On analytic bootstrap for interface and boundary CFT

We use analytic bootstrap techniques for a CFT with an interface or a boundary. Exploiting the analytic structure of the bulk and boundary conformal blocks we extract the CFT data. We further constrain the CFT data by applying the equation of motion to the boundary operator expansion. The method presented in this paper is general, and it is illustrated in the context of perturbative Wilson-Fisher theories. In particular, we find constraints on the OPE coefficients for the interface CFT in 4 − ϵ dimensions (upto order $$ \mathcal{O} $$ O (ϵ2)) with ϕ4-interactions in the bulk. We also compute the corresponding coefficients for the non-unitary ϕ3-theory in 6 − ϵ dimensions in the presence of a conformal boundary equipped with either Dirichlet or Neumann boundary conditions upto order $$ \mathcal{O} $$ O (ϵ), or an interface upto order $$ \mathcal{O}\left(\sqrt{\epsilon}\right) $$ O ϵ .

Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

Extension of Grimus–Stockinger formula from operator expansion of free Green function

The operator expansion of free Green function of Helmholtz equation for arbitrary N-dimensional space leads to asymptotic extension of three dimensions Grimus–Stockinger formula closely related to multipole expansion. Analytical examples inspired by neutrino oscillation and neutrino deficit problems are considered for relevant class of wave packets.

New s-parametrized quasiprobability distribution for fermion system and its application on fermion-counting

Based on the fermion operators' s-ordered rule, we introduce a new kind of s-ordered quasiprobability distributions [Formula: see text], which is defined by the supertrace different from the other definition introduced by Cahill and Glauber [Phys. Rev. A59, 1538 (1999)]. We further obtain the s-parametrized operator expansion formula of fermion density operator for multi-mode case. At last, we apply it to deriving new multi-mode fermion-counting formula, which would be convenient to calculate the probability of counting n fermions.