Correlation functions of flavor multiplets in 4d N=1 Superconformal Field Theories
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Vichi, Alessandro
Parole chiave
conformal field theory
flavor symmetry
OPE coefficients
superconformal field theory
Data inizio appello
13/12/2021
Consultabilità
Non consultabile
Data di rilascio
13/12/2091
Riassunto
Conformal Field Theories (CFTs) are very interesting object: their enhanced symmetry offers the possibility to study and solve them only using first principles, without relying on perturbative approaches. Recently, the conformal bootstrap approach has proven very effective in this direction and has offered a new way to explore the space of CFTs. A key ingredients of this method are the conformal blocks, whose starting point is the study of three-point functions of conformal primaries. The already powerful constraints imposed by conformal symmetry become stronger when the theory under exam is supersymmetric. In this context it is necessary to compute superconformal blocks, namely linear combination of conformal ones. This thesis aims to analyze 4d N = 1 Superconformal Field Theories (SCFTs) which enjoy a flavor symmetry. A prototypical example are the infrared fixed points of superQCD in the conformal window. In that case the flavor symmetry is SU(N) × SU(N). We want to study the conserved current, to lay the groundwork for an indepth study of theories with any global symmetry. In 4d N = 1 SCFTs, flavor currents jµ are part of a short supermultiplets, whose superprimary is a scalar operator J. In this work we start from the most general three-point function involving two flavor supermultiplets and a third generic supermultiplet. We begin by showing that in superspace there are only two independent structures for which such correlator is non-zero and this constrains the third supermultiplet to have vanishing R-charge and to transform in a suitable Lorentz representations (j, ¯j) such that |j − ¯j| = 0, 2. Once we have obtained the more generic form of the three-point function, in order to find the OPE coefficients of the current, it is necessary to expand the correlator in its components. In our work we focus on extracting all three-point functions involving a flavor current, the scalar superprimary and a third conformal primary. To this aim we introduce differential operators acting in superspace, projecting the supermultiplets onto its components. The striking consequence of this formalism is that we easily obtain linear relations among operators in the same supermultiplet. Finally, we obtain all OPE coefficients for the non supersymmetric correlation function ⟨OjµJ⟩. This allows to write the superconfromal blocks as a linear combination of non-supersymmetric blocks, which are known. The next logical step is to expand the same superspace correlator further and extract all three-point functions involving two conserved current and a third operator. These correlators, combined with our results, will allow a numerical bootstrap study of the four-point function ⟨jµjνjρjσ⟩, opening a window on all 4d N = 1 SCFTs enjoying a global SU(N) symmetry.