Transdimensional Defects

TL;DR

This paper introduces a new parameter, δ, to interpolate between different defect dimensions in conformal field theories, enabling a continuous spectrum of defect types and enriching the study of defect CFTs.

Contribution

The work develops a novel framework using δ to interpolate between defect dimensions, extending the analysis of conformal defects in various CFTs and providing detailed calculations.

Findings

δ allows continuous interpolation between defect dimensions.

New defect types are identified at integer and non-integer dimensions.

Framework applies to free, interacting, and large-N CFTs across multiple dimensions.

Abstract

This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard $\varepsilon$ expansion interpolates between integer spacetime dimensions, a new parameter, $\delta$, is used to interpolate between different integer-dimensional defects. The ensuing framework is explored in detail for defects of dimension $p=2+\delta$ in both free and interacting $O(N)$ bulk conformal field theories (CFTs) in $d=4-\varepsilon$. Comprehensive calculations are performed to first and second order in $\varepsilon$ and to high or all orders in $\delta$. Additionally, in the large-$N$ limit, the interpolation between defects of dimensions $p=1$ and $p=2$ is analysed for spacetime dimensions $4\leq d\leq 6$. The new parameter $\delta$ provides a natural enrichment of the space of defect CFTs and allows to find new integer dimension or co-dimension defects.