Abstract
We study gapped 4d quantum field theories (QFTs) obtained from a relevant deformation of a UV conformal field theory (CFT). For simplicity, we assume the existence of a ℤ2 symmetry and a single ℤ2-odd stable particle and no ℤ2-even particles at low energies. Using unitarity, crossing and the assumption of maximal analyticity we compute numerically a lower bound on the value of the a-anomaly of the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering amplitude of the particle.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part I. QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part II. Two dimensional amplitudes, JHEP 11 (2017) 143 [arXiv:1607.06110] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part III. Higher dimensional amplitudes, JHEP 12 (2019) 040 [arXiv:1708.06765] [INSPIRE].
N. Doroud and J. Elias Miró, S-matrix bootstrap for resonances, JHEP 09 (2018) 052 [arXiv:1804.04376] [INSPIRE].
Y. He, A. Irrgang and M. Kruczenski, A note on the S-matrix bootstrap for the 2d O(N) bosonic model, JHEP 11 (2018) 093 [arXiv:1805.02812] [INSPIRE].
L. Córdova and P. Vieira, Adding flavour to the S-matrix bootstrap, JHEP 12 (2018) 063 [arXiv:1805.11143] [INSPIRE].
A.L. Guerrieri, J. Penedones and P. Vieira, Bootstrapping QCD using pion scattering amplitudes, Phys. Rev. Lett. 122 (2019) 241604 [arXiv:1810.12849] [INSPIRE].
M.F. Paulos and Z. Zheng, Bounding scattering of charged particles in 1 + 1 dimensions, JHEP 05 (2020) 145 [arXiv:1805.11429] [INSPIRE].
A. Homrich, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part IV. Multiple amplitudes, JHEP 11 (2019) 076 [arXiv:1905.06905] [INSPIRE].
J. Elias Miró, A.L. Guerrieri, A. Hebbar, J. Penedones and P. Vieira, Flux tube S-matrix bootstrap, Phys. Rev. Lett. 123 (2019) 221602 [arXiv:1906.08098] [INSPIRE].
L. Córdova, Y. He, M. Kruczenski and P. Vieira, The O(N) S-matrix monolith, JHEP 04 (2020) 142 [arXiv:1909.06495] [INSPIRE].
C. Bercini, M. Fabri, A. Homrich and P. Vieira, S-matrix bootstrap: supersymmetry, Z2, and Z4 symmetry, Phys. Rev. D 101 (2020) 045022 [arXiv:1909.06453] [INSPIRE].
B. Gabai and X. Yin, On the S-matrix of Ising field theory in two dimensions, JHEP 10 (2022) 168 [arXiv:1905.00710] [INSPIRE].
A. Bose, P. Haldar, A. Sinha, P. Sinha and S.S. Tiwari, Relative entropy in scattering and the S-matrix bootstrap, SciPost Phys. 9 (2020) 081 [arXiv:2006.12213] [INSPIRE].
A. Bose, A. Sinha and S.S. Tiwari, Selection rules for the S-matrix bootstrap, SciPost Phys. 10 (2021) 122 [arXiv:2011.07944] [INSPIRE].
M. Correia, A. Sever and A. Zhiboedov, An analytical toolkit for the S-matrix bootstrap, JHEP 03 (2021) 013 [arXiv:2006.08221] [INSPIRE].
M. Kruczenski and H. Murali, The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary, JHEP 04 (2021) 097 [arXiv:2012.15576] [INSPIRE].
A.L. Guerrieri, J. Penedones and P. Vieira, S-matrix bootstrap for effective field theories: massless pions, JHEP 06 (2021) 088 [arXiv:2011.02802] [INSPIRE].
A. Hebbar, D. Karateev and J. Penedones, Spinning S-matrix bootstrap in 4d, JHEP 01 (2022) 060 [arXiv:2011.11708] [INSPIRE].
D. Karateev, S. Kuhn and J. Penedones, Bootstrapping massive quantum field theories, JHEP 07 (2020) 035 [arXiv:1912.08940] [INSPIRE].
D. Karateev, Two-point functions and bootstrap applications in quantum field theories, JHEP 02 (2022) 186 [arXiv:2012.08538] [INSPIRE].
A.L. Guerrieri, A. Homrich and P. Vieira, Dual S-matrix bootstrap. Part I. 2D theory, JHEP 11 (2020) 084 [arXiv:2008.02770] [INSPIRE].
P. Tourkine and A. Zhiboedov, Scattering from production in 2d, JHEP 07 (2021) 228 [arXiv:2101.05211] [INSPIRE].
A. Guerrieri, J. Penedones and P. Vieira, Where is string theory in the space of scattering amplitudes?, Phys. Rev. Lett. 127 (2021) 081601 [arXiv:2102.02847] [INSPIRE].
Y. He and M. Kruczenski, S-matrix bootstrap in 3 + 1 dimensions: regularization and dual convex problem, JHEP 08 (2021) 125 [arXiv:2103.11484] [INSPIRE].
J. Elias Miró and A. Guerrieri, Dual EFT bootstrap: QCD flux tubes, JHEP 10 (2021) 126 [arXiv:2106.07957] [INSPIRE].
A. Guerrieri and A. Sever, Rigorous bounds on the analytic S matrix, Phys. Rev. Lett. 127 (2021) 251601 [arXiv:2106.10257] [INSPIRE].
H. Chen, A.L. Fitzpatrick and D. Karateev, Bootstrapping 2d ϕ4 theory with Hamiltonian truncation data, JHEP 02 (2022) 146 [arXiv:2107.10286] [INSPIRE].
L. Córdova, Y. He and M.F. Paulos, From conformal correlators to analytic S-matrices: CFT1/QFT2, JHEP 08 (2022) 186 [arXiv:2203.10840] [INSPIRE].
J. Albert and L. Rastelli, Bootstrapping pions at large N, JHEP 08 (2022) 151 [arXiv:2203.11950] [INSPIRE].
A. Sinha and A. Zahed, Crossing symmetric dispersion relations in quantum field theories, Phys. Rev. Lett. 126 (2021) 181601 [arXiv:2012.04877] [INSPIRE].
S.D. Chowdhury, K. Ghosh, P. Haldar, P. Raman and A. Sinha, Crossing symmetric spinning S-matrix bootstrap: EFT bounds, SciPost Phys. 13 (2022) 051 [arXiv:2112.11755] [INSPIRE].
H. Chen, A.L. Fitzpatrick and D. Karateev, Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2, arXiv:2207.12448 [INSPIRE].
J. Elias Miro, A. Guerrieri and M.A. Gumus, Bridging positivity and S-matrix bootstrap bounds, arXiv:2210.01502 [INSPIRE].
M. Kruczenski, J. Penedones and B.C. van Rees, Snowmass white paper: S-matrix bootstrap, arXiv:2203.02421 [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].
D. Poland and D. Simmons-Duffin, Snowmass white paper: the numerical conformal bootstrap, in 2022 Snowmass summer study, (2022) [arXiv:2203.08117] [INSPIRE].
Z. Komargodski and A. Schwimmer, On renormalization group flows in four dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
J.L. Cardy, Is there a c theorem in four-dimensions?, Phys. Lett. B 215 (1988) 749 [INSPIRE].
H. Osborn, Derivation of a four-dimensional c theorem, Phys. Lett. B 222 (1989) 97 [INSPIRE].
I. Jack and H. Osborn, Analogs for the c theorem for four-dimensional renormalizable field theories, Nucl. Phys. B 343 (1990) 647 [INSPIRE].
Z. Komargodski, The constraints of conformal symmetry on RG flows, JHEP 07 (2012) 069 [arXiv:1112.4538] [INSPIRE].
M.A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the asymptotics of 4D quantum field theory, JHEP 01 (2013) 152 [arXiv:1204.5221] [INSPIRE].
Z. Komargodski, Renormalization group flows and anomalies, Les Houches Lect. Notes 97 (2015) 255.
V. Niarchos, C. Papageorgakis, A. Pini and E. Pomoni, (Mis-)matching type-B anomalies on the Higgs branch, JHEP 01 (2021) 106 [arXiv:2009.08375] [INSPIRE].
E. Andriolo, V. Niarchos, C. Papageorgakis and E. Pomoni, Covariantly constant anomalies on conformal manifolds, arXiv:2210.10891 [INSPIRE].
D. Karateev, Z. Komargodski, J. Penedones and B. Sahoo, Probing the c-anomaly in 4d QFTs, in progress.
A. Schwimmer and S. Theisen, Spontaneous breaking of conformal invariance and trace anomaly matching, Nucl. Phys. B 847 (2011) 590 [arXiv:1011.0696] [INSPIRE].
A. Sen, Subleading soft graviton theorem for loop amplitudes, JHEP 11 (2017) 123 [arXiv:1703.00024] [INSPIRE].
S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen and M. Verma, Subleading soft theorem for multiple soft gravitons, JHEP 12 (2017) 150 [arXiv:1707.06803] [INSPIRE].
A. Laddha and A. Sen, Sub-subleading soft graviton theorem in generic theories of quantum gravity, JHEP 10 (2017) 065 [arXiv:1706.00759] [INSPIRE].
P. Di Vecchia, R. Marotta, M. Mojaza and J. Nohle, New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order, Phys. Rev. D 93 (2016) 085015 [arXiv:1512.03316] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, Double-soft behavior of the dilaton of spontaneously broken conformal invariance, JHEP 09 (2017) 001 [arXiv:1705.06175] [INSPIRE].
A.L. Guerrieri, Y.-T. Huang, Z. Li and C. Wen, On the exactness of soft theorems, JHEP 12 (2017) 052 [arXiv:1705.10078] [INSPIRE].
D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB, arXiv:1909.09745 [INSPIRE].
C. Lopez and G. Mennessier, Bounds on the π0π0 amplitude, Nucl. Phys. B 118 (1977) 426 [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
H. Elvang, D.Z. Freedman, L.-Y. Hung, M. Kiermaier, R.C. Myers and S. Theisen, On renormalization group flows and the a-theorem in 6d, JHEP 10 (2012) 011 [arXiv:1205.3994] [INSPIRE].
S. Kundu, Renormalization group flows, the a-theorem and conformal bootstrap, JHEP 05 (2020) 014 [arXiv:1912.09479] [INSPIRE].
C.G. Callan Jr., S.R. Coleman and R. Jackiw, A new improved energy-momentum tensor, Annals Phys. 59 (1970) 42 [INSPIRE].
Wolfram research, DiracDelta function, https://functions.wolfram.com/GeneralizedFunctions/DiracDelta/.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2204.01786
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Karateev, D., Marucha, J., Penedones, J. et al. Bootstrapping the a-anomaly in 4d QFTs. J. High Energ. Phys. 2022, 136 (2022). https://doi.org/10.1007/JHEP12(2022)136
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2022)136