Boundary and Defect CFT: Open Problems and Applications

TL;DR

The proceedings map out a broad, interconnected program for boundary and defect CFT, weaving together RG domain walls, holographic duals, integrability, and topological phases to tackle open problems across high-energy and condensed-matter physics. A common toolkit emerges: variational boundary-state analyses, truncated conformal space approaches, holographic Kondo constructions, Calogero–Sutherland defect blocks, and data-driven bootstrap concepts applied to defect correlators. Concrete results include RG boundaries in Ising theory, explicit double-trace interfaces and g-functions, holographic impurity entropy reductions, and novel constructions of defects in minimal models and higher-dimensional theories. Collectively, the work advances a unified perspective on how boundaries and defects shape the landscape of conformal field theories and their applications.

Abstract

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.

Figures (6)

• Figure 1: We consider two geometries of Luttinger dot system; (a) embedded and (b) side-coupled. The embedded geometry also includes a Coulomb interaction between the dot and leads. Once unfolded the side-coupled and embedded geometries are the same but with the latter containing non local interactions.
• Figure 2: (Color Online) The amplitudes are related by a consistent set of $S$-matrices.
• Figure 3: (Color Online). The dot occupation at small (left) and large (right) dot energy, $\epsilon_0/\Gamma$, for different values of $K>1$. The effect of attractive interactions is to suppress the dot occupation as compared to the non interacting case (dashed line). This effect becomes stronger for increasing $K$.
• Figure 4: (Color Online).The dot occupation at small (left) and large (right) dot energy for different values of $K$. The effect of repulsive interactions $K<1$ is to enhance the dot occupation as compared to the non interacting case (dashed line) with the effect increasing as $K$ decreases.
• Figure 5: (Color Online): The dot occupation for fixed $\epsilon_o/\Gamma$ as a function of temperature. The interaction is taken to be $K=\frac{4}{3}$ (dot-dashed lines), $K=1$ (dashed lines) and $K=\frac{2}{3}$ (solid lines). We see the enhancement and suppression of the dot occupation for repulsive and attractive interaction with the effect most pronounced as the temperature is lowered.