Built on

F. E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions , Phys. Rev. 110
1958
Earlier work this paper cites.
H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems , Proc. Roy. Soc. Lond. A269
1962
Earlier work this paper cites.
R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times , Proc. Roy. Soc. Lond. A270
1962
Earlier work this paper cites.
S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current , Phys. Rev. 137
1965
Earlier work this paper cites.
S. Weinberg, Infrared photons and gravitons , Phys. Rev. 140
1965
Earlier work this paper cites.
J. A. Cronin, Phenomenological model of strong and weak interactions in chiral U(3) x U(3) , Phys. Rev. 161
1967
Earlier work this paper cites.
S. Weinberg, Dynamical approach to current algebra , Phys. Rev. Lett. 18
1967
Earlier work this paper cites.
S. Weinberg, Nonlinear realizations of chiral symmetry , Phys. Rev. 166
1968
Earlier work this paper cites.
T. H. Burnett and N. M. Kroll, Extension of the low soft photon theorem , Phys. Rev. Lett. 20
1968
Earlier work this paper cites.
J. Wess and B. Zumino, Consequences of anomalous ward identities , Physics Letters B 37
1971
Earlier work this paper cites.
G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int. J. Theor. Phys. 10
1974
Earlier work this paper cites.
E. Witten, Global aspects of current algebra , Nuclear Physics B 223
1983
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes , Nucl. Phys. B435
1995
Earlier work this paper cites.
E. Witten, Perturbative gauge theory as a string theory in twistor space , Commun. Math. Phys. 252
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory , Phys. Rev. D70
2004
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl. Phys. B715
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, The Amplituhedron , JHEP 10
Original
2007
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory? , JHEP 09
Original
2010
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory , Phys. Rev. D82
Original
2010
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-Matrix in Twistor Space , JHEP 03
Original
2010
Earlier work this paper cites.

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2016

A Periodic Table of Effective Field Theories

Cheung, Clifford, Kampf, Karol, Novotny, Jiri et al.

Understand

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix.

To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension.
Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space.
Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior.

Built on

F. E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions , Phys. Rev. 110
1958
Earlier work this paper cites.
H. Bondi, M. G. J. van der Burg and A. W. K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems , Proc. Roy. Soc. Lond. A269
1962
Earlier work this paper cites.
R. K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times , Proc. Roy. Soc. Lond. A270
1962
Earlier work this paper cites.
S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current , Phys. Rev. 137
1965
Earlier work this paper cites.
S. Weinberg, Infrared photons and gravitons , Phys. Rev. 140
1965
Earlier work this paper cites.
J. A. Cronin, Phenomenological model of strong and weak interactions in chiral U(3) x U(3) , Phys. Rev. 161
1967
Earlier work this paper cites.
S. Weinberg, Dynamical approach to current algebra , Phys. Rev. Lett. 18
1967
Earlier work this paper cites.
S. Weinberg, Nonlinear realizations of chiral symmetry , Phys. Rev. 166
1968
Earlier work this paper cites.
T. H. Burnett and N. M. Kroll, Extension of the low soft photon theorem , Phys. Rev. Lett. 20
1968
Earlier work this paper cites.
J. Wess and B. Zumino, Consequences of anomalous ward identities , Physics Letters B 37
1971
Earlier work this paper cites.
G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int. J. Theor. Phys. 10
1974
Earlier work this paper cites.
E. Witten, Global aspects of current algebra , Nuclear Physics B 223
1983
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes , Nucl. Phys. B435
1995
Earlier work this paper cites.
E. Witten, Perturbative gauge theory as a string theory in twistor space , Commun. Math. Phys. 252
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory , Phys. Rev. D70
2004
Earlier work this paper cites.
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons , Nucl. Phys. B715
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, The Amplituhedron , JHEP 10
Original
2007
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes , Phys. Rev. D78
Original
2008
Earlier work this paper cites.
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity , Phys. Rev. D79
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory? , JHEP 09
Original
2010
Earlier work this paper cites.
Z. Bern, J. J. M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory , Phys. Rev. Lett. 105
Original
2010
Earlier work this paper cites.
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory , Phys. Rev. D82
Original
2010
Earlier work this paper cites.
N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-Matrix in Twistor Space , JHEP 03
Original
2010
Earlier work this paper cites.