Polyglutamic acid is a chain of glutamic acid molecules — a polypeptide — produced by bacterial fermentation. It is the substance that makes natto stringy.
On the skin it works as a humectant. Humectants attract water molecules and hold them in the outer layer of the skin, which makes that layer swell slightly. Swollen surface skin is smoother, less flaky and reflects light more evenly, so fine dehydration lines look softer. Glycerin and hyaluronic acid do the same job by the same principle.
What is a bit different about polyglutamic acid is that it is a large molecule and it dries down into a thin, flexible film. That film gives it a mild secondary sealing effect — it slows water leaving as well as pulling it in — and it is why the finish feels slightly tacky and slightly plumping in a way that a thin hyaluronic acid serum does not.
On the marketing claim. You will see polyglutamic acid described as many times more hydrating than hyaluronic acid, usually with a specific multiplier attached. That figure is not something you can trace to convincing human data, and how much water a molecule holds in a test tube does not translate into how much it hydrates skin. The honest position is that polyglutamic acid is a legitimate humectant with a pleasant film-forming quality and comparatively little published human evidence behind it.
Polyglutamic acid is well tolerated. There is not much of a side effect profile, partly because it is mild and partly because it has not been studied heavily.
There is no group that needs to avoid polyglutamic acid on safety grounds. It is a mild, inert humectant with no known systemic effects, and it is fine in pregnancy and breastfeeding.
Two practical reasons to skip it.
If your skin is dry rather than dehydrated — flaky, rough and short of oil rather than short of water — a humectant serum is not what you need. An emollient or occlusive will do more. See dry skin.
If you already own a hyaluronic acid or glycerin serum you are happy with, adding this one is unlikely to be noticeable. They do the same job.
A note on soy. Polyglutamic acid is produced by fermenting bacteria, often grown on soybeans. The finished ingredient is a polypeptide of glutamic acid and is not soy protein, and topical reactions in soy-allergic people have not been a recognized problem. If you have a severe soy allergy, patch test.
If you have sensitive skin and have reacted to a serum containing it, the fragrance or preservative is a more likely culprit than the polyglutamic acid.