Document Zbl 0787.58049

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Math. Phys.</a> <a href="/?q=in%3A16867" title="Articles in this Issue">158, No. 3, 569-644 (1993)</a>. </div> <div class="abstract">Summary: We find a relation between the spectrum of solitons of massive $N = 2$ quantum field theories in $d = 2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric $N = 2$ conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A509904">Cited in <strong>4</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A509904">Cited in <strong>170</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A58Z05" title="MSC2020">58Z05</a> </td> <td class="space"> Applications of global analysis to the sciences </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81T40" title="MSC2020">81T40</a> </td> <td class="space"> Two-dimensional field theories, conformal field theories, etc. in quantum mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A81T60" title="MSC2020">81T60</a> </td> <td class="space"> Supersymmetric field theories in quantum mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconformal+field+theory">conformal field theory</a>; <a href="/?q=ut%3Achiral+fields">chiral fields</a>; <a href="/?q=ut%3ALandau-Ginzburg+solitons">Landau-Ginzburg solitons</a>; <a href="/?q=ut%3Asupersymmetry">supersymmetry</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0787.58049" data-ciurl="/ci/00509904" data-biburl="/bibtex/00509904.bib" data-amsurl="/amsrefs/00509904.bib" data-xmlurl="/xml/00509904.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00509904.pdf" title="Zbl 0787.58049 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF02096804" aria-label="DOI for “On classification of $N=2$ supersymmetric theories”" title="10.1007/BF02096804">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/hep-th/9211097"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Zamolodchikov, A.B., Zamolodchikov, Al.B.: Ann. 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