Local food is Cantonese, like Hong Kong and Guangzhou.
But the real point of Shenzhen is that it's a city of immigrants from all over China, so whatever local Chinese cuisine you want, you can find it in Shenzhen. Also, Shenzhen's a relatively rich region, so it attracts first-quality chefs from throughout China.
That's why just about everyone here discussing Shenzhen points you to food.