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We introduce a systematic method to derive the effective action for domain walls directly from the scalar field theory that gives rise to their solitonic solutions. The effective action for the Goldstone mode, which characterizes the soliton’s position, is shown to consist of the Nambu-Goto action supplemented by higher-order curvature invariants associated to its worldvolume metric. Our approach constrains the corrections to a finite set of Galileon terms, specifying both their functional forms and the procedure to compute their coefficients. We do a collection of tests across various models in 2 +1 and 3 +1 dimensions that confirm the validity of this framework. Additionally, the method is extended to include bound scalar fields living on the world sheet, along with their couplings to the Goldstone mode. These interactions reveal a universal nonminimal coupling of these scalar fields to the Ricci scalar on the world sheet. A significant consequence of this coupling is the emergence of a parametric instability, driven by interactions between the bound states and the Goldstone mode. 

Abstract We perform a detailed comparison of the dynamics of cosmic stringloops obtained in cosmological field theory simulations with their expected motion according to theNambu-Goto action. We demonstrate that these loops follow thetrajectories predicted within the NG effective theory except in regionsof high curvature where energy is emitted from the loop in the form of massiveradiation. This energy loss continues for all the loopsstudied in this simulation until they self-intersect or become small enough that they annihilateand disappear well before they complete a single oscillation. We comment on the relevance of thisinvestigation to the interpretation of the results from cosmological field theory simulationsas well as their extrapolation to a cosmological context.