There is a useful overview by Phillip Vannini1
Theoretically, non-representational theory stands as a synthesizing effort to amalgamate diverse but interrelated theoretical perspectives, such as actor-network theory, biological philosophy, neomaterialism, process philosophy, speculative realism, social ecology, performance theory, poststructuralist feminism, critical theory, postphenomenology, and pragmatism. Its typical reference lists therefore tend to feature names of philosophers like Michelle Serres, Bruno Latour, Michel de Certeau, Judith Butler, Elizabeth Grosz, Donna Haraway, Erving Goffman, Alphonso Lingis, Brian Massumi, Maurice Merleau-Ponty, Tim Ingold, Emmanuel Levinas, Alfred North Whitehead, Isabelle Stengers, Maurice Blanchot, Jean Luc Nancy, Alain Badiou, Gilbert Simondon, Nigel Thrift, and probably most commonly of all Gilles Deleuze and Felix Guattari.
Due to its eclectic character it is quite difficult to summarize non-representational theory’s diverse ideas succinctly. Thrift’s (2008) work is quite helpful in this regard. In a difficult but remarkably clear, well-organized, and contagiously enthusiastic opening chapter to his foundational volume on the topic, Thrift outlines seven core principles, or ideal qualities, of non-representational theory. Thrift is quick to point out that his intent in territorializing non-representational theory is not to systematize it but rather to outline the potentials of a new experimental genre: a hybrid genre for a hybrid world.
The Thrift referred to is: Thrift, N. J. (2008). Non-representational theory : space, politics, affect. Milton Park, Abingdon, Oxon ; New York, NY: Routledge.
So here are some names and some labels that might ring bells. I think it is a bit of a stretch to include critical theory, given that a lot of that would sit in what you could call a representational idiom.
Di Mulcahy has written a good paper that usefully introduces the notion in an education setting: Mulcahy, D. (2010). Assembling the ‘Accomplished’ Teacher: The performativity and politics of professional teaching standards. Educational Philosophy and Theory, 43(Suppl), 94-113. doi:10.1111/j.1469-5812.2009.00617.x