Abstract: Imaginary multiplicative chaos is a one-parameter family of random fields formally defined as the complex exponential of a multiple of the Gaussian free field (GFF). These fields are conjectured to arise as the scaling limit of certain two-dimensional statistical mechanics models at criticality. In this talk, we present a new decomposition of imaginary chaos (or more precisely, its real and imaginary parts) into a sum of signed measures, obtained by exploring the excursions of the GFF between specific heights.

To motivate this construction, we begin with its discrete analogue in the XOR-Ising model, where rigorous scaling limit results are available. In this setting, the decomposition arises naturally from the clusters of the double random current (DRC) representation. This naturally leads us to the continuum setting, which closely mirrors the structure found in the discrete. After introducing the relevant notions in the continuum, we describe the construction of the decomposition and sketch the proofs of the main inputs involved.

Based on joint work with Avelio Sepúlveda.