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SUMMARY:Point of a $\\psi^4_d$ Fermionic Theory: Anomalous Exponent and Sc
 aling Operators
DTSTART:20251126T093000Z
DTEND:20251126T103000Z
DTSTAMP:20260425T144200Z
UID:indico-event-15130@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Giuseppe Scola (SISSA\, Trieste)\n\nSeed Seminar of 
 Mathematics and Physics\nFall' 25: Random Forests and Fermionic Field Theo
 ries \nWe consider the Renormalization Group (RG) fixed-point theory asso
 ciated with a fermionic $\\psi^4_d$ model in d=1\,2\,3 with fractional k
 inetic term\, whose scaling dimension is fixed so that the quartic interac
 tion is weakly relevant in the RG sense. The model is defined in terms of 
 a Grassmann functional integral with interaction $V^*$\, solving a fixed-p
 oint RG equation in the presence of external fields\, and a fixed ultravio
 let cutoff. We define and construct the field and density scale-invariant 
 response functions\, and prove that the critical exponent of the former is
  the naive one\, while that of the latter is anomalous and analytic. We co
 nstruct the corresponding (almost-)scaling operators\, whose two point cor
 relations are scale-invariant up to a remainder term\, which decays like a
  stretched exponential at distances larger than the inverse of the ultravi
 olet cutoff. Our proof is based on constructive RG methods and\, specifica
 lly\, on a convergent tree expansion for the generating function of correl
 ations\, which generalizes the approach developed by three of the authors 
 in a previous publication (Giuliani et al. in JHEP 01:026\, 2021. doi.org
 /10.1007/JHEP01(2021)026). CMP 406.10 (2025): 257\, joint work with A. Giu
 liani\, V. Mastropietro and S. Rychkov.\n========\nPour être informé des
  prochains séminaires vous pouvez vous abonner à la liste de diffusion e
 n écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscr
 ibe seminaire_mathematique PRENOM NOM"(indiquez vos propres prénom et nom
 ) et laissez le corps du message vide.\n\nhttps://indico.math.cnrs.fr/even
 t/15130/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/15130/
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