Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the minimum of k-coincident fuzzy spheres.Comment: 35 pages, LaTeX2e, final version accepted in Nucl. Phys.

Does Yang-Mills theory describe quantum gravity?

The strongest version of the gauge/gravity duality conjecture relates the 1/N correction in super Yang-Mills theory and the quantum correction in superstring theory. We perform a quantitative test of this conjecture at finite temperature, by studying the D0-brane matrix quantum mechanics and the black zero-brane in type IIA superstring theory. We find good agreement, which strongly suggests that the super Yang-Mills theory does provide us with a nonperturbative formulation of quantum gravity through the gauge/gravity duality.Comment: Numerical data suggests the answer is yes. Talk at Workshop on Noncommutative Field Theory and Gravity, 13th Hellenic School and Workshops on Elementary Particle Physics and Gravity, at the Corfu Summer Institute, Greece, on Sept 10, 2013. A short and easy introduction for hep-lat/hep-ph people and student

Monte Carlo approach to the string/M-theory

It has long been conjectured that certain supersymmetric Yang-Mills (SYM) theories provide us with nonperturbative formulations of the string/M-theory. Although the supersymmetry (SUSY) on lattice is notoriously difficult in general, for a class of theories important for the string/M-theory various lattice and non-lattice methods, which enable us to study them on computers, have been proposed by now. In this talk, firstly I explain how SYM and string/M-theory are related. Then I explain why the lattice SUSY is difficult in general, and how the difficulties are solved in theories related to string/M-theory. Then I review the status of the simulations. It is explained that some stringy effects are correctly incorporated in SYM. Furthermore, concrete values can be obtained from the SYM side, even when a direct calculation on the string theory side is impossible by the state-of-the-art techniques. We also comment on other recent developments, including the membrane mini-revolution in 2008 and simulation of the matrix model formulation of the string theory.Comment: 17 pages, 7 figures. Plenary talk presented at the 30th International Symposium on Lattice Field Theory - Lattice 2012, June 24-29, 2012 Cairns, Australi