I, an overview is given on the so-called Matrix theory in the light-front gauge as a proposal for a concrete and non-perturbative formulation of M-theory. I emphasize motivations towards its covariant formulation. Then, in part II, I turn the subject to the so-called Nambu bracket and Nambu mechanics, which were proposed by Nambu in 1973 as a possible extension of the ordinary Hamiltonian mechanics. After reviewing briefly Nambu’s original work, it will be explained why his idea may be useful in exploring higher symmetries which would be required for covariant formulations of Matrix theory. Then, using this opportunity, some comments on the nature of Nambu mechanics and its quantization are given incidentally: though they are not particularly relevant for our specialized purpose of constructing covariant Matrix theory, they may be of some interests for further developments in view of possible other applications of Nambu mechanics. The details will be relegated to forthcoming publications. In part III, I give an expository account of the basic ideas and main results from my recent attempt to construct a covariantized Matrix theory on the basis of a simple matrix version of Nambu bracket equipped with some auxiliary variables, which characterize the scale of M-theory and simultaneously play a crucial role in realizing (dynamical) supersymmetry in a covariant fashion.

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).