The problem with many teriyaki sauces, especially the store-bought variety, is that these sauces tend to be too thin for certain uses. While this thin viscosity is good for applications like marinades, thin sauces tend to make poor finishing sauces and glazes. However, there are a number of methods to increase the viscosity of these sauces using sauce thickeners. Cornstarch is a popular sauce thickener for many Asian sauces, like teriyaki sauce; however, you also have other options.
Arrowroot, like cornstarch, is also an easy-to-use, starch-based thickener. It has a few advantages over cornstarch, as it can stand up to longer periods and higher degrees of heat, works fine with acidic sauces and it has a more neutral taste than cornstarch. On the downside, arrowroot is much more expensive than cornstarch. Like cornstarch, you should mix the arrowroot with cold water into a slurry before adding to a sauce. It takes about 30 seconds for arrowroot to thicken a sauce once you add it.
Xanthan gum belongs to a class of thickeners called "hydrocolloids." Hydrocolloids work by controlling the structure of water; the molecular structure of these substances increase the viscosity and thickness of liquids. One of the easiest hydrocolloids to use is xanthan gum; you only need a small amount to thicken a sauce -- and it work as a thickener in either warm or cold liquids. To effectively incorporate xanthan gum into your sauce, add it utilizing a blender or mixer. You can also incorporate it using a hand whisk; however, this method is trickier because of the rapid rate at which xanthan gum thickens.
A roux is a traditional thickener in French cooking. Essentially a cooked combination of flour and a fat -- typically butter -- a roux can range in color from blonde to dark brown or chocolate. The color comes from toasting the flour in butter -- longer cooking times and more heat result in a darker roux. A white roux has a very subtle, almost pasty taste, while a darker roux has a more assertive and nutty taste. For teriyaki sauce -- given the aggressive, salty, and umami flavors -- a brown or dark brown roux works best, adding a nice depth of flavor to the sauce.
Butter is classically used as a sauce thickener in a number of French sauces like Bordelaise. The technique involved is called "mounting" butter. This is, however, probably one of the most difficult techniques to thicken sauces. To mount butter, you have to slowly add small amounts of chilled butter to a finished, unthickened, slightly cooled down -- but still warm -- sauce. The trick in getting this technique to work properly is getting the heat just right. The sauce needs to be warm enough to melt the butter, but not so warm as to allow it to separate. If the butter separates or breaks, it loses its ability to thicken the sauce, and you end up with just buttery grease and milk solids in the sauce.