From scale invariance to lorentz symmetry

Physical Review Letters

Volumn 112, Issue 24, 2014, Pages

  Sibiryakov, Sergey ^a,b,c  

^a CERN   (Switzerland)

^b EPFL   (Switzerland)

^c INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; GROUP THEORY;

FINITE VELOCITY; INFINITE DIMENSIONAL; INVARIANT FIELD; LORENTZ; LORENTZ GROUP; OPERATOR ALGEBRAS; SCALE INVARIANCE; STANDARD ASSUMPTIONS;

INVARIANCE;

EID: 84902770678     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.241602     Document Type: Article

References (28)

1. A.B. Zamolodchikov, Pis'ma Zh. Eksp. Teor. Fiz. 43, 565 (1986) PZETAB 0370-274X
2. [A.B. Zamolodchikov JETP Lett. 43, 730 (1986)]. JTPLA2 0021-3640
3. J. Polchinski, Nucl. Phys. B303, 226 (1988). NUPBBO 0550-3213 10.1016/0550-3213(88)90179-4
4. M.A. Luty, J. Polchinski, and R. Rattazzi, J. High Energy Phys. 01 (2013) 152. JHEPFG 1029-8479 10.1007/JHEP01(2013)152
5. A. Dymarsky, Z. Komargodski, A. Schwimmer, and S. Theisen, arXiv:1309.2921.
6. H.B. Nielsen and M. Ninomiya, Nucl. Phys. B141, 153 (1978). NUPBBO 0550-3213 10.1016/0550-3213(78)90341-3
7. S. Chadha and H.B. Nielsen, Nucl. Phys. B217, 125 (1983). NUPBBO 0550-3213 10.1016/0550-3213(83)90081-0
8. R. Iengo, J.G. Russo, and M. Serone, J. High Energy Phys. 11 (2009) 020. JHEPFG 1029-8479 10.1088/1126-6708/2009/11/020
9. G.F. Giudice, M. Raidal, and A. Strumia, Phys. Lett. B 690, 272 (2010). PYLBAJ 0370-2693 10.1016/j.physletb.2010.05.029
10. M.M. Anber and J.F. Donoghue, Phys. Rev. D 83, 105027 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.105027
11. O. Vafek, Z. Tesanovic, and M. Franz, Phys. Rev. Lett. 89, 157003 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.157003
12. M. Franz, Z. Tesanovic, and O. Vafek, Phys. Rev. B 66, 054535 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.66.054535
13. D.J. Lee and I.F. Herbut, Phys. Rev. B 66, 094512 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.66.094512
14. I.F. Herbut, V. Juricic, and B. Roy, Phys. Rev. B 79, 085116 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.79.085116
15. A. Giuliani, V. Mastropietro, and M. Porta, Ann. Phys. (Amsterdam) 327, 461 (2012). APNYA6 0003-4916 10.1016/j.aop.2011.10.007
16. T. Grover, D.N. Sheng, and A. Vishwanath, Science, 344, 280 (2014). SCIEAS 0036-8075 10.1126/science.1248253
17. R. Sundrum, Phys. Rev. D 86, 085025 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.86.085025
18. G. Bednik, O. Pujolàs and S. Sibiryakov, J. High Energy Phys. 11 (2013) 064. JHEPFG 1029-8479 10.1007/JHEP11(2013)064
19. It is worth pointing out the difference from [19] which studies the consequences of chiral scale invariance and, thus, introduces from the beginning a predefined light-cone structure.
20. D.M. Hofman and A. Strominger, Phys. Rev. Lett. 107, 161601 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.161601
21. An elementary example of the latter situation is provided by a theory of several massless fields-scalars or fermions-propagating with different velocities.
22. The reader should not be confused by the relativistic notations: though we use the space-time indices (Equation presented), etc., that take values (Equation presented), we cannot raise or lower them due to the absence of a Lorentz metric. We will, sometime, combine the time and space coordinates into a single vector (Equation presented) with (Equation presented), (Equation presented). Summation over repeated indices is assumed unless stated otherwise.
23. J. Wess, Nuovo Cimento 18, 1086 (1960). NUCIAD 0029-6341 10.1007/BF02733168
24. In fact, it is sufficient to make this assumption only for the level (Equation presented) containing the (improved) EMT.
25. This is trivially valid for a ((Equation presented))-dimensional relativistic theory where the EMT decomposes into the left- and right-moving parts, (Equation presented), and hence, its Fourier transform is localized on the light cone.
26. Note that (Equation presented) is related to the imaginary part of the retarded Green's function in the thermal state: (Equation presented).
27. It cannot contain derivatives of the (Equation presented) function as in the vicinity of (Equation presented) the matrix element (Equation presented) is a product of a positive distribution (Equation presented) and a bounded function (Equation presented).
28. If one imposes invariance under spatial parity, it is possible to show that the eigenvalues (Equation presented) come in sign-symmetric pairs (Equation presented). Then, the partial EMTs (24) can be grouped into EMTs of parity-symmetric subsystems.