Abstract
We use analytical bootstrap techniques to study supersymmetric monodromy defects in the critical Wess-Zumino model. In preparation for this result we first study two related systems which are interesting on their own: general monodromy defects (no susy), and the ε-expansion bootstrap for the Wess-Zumino model (no defects). For general monodromy defects, we extend previous work on codimension-two conformal blocks and the Lorentzian inversion formula in order to accommodate parity-odd structures. In the Wess-Zumino model, we bootstrap four-point functions of chiral operators in the ε-expansion, with the goal of obtaining spectral information about the bulk theory. We then proceed to bootstrap two-point functions of chiral operators in the presence of a monodromy defect, and obtain explicit expressions in terms of novel special functions which we analyze in detail. Several of the results presented in this paper are quite general and should be applicable to other setups.
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References
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFTd, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
F. Gliozzi, P. Liendo, M. Meineri and A. Rago, Boundary and Interface CFTs from the Conformal Bootstrap, JHEP 05 (2015) 036 [Erratum ibid. 12 (2021) 093] [arXiv:1502.07217] [INSPIRE].
M. Billó, M. Caselle, D. Gaiotto, F. Gliozzi, M. Meineri and R. Pellegrini, Line defects in the 3d Ising model, JHEP 07 (2013) 055 [arXiv:1304.4110] [INSPIRE].
D. Gaiotto, D. Mazáč and M.F. Paulos, Bootstrapping the 3d Ising twist defect, JHEP 03 (2014) 100 [arXiv:1310.5078] [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Yukawa CFTs and Emergent Supersymmetry, PTEP 2016 (2016) 12C105 [arXiv:1607.05316] [INSPIRE].
J. Rong and N. Su, Bootstrapping the minimal \( \mathcal{N} \) = 1 superconformal field theory in three dimensions, JHEP 06 (2021) 154 [arXiv:1807.04434] [INSPIRE].
A. Atanasov, A. Hillman and D. Poland, Bootstrapping the Minimal 3D SCFT, JHEP 11 (2018) 140 [arXiv:1807.05702] [INSPIRE].
S. Yamaguchi, The ϵ-expansion of the codimension two twist defect from conformal field theory, PTEP 2016 (2016) 091B01 [arXiv:1607.05551] [INSPIRE].
A. Söderberg, Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect, JHEP 03 (2018) 058 [arXiv:1706.02414] [INSPIRE].
S. Giombi, E. Helfenberger, Z. Ji and H. Khanchandani, Monodromy defects from hyperbolic space, JHEP 02 (2022) 041 [arXiv:2102.11815] [INSPIRE].
A. Antunes, Conformal bootstrap near the edge, JHEP 10 (2021) 057 [arXiv:2103.03132] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
A. Bissi, T. Hansen and A. Söderberg, Analytic Bootstrap for Boundary CFT, JHEP 01 (2019) 010 [arXiv:1808.08155] [INSPIRE].
D. Mazáč, L. Rastelli and X. Zhou, An analytic approach to BCFTd, JHEP 12 (2019) 004 [arXiv:1812.09314] [INSPIRE].
A. Kaviraj and M.F. Paulos, The Functional Bootstrap for Boundary CFT, JHEP 04 (2020) 135 [arXiv:1812.04034] [INSPIRE].
A. Gimenez-Grau, P. Liendo and P. van Vliet, Superconformal boundaries in 4 − ϵ dimensions, JHEP 04 (2021) 167 [arXiv:2012.00018] [INSPIRE].
P. Dey and A. Söderberg, On analytic bootstrap for interface and boundary CFT, JHEP 07 (2021) 013 [arXiv:2012.11344] [INSPIRE].
S. Caron-Huot, Analyticity in Spin in Conformal Theories, JHEP 09 (2017) 078 [arXiv:1703.00278] [INSPIRE].
M. Lemos, P. Liendo, M. Meineri and S. Sarkar, Universality at large transverse spin in defect CFT, JHEP 09 (2018) 091 [arXiv:1712.08185] [INSPIRE].
P. Liendo, Y. Linke and V. Schomerus, A Lorentzian inversion formula for defect CFT, JHEP 08 (2020) 163 [arXiv:1903.05222] [INSPIRE].
R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, Conformal Bootstrap in Mellin Space, Phys. Rev. Lett. 118 (2017) 081601 [arXiv:1609.00572] [INSPIRE].
R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, A Mellin space approach to the conformal bootstrap, JHEP 05 (2017) 027 [arXiv:1611.08407] [INSPIRE].
P. Dey, A. Kaviraj and A. Sinha, Mellin space bootstrap for global symmetry, JHEP 07 (2017) 019 [arXiv:1612.05032] [INSPIRE].
P. Dey and A. Kaviraj, Towards a Bootstrap approach to higher orders of ϵ-expansion, JHEP 02 (2018) 153 [arXiv:1711.01173] [INSPIRE].
L.F. Alday, J. Henriksson and M. van Loon, Taming the ϵ-expansion with large spin perturbation theory, JHEP 07 (2018) 131 [arXiv:1712.02314] [INSPIRE].
J. Henriksson and M. Van Loon, Critical O(N) model to order ϵ4 from analytic bootstrap, J. Phys. A 52 (2019) 025401 [arXiv:1801.03512] [INSPIRE].
J. Henriksson, S.R. Kousvos and A. Stergiou, Analytic and Numerical Bootstrap of CFTs with O(m) × O(n) Global Symmetry in 3D, SciPost Phys. 9 (2020) 035 [arXiv:2004.14388] [INSPIRE].
J. Henriksson and A. Stergiou, Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry, SciPost Phys. 11 (2021) 015 [arXiv:2101.08788] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazáč and M.F. Paulos, Bootstrapping SCFTs with Four Supercharges, JHEP 08 (2015) 142 [arXiv:1503.02081] [INSPIRE].
N. Bobev, S. El-Showk, D. Mazáč and M.F. Paulos, Bootstrapping the Three-Dimensional Supersymmetric Ising Model, Phys. Rev. Lett. 115 (2015) 051601 [arXiv:1502.04124] [INSPIRE].
L. Bianchi, A. Chalabi, V. Procházka, B. Robinson and J. Sisti, Monodromy defects in free field theories, JHEP 08 (2021) 013 [arXiv:2104.01220] [INSPIRE].
J.S. Dowker, Remarks on spherical monodromy defects for free scalar fields, arXiv:2104.09419 [INSPIRE].
M. Isachenkov, P. Liendo, Y. Linke and V. Schomerus, Calogero-Sutherland Approach to Defect Blocks, JHEP 10 (2018) 204 [arXiv:1806.09703] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT, JHEP 03 (2017) 086 [arXiv:1612.08471] [INSPIRE].
D. Simmons-Duffin, D. Stanford and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, JHEP 07 (2018) 085 [arXiv:1711.03816] [INSPIRE].
A. Bissi, P. Dey and T. Hansen, Dispersion Relation for CFT Four-Point Functions, JHEP 04 (2020) 092 [arXiv:1910.04661] [INSPIRE].
J. Barrat, A. Gimenez-Grau and P. Liendo, Bootstrapping holographic defect correlators in \( \mathcal{N} \) = 4 super Yang-Mills, JHEP 04 (2022) 093 [arXiv:2108.13432] [INSPIRE].
E. Lauria, P. Liendo, B.C. Van Rees and X. Zhao, Line and surface defects for the free scalar field, JHEP 01 (2021) 060 [arXiv:2005.02413] [INSPIRE].
C. Behan, L. Di Pietro, E. Lauria and B.C. Van Rees, Bootstrapping boundary-localized interactions, JHEP 12 (2020) 182 [arXiv:2009.03336] [INSPIRE].
L. Bianchi and M. Lemos, Superconformal surfaces in four dimensions, JHEP 06 (2020) 056 [arXiv:1911.05082] [INSPIRE].
A. Kaviraj, S. Rychkov and E. Trevisani, Random Field Ising Model and Parisi-Sourlas supersymmetry. Part I. Supersymmetric CFT, JHEP 04 (2020) 090 [arXiv:1912.01617] [INSPIRE].
A. Kaviraj, S. Rychkov and E. Trevisani, Random field Ising model and Parisi-Sourlas supersymmetry. Part II. Renormalization group, JHEP 03 (2021) 219 [arXiv:2009.10087] [INSPIRE].
J. Liu, D. Meltzer, D. Poland and D. Simmons-Duffin, The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT, JHEP 09 (2020) 115 [Erratum ibid. 01 (2021) 206] [arXiv:2007.07914] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].
L.F. Alday, Solving CFTs with Weakly Broken Higher Spin Symmetry, JHEP 10 (2017) 161 [arXiv:1612.00696] [INSPIRE].
L.F. Alday, J. Henriksson and M. van Loon, An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2, JHEP 01 (2020) 063 [arXiv:1907.02445] [INSPIRE].
M. Lemos, B.C. van Rees and X. Zhao, Regge trajectories for the (2, 0) theories, JHEP 01 (2022) 022 [arXiv:2105.13361] [INSPIRE].
D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [INSPIRE].
N. Bobev, E. Lauria and D. Mazáč, Superconformal Blocks for SCFTs with Eight Supercharges, JHEP 07 (2017) 061 [arXiv:1705.08594] [INSPIRE].
N.B. Agmon and Y. Wang, Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines, arXiv:2009.06650 [INSPIRE].
D. Poland and D. Simmons-Duffin, Bounds on 4D Conformal and Superconformal Field Theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, Z.U. Khandker, D. Li, D. Poland and D. Simmons-Duffin, Covariant Approaches to Superconformal Blocks, JHEP 08 (2014) 129 [arXiv:1402.1167] [INSPIRE].
I. Burić and V. Schomerus, Defect Conformal Blocks from Appell Functions, JHEP 05 (2021) 007 [arXiv:2012.12489] [INSPIRE].
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Gimenez-Grau, A., Liendo, P. Bootstrapping monodromy defects in the Wess-Zumino model. J. High Energ. Phys. 2022, 185 (2022). https://doi.org/10.1007/JHEP05(2022)185
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DOI: https://doi.org/10.1007/JHEP05(2022)185