Low Carb Foods High in Polyphenols and Antioxidants. Want to know which low carb foods are high in health protective polyphenols? This article explains ten of them in extensive detail. These are some of the healthiest foods on the planet and they are all compatible with low carb, paleo, and keto diets. The 10 low carb foods are blackcurrants, cinnamon, dark chocolate, coffee, red wine, pecans, blueberries, green tea, blackberries, and black tea. All have more antioxidants than vegetables!