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Is work on solitons in QFT's focused on finding solutions that could represent the fundamental particles of the Standard Model, or is the work focused on finding particles Beyond The Standard Model? If the work is primarily BTSM, is it still possible that solitons represent the SM particles?

My related question is: is there any possible relationship between solitions in N-dimensional QFT's, and string theory? Is there a possible duality in which strings are just solitions in a QFT? Or is that just silly and impossible?

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First of all, most of the work on solitons is formal theory - analyses of soliton solutions in QFTs that are interesting theoretically but that are known not to describe the Universe around us. Second, when one wants models of particle physics in our world, solitons typically carry "exotic" e.g. magnetic monopole charges, so they're bound to be heavy. This application of solitons is a small fraction of the soliton literature. Third, an even smaller fraction are exceptions - e.g. magnetic monopole description of quarks and leptons via the "electromagnetically dual" gauge group. – Luboš Motl Jan 30 '13 at 12:34
There are lots of solitons solving effective equations to string theory; D-branes are additionally "characteristic new string theory's solitons", too. There are tons of relationships between various QFT solitons and stringy solitons, between stringy solitons of 2 kinds, and so on. So generally, all the answers to the "are there" questions are Yes. Your last one is the only exception. Fundamental strings can't be solitons, almost by definition. A soliton is by definition "non-fundamental". Fundamental strings means taht everything else - incl. "solitons" - is made from them. – Luboš Motl Jan 30 '13 at 12:37
However, fundamental strings may become solitons constructed from other objects/fields at strong coupling (when they're no longer "fundamental" in the physical sense). In type IIB string theory, for example, fundamental F-strings are dual to D1-branes, so each may be interpreted as solitons created from fields whose elementary excitations are the other objects. But as long as one stays at the weak coupling where F-strings are "really fundamental", it's true by definition that these F-strings can't be solitons. Solitons, in general, are heavy, non-fundamental particles. – Luboš Motl Jan 30 '13 at 12:38

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