Consider a Brownian loop soup L^θ_D with subcritical intensity θ ∈ (0, 1/2] in some 2D bounded simply connected domain. We define and study the properties of a conformally invariant field h_θ naturally associated to L^θ_D. Informally, this field is a signed version of the local time of L^θ_D to the power 1 − θ. When θ = 1/2, h_θ is a Gaussian free field (GFF) in D. Our construction of h_θ relies on the multiplicative chaos M_γ associated with L^θ_D, as introduced in [ABJL23]. Assigning independent symmetric signs to each cluster, we restrict M γ to positive clusters. We prove that, when θ = 1/2, the resulting measure M^+_γ corresponds to the exponential of γ times a GFF. At this intensity, the GFF can be recovered by differentiating at γ = 0 the measure M^+_γ. When θ < 1/2, we show that M^+_γ has a nondegenerate fractional derivative at γ = 0 defining a random generalised function h_θ. We establish a result which is analogous to the recent work [ALS23] in the GFF case (θ = 1/2), but for h_θ with θ ∈ (0, 1/2]. Relying on the companion article [JLQ23], we prove that each cluster of L^θ_D possesses a nondegenerate Minkowski content in some non-explicit gauge function r → r^2 | log r|^{1−θ+o(1)}. We then prove that h_θ agrees a.s. with the sum of the Minkowski content of each cluster multiplied by its sign. We further extend the couplings between CLE_4 , SLE_4 and the GFF [SS13, MS] to h_θ for θ ∈ (0, 1/2]. We then prove that h_θ agrees a.s. with the sum of the Minkowski content of each cluster multiplied by its sign. We further extend the couplings between CLE4, SLE4 and the GFF to h_θ for θ∈(0,1/2]. We show that the (non-nested) CLE_κ loops form level lines for hθ and that there exists a constant height gap between the values of the field on either side of the CLE loops.