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We introduce a natural "massive" version of the Brownian loop soup of Lawlerand Werner which displays conformal covariance and exponential decay. We showthat this massive Brownian loop soup arises as the near-critical scaling limitof a random walk loop soup with killing and is related to the massive SLE(2)identified by Makarov and Smirnov as the near-critical scaling limit of aloop-erased random walk with killing. We conjecture that the massive Brownianloop soup describes the zero level lines of the massive Gaussian free field,and discuss possible relations to other models, such as Ising, in theoff-critical regime.

Off-Criticality and the Massive Brownian Loop Soup