Interest in conformal symmetry dates back at least fifty years, to the work of Migdal and others, who showed that it constrains the form of three-point correlation functions and connects naturally with critical phenomena. Since then, conformal symmetry has become a powerful tool for computing physical observables and, in some cases, for solving quantum field theories exactly, most notably in two dimensions.
More recently, conformal symmetry has begun to receive attention within the functional renormalization group (FRG). The study of its interplay with standard FRG approximation schemes, and in particular with the derivative expansion (DE), is even more recent and remains largely unexplored. In this talk, we explain how conformal symmetry is realized in the FRG and examine the consequences of employing the derivative expansion (DE). We then propose a framework for incorporating conformal symmetry systematically into the derivative expansion.
LAST-MODIFIED:20260910T195032Z SEQUENCE:41 LOCATION: GEO:0.00000000;0.00000000 X-LOCATION-DISPLAYNAME:Salle 523, couloir 12-13, 5è étage X-ACCESS:1 X-HITS:212 X-COLOR:8816b8 X-SHOW-END-TIME:1 END:VEVENT BEGIN:VEVENT DTSTART;TZID=Europe/Paris:20261001T140000 DTEND;TZID=Europe/Paris:20261001T153000 UID:090F523A-C93D-454B-A851-D08100888A23 SUMMARY:[Séminaire FRG] Nicolás Wschebor (Univ. Montevideo) CREATED:20260928T075634Z DTSTAMP:20260928T075634Z URL:https://www.lptmc.jussieu.fr/vie-scientifique/listeseminaires/seminaire-frg-nicolas-wschebor-univ-montevideo DESCRIPTION:Is the stability matrix of the FRG flow around a fixed point self-adjoint?\NAbstract: In unitary conformal field theories, it has been shown that the spectrum of scaling dimensions is real and bounded from above. FRG analysis always reveals a discrete spectrum with real parts bounded from above, but complex eigenvalues are often obtained. The aim of this talk, which relates to ongoing work, is to analyse the extent to which these complex values are physical or spurious. We will review the main characteristics of the spectrum obtained in the Derivative Expansion of the FRG. We will then analyse whether the results obtained in unitary conformal field theories are consistent with these findings. Finally, we will prove that the LPA equation for any scalar theory with a real fixed point potential has a stability matrix operator which, when combined with an appropriate scalar product, is self-adjoint. This implies that, for eigenperturbations with bounded norm, have eigenvalues which form a discrete and real spectrum in LPA approximation (for real fixed points). Finally, we will discuss the extent to which this result can be generalised to more complex approximations. X-ALT-DESC;FMTTYPE=text/html:Abstract: In unitary conformal field theories, it has been shown that the spectrum of scaling dimensions is real and bounded from above. FRG analysis always reveals a discrete spectrum with real parts bounded from above, but complex eigenvalues are often obtained. The aim of this talk, which relates to ongoing work, is to analyse the extent to which these complex values are physical or spurious. We will review the main characteristics of the spectrum obtained in the Derivative Expansion of the FRG. We will then analyse whether the results obtained in unitary conformal field theories are consistent with these findings. Finally, we will prove that the LPA equation for any scalar theory with a real fixed point potential has a stability matrix operator which, when combined with an appropriate scalar product, is self-adjoint. This implies that, for eigenperturbations with bounded norm, have eigenvalues which form a discrete and real spectrum in LPA approximation (for real fixed points). Finally, we will discuss the extent to which this result can be generalised to more complex approximations.
LAST-MODIFIED:20260928T075849Z SEQUENCE:135 LOCATION: GEO:0.00000000;0.00000000 X-LOCATION-DISPLAYNAME:Salle 523, couloir 12-13, 5è étage X-ACCESS:1 X-HITS:159 X-COLOR:8816b8 X-SHOW-END-TIME:1 END:VEVENT END:VCALENDAR