The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

An improved single-plaquette gauge action

We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects.

Strain-gauge, brushless torque meter

A torque meter comprising hollow-keyed, input and output female shafts adapted to receive the male shafts of the power source and machine respectively. Each shaft has a circular flange whose face is perpendicular to the center line of the shafts. Each flange has a plurality of equally spaced cylindrical recesses machined into the inside face thereto adapted to receive conical inserts therein. Balls are contained by the conical inserts and transmit the rotational movement from the input to the output shaft. A stationary housing extends around the input and output shaft and has a transducer shell secured thereto. When force is applied to the input shaft to cause movement, the balls encounter torsional resistance which causes the balls to roll up the ramps of the conical seat inserts to separate the two torque flanges. The force transmitted through the balls causes rotation to the output shaft and produces tension to the stationary transducer shell. The stationary transducer shell is instrumented with semi-conductor strain gauges.