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1. Codimension one defects in free scalar field theory

   https://doi.org/10.1007/JHEP06(2025)065  

   Kim, Seolhwa; Kraus, Per; Sun, Zhengdi (June 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as special cases. Our analysis is based on the interplay between two complementary descriptions, the first involving matching conditions imposed on fields and their derivatives across the defect, and the second on the resummation of perturbation theory in terms of renormalized defect couplings. Using either description as appropriate we compute a variety of observables: correlators of fields in the presence of such defects; the defect anomalous dimension; multiple defects and their fusion; canonical quantization and instabilities; ring shaped defects with application to the g-theorem and the entanglement entropy of accelerating defects; defects on the torus and Cardy formulas for the asymptotic density of states of the defect Hilbert space; and quenches produced by spacelike defects. The simplicity of the model allows for explicit computation of all these quantities, and provides a starting point for more complicated theories involving interactions. 

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2. Line defects in fermionic CFTs

   https://doi.org/10.1007/JHEP08(2023)224  

   Giombi, Simone; Helfenberger, Elizabeth; Khanchandani, Himanshu (August 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We study line defects in the fermionic CFTs in the Gross-Neveu-Yukawa universality class in dimensions 2< d <4. These CFTs may be described as the IR fixed points of the Gross-Neveu-Yukawa (GNY) model ind= 4 −ϵ, or as the UV fixed points of the Gross-Neveu (GN) model, which can be studied using the largeNexpansion in 2< d <4. These models admit natural line defects obtained by integrating over a line either the scalar field in the GNY description, or the fermion bilinear operator in the GN description. We compute the beta function for the defect RG flow using both the epsilon expansion and the largeNapproach, and find IR stable fixed points for the defect coupling, thus providing evidence for a non-trivial IR DCFT. We also compute some of the DCFT observables at the fixed point, and check that theg-function associated with the circular defect is consistent with theg-theorem for the defect RG flow. 

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3. Duality defect in a deformed transverse-field Ising model

   https://doi.org/10.1103/ctxg-k3b6  

   Yan, Fei; Konik, Robert; Mitra, Aditi (August 2025, Physical Review Research)

   Physical quantities with long lifetimes have both theoretical significance in the study of quantum many-body systems and practical implications for quantum technologies. In this manuscript, we investigate the roles played by topological defects in the construction of quasiconserved quantities, using as a prototypical example the Kramers-Wannier duality defect in a deformed one-dimensional quantum transverse-field Ising model. We construct the duality defect Hamiltonian in three different ways: half-chain Kramers-Wannier transformation, utilization of techniques in the Ising fusion category, and defect-modified weak integrability breaking deformation. The third method is also applicable for the study of generic integrable defects under weak integrability breaking deformations. We also work out the deformation of defect-modified higher charges in the model and study their slower decay behavior. Furthermore, we consider the corresponding duality defect twisted deformed Floquet transverse-field Ising model and investigate the stability of the isolated zero mode associated with the duality defect in the integrable Floquet Ising model, under such weak integrability breaking deformation. 

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4. Topological defects in Floquet circuits

   https://doi.org/10.21468/SciPostPhys.16.3.075  

   Tan, Mao Tian; Wang, Yifan; Mitra, Aditi (March 2024, SciPost Physics)

   We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of “space-like” defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of “time-like” defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations. 

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5. Notes on a surface defect in the O(N) model

   https://doi.org/10.1007/JHEP12(2023)004  

   Giombi, Simone; Liu, Bowei (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We study a surface defect in the free and criticalO(N) vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of thed-dimensional CFT. We compute the beta function for the corresponding defect renormalization group (RG) flow, and provide evidence that at long distances the system flows to a nontrivial defect conformal field theory (DCFT). We use epsilon and largeNexpansions to compute several physical quantities in the DCFT, finding agreement across different expansion methods. We also compute the defect free energy, and check consistency with the so-calledb-theorem for RG flows on surface defects. 

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