Abstract
We consider line defects in d-dimensional conformal field theories (CFTs). The ambient CFT places nontrivial constraints on renormalization group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in four dimensions.
Highlights
Introduction.—In lattice systems, in order to understand the physics on different length scales, we perform blockspin transformations, eliminating degrees of freedom that live at short distances
The number of degrees of freedom per lattice site is roughly speaking the number of fields and this raises the question of whether the number of fields decreases as we probe physics of longer and longer distances
The focus of this Letter is the physics of one-dimensional defects in a conformal field theories (CFTs)
Summary
Introduction.—In lattice systems, in order to understand the physics on different length scales, we perform blockspin transformations, eliminating degrees of freedom that live at short distances. Ludwig [39] for the decreasing entropy function on line defects in two dimensions and its subsequent proofs [42] At the fixed point of the (defect) renormalization group flow, the straight line defect preserves the subgroup SLð2; RÞ ×
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