Yes, you can use The Ordinary Alpha Arbutin under your eyes. Alpha Arbutin is a skin-lightening ingredient that helps to reduce the appearance of dark spots and hyperpigmentation. It works by inhibiting the enzyme responsible for melanin production in the skin.

When applying Alpha Arbutin under the eyes, it can help to lighten any dark circles or discoloration in that area. However, it is important to keep in mind that the skin around the eyes is delicate and sensitive, so it's crucial to be gentle when applying any products in this area.

To use Alpha Arbutin under the eyes, take a small amount and gently pat it into the skin using your ring finger. Avoid tugging or pulling on the skin, as this can cause irritation. It's also important to note that Alpha Arbutin should always be followed by a moisturizer or eye cream to provide hydration and further protect the delicate skin.

If you have any concerns or specific skin conditions, it's always a good idea to consult with a dermatologist or skincare professional before incorporating any new products into your routine.