Superconformal boundaries in 4 − ϵ dimensions

Abstract

Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

Defect conformal blocks from Appell functions

“…These can be studied with several non-perturbative techniques including the conformal bootstrap, see e.g. [36][37][38][39][40][41]. Assuming the successful extension of our work to spinning defect correlators, see previous paragraph, it seems likely that the approach to superconformal blocks we developed in [23,42,43] for bulk four-point functions can be extended to theories with defects.…”

Conformal bootstrap near the edge

“…To reproduce this result, we need techniques to handle the infinite sums of blocks. Such techniques were used in the BCFT bootstrap to obtain order 2 results [14] and it should be possible to adapt them to the order problem in our setup (see also [49]). We leave this exploration for future work.…”

On analytic bootstrap for interface and boundary CFT

“…Let us proceed with bootstrapping the correlator at order 2 using the method described in section 2. 10 The boundary conformal blocks G boe (∆ 0 , ξ) and G boe (∆ 1 , ξ) cannot be expanded using the Mathematica package HypExp [28] since it only expands hypergeometric functions with parameters linear terms in . However, the same algorithm can still be used.…”

“…Bootstrap techniques for BCFT and ICFT were studied in [1]. See [4][5][6][7][8][9][10][11] for recent works on BCFTs.…”