[Séminaire FRG] Nicolás Wschebor (Univ. Montevideo)

Is the stability matrix of the FRG flow around a fixed point self-adjoint?

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.