Surface defects in the $O(N)$ model

TL;DR

This paper investigates surface defects in the critical $O(N)$ model across dimensions and $N$, identifying new conformal defects and analyzing their properties using combined analytical techniques.

Contribution

It introduces new conformal surface defects in the $O(N)$ model and explores their RG flows, symmetry breaking, and physical characteristics across different dimensions and $N$ values.

Findings

Discovery of new conformal defects in the $O(N)$ model.

Identification of fixed points related to known phase transitions.

Characterization of defects via conformal anomaly coefficients and 1-point functions.

Abstract

I study the two-dimensional defects of the $d$ dimensional critical $O(N)$ model and the defect RG flows between them. By combining the $\epsilon$-expansion around $d = 4$ and $d = 6$ as well as large $N$ techniques, I find new conformal defects and examine their behavior across dimensions and at various $N$. I discuss how some of these fixed points relate to the known ordinary, special and extraordinary transitions in the 3d theory, as well as examine the presence of new symmetry breaking fixed points preserving an $O(p) \times O(N-p)$ subgroup of $O(N)$ for $N \le N_c$ (with the estimate $N_c = 6$). I characterise these fixed points by obtaining their conformal anomaly coefficients, their 1-point functions and comment on the calculation of their string potential. These results establish surface operators as a viable approach to the characterisation of interface critical phenomena in the 3d critical $O(N)$ model.