Abstract
We investigate the RG domain wall between neighboring \( {A}_2^{(p)} \) minimal CFT models and establish the map between UV and IR fields (matrix of mixing coefficients). A particular RG invariant set of six primary and four descendant fields is analyzed in full details. Using the algebraic construction of the RG domain wall we compute the UV/IR mixing matrix. To test our results we show that it diagonalizes the matrix of anomalous dimensions previously known from perturbative analysis. It is important to note that the diagonalizing matrix can not be found from perturbative analysis solely due to degeneracy of anomalous dimensions. The same mixing coefficients are used to explore anomalous W-weights as well.
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References
A.B. Zamolodchikov, Renormalization Group and Perturbation Theory Near Fixed Points in Two-Dimensional Field Theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [INSPIRE].
R. Poghossian, Two Dimensional Renormalization Group Flows in Next to Leading Order, JHEP 01 (2014) 167 [arXiv:1303.3015] [INSPIRE].
R.G. Poghossian, Study of the Vicinities of Superconformal Fixed Points in Two-dimensional Field Theory, Sov. J. Nucl. Phys. 48 (1988) 763 [INSPIRE].
D.A. Kastor, E.J. Martinec and S.H. Shenker, RG Flow in N = 1 Discrete Series, Nucl. Phys. B 316 (1989) 590 [INSPIRE].
C. Crnkovic, G.M. Sotkov and M. Stanishkov, Renormalization Group Flow for General SU(2) Coset Models, Phys. Lett. B 226 (1989) 297 [INSPIRE].
C. Ahn and M. Stanishkov, On the Renormalization Group Flow in Two Dimensional Superconformal Models, Nucl. Phys. B 885 (2014) 713 [arXiv:1404.7628] [INSPIRE].
F. Ravanini, Thermodynamic Bethe ansatz for Gk ⨂ Gl/Gk + l coset models perturbed by their ϕ1,1,Adj operator, Phys. Lett. B 282 (1992) 73 [hep-th/9202020] [INSPIRE].
A.B. Zamolodchikov, Infinite Additional Symmetries in Two-Dimensional Conformal Quantum Field Theory, Theor. Math. Phys. 65 (1985) 1205 [INSPIRE].
S.L. Lukyanov and V. Fateev, Additional Symmetries and Exactly Solvable Models in Two Dimensional Conformal Field Theory: Physics Reviews, CRC Press (1991) [ISBN: 9783718650477].
H. Poghosyan and R. Poghossian, RG flow between W3 minimal models by perturbation and domain wall approaches, JHEP 08 (2022) 307 [arXiv:2205.05091] [INSPIRE].
H. Poghosyan and R. Poghossian, RG flows between W3 minimal models, PoS Regio2021 (2022) 039 [INSPIRE].
D. Gaiotto, Domain Walls for Two-Dimensional Renormalization Group Flows, JHEP 12 (2012) 103 [arXiv:1201.0767] [INSPIRE].
A. Poghosyan and H. Poghosyan, Mixing with descendant fields in perturbed minimal CFT models, JHEP 10 (2013) 131 [arXiv:1305.6066] [INSPIRE].
G. Poghosyan and H. Poghosyan, RG domain wall for the N = 1 minimal superconformal models, JHEP 05 (2015) 043 [arXiv:1412.6710] [INSPIRE].
A. Konechny and C. Schmidt-Colinet, Entropy of conformal perturbation defects, J. Phys. A 47 (2014) 485401 [arXiv:1407.6444] [INSPIRE].
I. Brunner and C. Schmidt-Colinet, Reflection and transmission of conformal perturbation defects, J. Phys. A 49 (2016) 195401 [arXiv:1508.04350] [INSPIRE].
A. Konechny, RG boundaries and interfaces in Ising field theory, J. Phys. A 50 (2017) 145403 [arXiv:1610.07489] [INSPIRE].
A. Konechny, Properties of RG interfaces for 2D boundary flows, JHEP 05 (2021) 178 [arXiv:2012.12361] [INSPIRE].
E.M. Brehm and I. Brunner, Entanglement entropy through conformal interfaces in the 2D Ising model, JHEP 09 (2015) 080 [arXiv:1505.02647] [INSPIRE].
F. Gliozzi, P. Liendo, M. Meineri and A. Rago, Boundary and Interface CFTs from the Conformal Bootstrap, JHEP 05 (2015) 036 [arXiv:1502.07217] [INSPIRE].
T. Gannon, The Classification of affine SU(3) modular invariant partition functions, Commun. Math. Phys. 161 (1994) 233 [hep-th/9212060] [INSPIRE].
P. Goddard, A. Kent and D.I. Olive, Virasoro Algebras and Coset Space Models, Phys. Lett. B 152 (1985) 88 [INSPIRE].
V.G. Knizhnik and A.B. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
S. Fredenhagen and T. Quella, Generalised permutation branes, JHEP 11 (2005) 004 [hep-th/0509153] [INSPIRE].
I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [INSPIRE].
Acknowledgments
The work of H.P. was supported by Armenian SCS grants 21AG-1C060, 20TTWS-1C035, and ANCEF 22AN:PS-mathph-2697. A.P. acknowledge the support in the framework of Armenian SCS grants 20TTWS-1C035, 21AG-1C062.
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Poghosyan, A., Poghosyan, H. A note on RG domain wall between successive \( {A}_2^{(p)} \) minimal models. J. High Energ. Phys. 2023, 72 (2023). https://doi.org/10.1007/JHEP08(2023)072
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DOI: https://doi.org/10.1007/JHEP08(2023)072