Modeling wave properties of light is an important milestone for advancing physically-based rendering. In this paper, we propose complex-valued holographic radiance fields, a method that optimizes scenes without relying on intensity-based intermediaries. By leveraging multi-view images, our method directly optimizes a scene representation using complex-valued Gaussian primitives representing amplitude and phase values aligned with the scene geometry. Our approach eliminates the need for computationally expensive holographic rendering that typically utilizes a single view of a given scene. This accelerates holographic rendering speed by 30x-10,000x while achieving on-par image quality with state-of-the-art holography methods, representing a promising step towards bridging the representation gap between modeling wave properties of light and 3D geometry of scenes.