Bootstat 2021: Conformal bootstrap and statistical models

Operator expansions, layer susceptibility and two-point functions in BCFT

26 mai 2021, 10:00

1h

Institut Pascal, Orsay, France & online

Lecture / lecture series

Orateur

Mykola Shpot (ICMP Lviv)

Description

We found that in boundary conformal field theories, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility.

This general property allows a direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs.

To show how it works we derive an explicit expression for the correlation function $⟨{\varphi }_i{\varphi }^i⟩$ of the $O(n)$ model at the extraordinary transition in $4-\epsilon$ dimensional semi-infinite space to order $O(\epsilon )$.

The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the $O(n)$ model to order $O({\epsilon }^2)$. These agree with the known results both in $\epsilon$ and large-$n$ expansions.

Documents de présentation

Boundary conformal field theory at the extraordinary transition.pdf

Operator expansions, layer susceptibility and two-point functions in BCFT.pdf

OperatorExpansions&Layer Susceptibility.pdf