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Phys."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n                     <\/jats:title><jats:p>We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which \u2014 according to the ODE\/IM correspondence \u2014 should correspond to excited states of the Quantum KdV model.<\/jats:p><jats:p>We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.<\/jats:p><jats:p>This allows us to associate to each partition of <jats:italic>N<\/jats:italic> a unique monster potential with <jats:italic>N<\/jats:italic> roots, of which we compute the spectrum. As a consequence, we prove \u2014 up to a few mathematical technicalities \u2014 that, fixed an integer <jats:italic>N<\/jats:italic> , the number of monster potentials with <jats:italic>N<\/jats:italic> roots coincides with the number of integer partitions of <jats:italic>N<\/jats:italic> , which is the dimension of the level <jats:italic>N<\/jats:italic> subspace of the quantum KdV model. In striking accordance with the ODE\/IM correspondence.<\/jats:p>","DOI":"10.1007\/jhep02(2021)059","type":"journal-article","created":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T22:52:05Z","timestamp":1612911125000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Counting monster potentials"],"prefix":"10.1007","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5288-4333","authenticated-orcid":false,"given":"Riccardo","family":"Conti","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7547-4804","authenticated-orcid":false,"given":"Davide","family":"Masoero","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,8]]},"reference":[{"key":"14785_CR1","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/BF02737517","volume":"49","author":"S Ahmed","year":"1979","unstructured":"S. Ahmed, M. Bruschi, F. 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