Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1508.04350 · Journal of Physics A Mathematical and Theoretical

Reflection and transmission of conformal perturbation defects

Ilka Brunner A, Cornelius Schmidt-Colinet

Published Apr 1, 2016• 17 citations
arXivHTMLPDF

Abstract

Abstract We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two-dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by perturbing the theory on one side of the defect line. We compute reflection and transmission coefficients in perturbation theory to third order in the coupling constant and check our calculations against exact constructions of RG interfaces between coset models.

DOI
10.1088/1751-8113/49/19/195401

Related papers

Entropy of conformal perturbation defects

Anatoly Konechny, Cornelius Schmidt-Colinet

We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.

arXiv:1407.6444•Jul 24, 2014•3 citations

Entropy of conformal perturbation defects

Anatoly Konechny, Cornelius Schmidt-Colinet

We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane.If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs.For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect.We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models  m with the boundary entropy of the defect constructed by Gaiotto (2012 J. High Energy Phys. JHEP12(2012) 103) and find a match at the first two orders in the m 1 expansion.

Journal of Physics A Mathematical and Theoretical•Nov 11, 2014•12 citations

Renormalization group defects for boundary flows

Anatoly Konechny

Recently, Gaiotto (2012 arXiv:1201.0767) considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet (UV) ones for a given renormalization group flow. In this paper, we propose that for a boundary RG flow in two dimensions there exist boundary condition changing fields (RG defect fields) linking the UV and the infrared (IR) conformal boundary conditions which carry similar information on the expansion of boundary fields at the fixed points. We propose an expression for a pairing between IR and UV operators in terms of a four-point function with two insertions of the RG defect fields. For the boundary flows in minimal models triggered by ψ 13 perturbation, we make an explicit proposal for the RG defect fields. We check our conjecture by a number of calculations done for the example of ( p , 2) → ( p − 1, 1)⊕( p + 1, 1) flows.

arXiv:1211.3665•Journal of Physics A Mathematical and Theoretical•Mar 20, 2013•6 citations

Renormalization group defects for boundary flows

Anatoly Konechny

Recently, Gaiotto (2012 arXiv:1201.0767) considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet (UV) ones for a given renormalization group flow. In this paper, we propose that for a boundary RG flow in two dimensions there exist boundary condition changing fields (RG defect fields) linking the UV and the infrared (IR) conformal boundary conditions which carry similar information on the expansion of boundary fields at the fixed points. We propose an expression for a pairing between IR and UV operators in terms of a four-point function with two insertions of the RG defect fields. For the boundary flows in minimal models triggered by ψ13 perturbation, we make an explicit proposal for the RG defect fields. We check our conjecture by a number of calculations done for the example of (p, 2) → (p − 1, 1)⊕(p + 1, 1) flows.

•Aug 17, 2016•4 citations

Renormalization Group Domain Walls from Phantom Symmetries

Jin Chen

We develop a systematic construction of renormalization group (RG) domain walls between two-dimensional rational conformal field theories. Using phantom currents, we consider an auxiliary chiral extension linked to the folded ultraviolet--infrared theory by a topological interface. The construction of RG walls then reduces to identifying suitable automorphism-twisted Cardy states in the auxiliary theory. We find two such types of automorphisms: outer automorphisms exchanging identical current algebra factors, as in Gaiotto's construction, and continuous inner automorphisms generated by the zero modes of spin-one phantom currents. In the latter case, the RG domain walls generically admit a continuous defect conformal manifold. We further show that, when an RG flow can be orbifolded to another one, the orbifold may lift defect conformal moduli of the RG brane constructed using inner automorphisms. The two types of RG branes can then be mapped to each other via a topological interface defined by the orbifold. We demonstrate the two types of RG brane construction via various examples of flows between non-unitary minimal models, from parafermions to minimal models, and between generalized parafermions. Many physical observables of the RG walls are computed non-perturbatively, including boundary entropies and spectra, and UV--IR operator mixings. We also find interesting nontrivial boundary monodromy: a closed cycle in the defect conformal moduli space can carry an RG domain wall into other distinct non-trivial conformal interfaces.

arXiv:2610.23529•Oct 16, 2026•0 citations

Defects and perturbation

Enrico M. Brehm

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

arXiv:2011.10795•Journal of High Energy Physics•Apr 1, 2021•2 citations
Abstract We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two-dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by perturbing the theory on one side of the defect line. We compute reflection and transmission coefficients in perturbation theory to third order in the coupling constant and check our calculations against exact constructions of RG interfaces between coset models.
We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.
We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane.If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs.For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect.We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models  m with the boundary entropy of the defect constructed by Gaiotto (2012 J. High Energy Phys. JHEP12(2012) 103) and find a match at the first two orders in the m 1 expansion.
Recently, Gaiotto (2012 arXiv:1201.0767) considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet (UV) ones for a given renormalization group flow. In this paper, we propose that for a boundary RG flow in two dimensions there exist boundary condition changing fields (RG defect fields) linking the UV and the infrared (IR) conformal boundary conditions which carry similar information on the expansion of boundary fields at the fixed points. We propose an expression for a pairing between IR and UV operators in terms of a four-point function with two insertions of the RG defect fields. For the boundary flows in minimal models triggered by ψ 13 perturbation, we make an explicit proposal for the RG defect fields. We check our conjecture by a number of calculations done for the example of ( p , 2) → ( p − 1, 1)⊕( p + 1, 1) flows.
Recently, Gaiotto (2012 arXiv:1201.0767) considered conformal defects which produce an expansion of infrared local fields in terms of the ultraviolet (UV) ones for a given renormalization group flow. In this paper, we propose that for a boundary RG flow in two dimensions there exist boundary condition changing fields (RG defect fields) linking the UV and the infrared (IR) conformal boundary conditions which carry similar information on the expansion of boundary fields at the fixed points. We propose an expression for a pairing between IR and UV operators in terms of a four-point function with two insertions of the RG defect fields. For the boundary flows in minimal models triggered by ψ13 perturbation, we make an explicit proposal for the RG defect fields. We check our conjecture by a number of calculations done for the example of (p, 2) → (p − 1, 1)⊕(p + 1, 1) flows.
We develop a systematic construction of renormalization group (RG) domain walls between two-dimensional rational conformal field theories. Using phantom currents, we consider an auxiliary chiral extension linked to the folded ultraviolet--infrared theory by a topological interface. The construction of RG walls then reduces to identifying suitable automorphism-twisted Cardy states in the auxiliary theory. We find two such types of automorphisms: outer automorphisms exchanging identical current algebra factors, as in Gaiotto's construction, and continuous inner automorphisms generated by the zero modes of spin-one phantom currents. In the latter case, the RG domain walls generically admit a continuous defect conformal manifold. We further show that, when an RG flow can be orbifolded to another one, the orbifold may lift defect conformal moduli of the RG brane constructed using inner automorphisms. The two types of RG branes can then be mapped to each other via a topological interface defined by the orbifold. We demonstrate the two types of RG brane construction via various examples of flows between non-unitary minimal models, from parafermions to minimal models, and between generalized parafermions. Many physical observables of the RG walls are computed non-perturbatively, including boundary entropies and spectra, and UV--IR operator mixings. We also find interesting nontrivial boundary monodromy: a closed cycle in the defect conformal moduli space can carry an RG domain wall into other distinct non-trivial conformal interfaces.