High Energy Theory Seminar

Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this paper, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has an UV description in terms of a local modification of the Hamiltonian, so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contains a wealth of conformal data, including the $g$-function, which is a RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators $\Delta^{+0}_\alpha$ and changing operators $\Delta^{+-}_\alpha$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularisation of 3D CFTs and study the magnetic line defect of 3D Ising CFT. Using exact diagonalisation, we report the non-perturbative results $g=0.6055(7),\Delta^{+0}_0=0.1076(9)$ and $\Delta^{+-}_0=0.84(4)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.

The talk is in 469 Lauritsen.

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