Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators

Abstract

We apply the numerical bootstrap program to chiral operators in fourdimensional N = 2 SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of N = 2 SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.

The most general 4 D $$ \mathcal{D} $$ N $$ \mathcal{N} $$ = 1 superconformal blocks for scalar operators

“…For non-vanishing r,r, and R, if certain fields Φ's in four-point function satisfy shortening conditions, like chirality, the tensor structures can be simplified and there will be strong constraints on the coefficients λ (i) Φ i Φ 2 O . In this case the superconformal blocks can be conveniently solved through superconformal Casimir approach [17,22,31]. As a nontrivial check, we compare our work with previous results on N = 1 superconformal blocks obtained from superconformal Casimir approach [17,22].…”

“…N = 1, 2 superconformal blocks of chiral-antichiral scalars are also presented in [22], in which the four-point correlator Φ 1Φ2 Φ 2Φ1 consists of chiral-antichiral scalars with arbitrary U(1) R-charges. For the N = 1 case, the superconformal blocks are related to above coefficients a i with the constraint r = −r and are well consistent with our results.…”

Long multiplet bootstrap

“…As was pointed out in [26] for a two-dimensional N = (1, 1) SCFT, if we restrict the external operators to be the superconformal primaries, i.e., setting all fermionic coordinates to zero, the superconformal blocks reduce to a sum of bosonic blocks. 22 Once again the non-trivial constraints should come from considering the correlation functions of external superdescendants.…”

Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows

“…There is at present no direct evidence for the existence of rank-0 N = 2 SCFTs. It is possible that N = 2 conformal bootstrap methods [7,8,45,46] could conceivably provide such evidence in the future. Also, it may be possible to adduce indirect evidence in favor of their existence by the following strategy.…”