I've just acquainted myself with 'effective field theories', and have found myself thinking about the following question. In the effective field programme we generate low-energy theories from high-energy theories by 'integrating out' the high-energy modes, and this process is said to be irreversible on the grounds that too much information is lost in this process for us to be able to reconstruct the original theory from the low-energy theory that results from this integration process. May I ask: does anyone know of a low-energy theory that can be shown to be a low-energy approximation of two (or more) distinct high-energy QFTs? I ask only because I think it would be very interesting if we could show that a given quantum field theory could be derived from a plurality of more fundamental theories. For then the irreversibility is not just a reflection of our inability to reconstruct some one unique theory from the integrated-out version but more a fact about how the world might be structured. Thanks folks!