This article considers how the emerging Artificial Intelligence (AI) research field is constructed, primarily in university settings. AI research is a site of significant national funding, industry investment, and media interest. As such, for researchers working across the resource-constrained science system, their relationship to the field is significant; legitimisation as an AI researcher can bring material and symbolic rewards. Through interviews (n = 90) with academics affiliated with AI-branded research organisations in the US, UK, and Australia, the article develops an empirical account of the construction of AI research as a high-dimensional field – a field that moves between multiple disciplinary and sectoral boundaries across national and international hierarchies. The article draws on the sociology of expertise and studies of research infrastructures to develop the conceptual frame of dimensionality to explain the vertical and horizontal dynamics informing the AI field's development. The article's contributions are its description of the emerging AI field, which complements critical studies of how the figure of AI is mobilised in other settings, and its extension of field theory to fluid spaces that leverage the boundary zone between several overlapping field arrangements.