Abstract
We consider defect operators in scalar field theories in dimensions d = 4 − ϵ and d = 6 − ϵ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the defect couplings go to infinity, the bulk theory becomes classical and the quantum defect theory can be solved order by order in perturbation theory. We compute the defect β functions to two loops and study the Renormalization Group flows. The defect fixed points can move and merge, leading to fixed point annihilation; and they exhibit a remarkable factorization property where the c-dependence gets disentangled from the coupling dependence.
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M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
G. Cuomo, Z. Komargodski and A. Raviv-Moshe, Renormalization Group Flows on Line Defects, Phys. Rev. Lett. 128 (2022) 021603 [arXiv:2108.01117] [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
A. Allais and S. Sachdev, Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory, Phys. Rev. B 90 (2014) 035131 [arXiv:1406.3022] [INSPIRE].
G. Cuomo, Z. Komargodski and M. Mezei, Localized magnetic field in the O(N) model, JHEP 02 (2022) 134 [arXiv:2112.10634] [INSPIRE].
G. Cuomo, Z. Komargodski, M. Mezei and A. Raviv-Moshe, Spin impurities, Wilson lines and semiclassics, JHEP 06 (2022) 112 [arXiv:2202.00040] [INSPIRE].
F.K. Popov and Y. Wang, Non-perturbative defects in tensor models from melonic trees, JHEP 11 (2022) 057 [arXiv:2206.14206] [INSPIRE].
D. Rodriguez-Gomez, A scaling limit for line and surface defects, JHEP 06 (2022) 071 [arXiv:2202.03471] [INSPIRE].
A. Bourget, D. Rodriguez-Gomez and J.G. Russo, A limit for large R-charge correlators in \( \mathcal{N} \) = 2 theories, JHEP 05 (2018) 074 [arXiv:1803.00580] [INSPIRE].
G. Arias-Tamargo, D. Rodriguez-Gomez and J.G. Russo, The large charge limit of scalar field theories and the Wilson-Fisher fixed point at ϵ = 0, JHEP 10 (2019) 201 [arXiv:1908.11347] [INSPIRE].
M. Watanabe, Accessing large global charge via the ϵ-expansion, JHEP 04 (2021) 264 [arXiv:1909.01337] [INSPIRE].
G. Badel, G. Cuomo, A. Monin and R. Rattazzi, The ϵ-expansion Meets Semiclassics, JHEP 11 (2019) 110 [arXiv:1909.01269] [INSPIRE].
L.A. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 1 [arXiv:2008.03308] [INSPIRE].
G. Cuomo, M. Mezei and A. Raviv-Moshe, Boundary conformal field theory at large charge, JHEP 10 (2021) 143 [arXiv:2108.06579] [INSPIRE].
M. Beccaria, S. Giombi and A. Tseytlin, Non-supersymmetric Wilson loop in \( \mathcal{N} \) = 4 SYM and defect 1d CFT, JHEP 03 (2018) 131 [arXiv:1712.06874] [INSPIRE].
M. Beccaria and A.A. Tseytlin, On non-supersymmetric generalizations of the Wilson-Maldacena loops in N = 4 SYM, Nucl. Phys. B 934 (2018) 466 [arXiv:1804.02179] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Higher order RG flow on the Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 01 (2022) 056 [arXiv:2110.04212] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Wilson loop in general representation and RG flow in 1D defect QFT, J. Phys. A 55 (2022) 255401 [arXiv:2202.00028] [INSPIRE].
S. Giombi, S. Komatsu and B. Offertaler, Large charges on the Wilson loop in \( \mathcal{N} \) = 4 SYM: matrix model and classical string, JHEP 03 (2022) 020 [arXiv:2110.13126] [INSPIRE].
S. Giombi, S. Komatsu and B. Offertaler, Large charges on the Wilson loop in \( \mathcal{N} \) = 4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve, JHEP 08 (2022) 011 [arXiv:2202.07627] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Wilson loops in large symmetric representations through a double-scaling limit, JHEP 08 (2022) 253 [arXiv:2206.09935] [INSPIRE].
A. Gimenez-Grau, E. Lauria, P. Liendo and P. van Vliet, Bootstrapping line defects with O(2) global symmetry, JHEP 11 (2022) 018 [arXiv:2208.11715] [INSPIRE].
A. Söderberg, Fusion of conformal defects in four dimensions, JHEP 04 (2021) 087 [arXiv:2102.00718] [INSPIRE].
A.G. Grozin, Lectures on multiloop calculations, Int. J. Mod. Phys. A 19 (2004) 473 [hep-ph/0307297] [INSPIRE].
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Rodriguez-Gomez, D., Russo, J.G. Defects in scalar field theories, RG flows and dimensional disentangling. J. High Energ. Phys. 2022, 167 (2022). https://doi.org/10.1007/JHEP11(2022)167
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DOI: https://doi.org/10.1007/JHEP11(2022)167