Parity-violating scalar-tensor theory

We investigate the parity-violating scalar-tensor theory and pay special attention to terms that are free of the Ostrogradsky ghost in the unitary gauge, i.e., when the scalar field possesses a timelike gradient. We exhaustively identify the generally covariant scalar-tensor theory (GST) monomials with parity violation up to

d = 4

, where

d

is the total number of derivatives in the unitary gauge. According to the correspondence between GST terms and the spatially covariant gravity (SCG) terms in the unitary gauge, we also exhaustively identify the SCG monomials with parity violation up to

d = 4

, where the Lie derivatives of the extrinsic curvature and the lapse function are necessarily introduced. We find a total of nine independent parity-violating SCG monomials, of which seven contain no higher-order Lie derivatives and are thus automatically free of ghosts, while two involve Lie derivatives of the extrinsic curvature and the lapse function and are thus potentially dangerous. By explicitly deriving their generally covariant correspondence, we obtain seven independent scalar-tensor terms dubbed the “Qi-Xiu” Lagrangians, which are the most general parity-violating scalar-tensor theories that are ghost-free in the unitary gauge up to

d = 4

. Our results include the existing theories in the literature, such as the Chern-Simons term and the chiral scalar-tensor theories, as special cases.

Note:

33 pages

derivative: Lie
parity: violation
field theory: scalar
scalar tensor
unitary gauge
covariance
ghost
curvature
gravitation
chiral

References(98)

Figures(0)

[1]

Question of Parity Conservation in Weak Interactions

T.D. Lee
(
- Columbia U.
)
,
Chen-Ning Yang
(
- Brookhaven
)

- Phys.Rev. 104 (1956) 254-258,
- Erratum - ibid. 106 (1957) 1371,
- Also in *Yang, C.N.: Selected Papers 1945-1980*, 189-193
•
DOI:
- 10.1103/PhysRev.104.254

[2]

Experimental Test of Parity Conservation in $\beta$ Decay

- Phys.Rev. 105 (1957) 1413-1414,
- In *Cahn, R.N., Goldhaber, G.: The experimental foundations of particle physics* 171-172
•
DOI:
- 10.1103/PhysRev.105.1413

[3]

New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Data

Yuto Minami
(
- KEK, Tsukuba
)
,
Eiichiro Komatsu
(
- Garching, Max Planck Inst. and
- Tokyo U.
)

- Phys.Rev.Lett. 125 (2020) 22, 221301
•
e-Print:
- 2011.11254
•
DOI:
- 10.1103/PhysRevLett.125.221301

[4]

Improved constraints on cosmic birefringence from the WMAP and Planck cosmic microwave background polarization data

Johannes R. Eskilt
(
- Oslo U.
)
,
Eiichiro Komatsu
(
- Garching, Max Planck Inst. and
- Tokyo U., IPMU
)

- Phys.Rev.D 106 (2022) 6, 063503
•
e-Print:
- 2205.13962
•
DOI:
- 10.1103/PhysRevD.106.063503

[5]

New physics from the polarized light of the cosmic microwave background

Eiichiro Komatsu
(
- Garching, Max Planck Inst. and
- Tokyo U., IPMU
)

- Nature Rev.Phys. 4 (2022) 7, 452-469,
- Nature Rev.Phys. 4 (2022) 452-469
•
e-Print:
- 2202.13919
•
DOI:
- 10.1038/s42254-022-00452-4

[6]

Probing Lorentz-violating electrodynamics with CMB polarization

Luca Caloni
(
- Ferrara U. and
- INFN, Ferrara
)
,
Serena Giardiello
(
- Ferrara U. and
- INFN, Ferrara and
- Cardiff U.
)
,
Margherita Lembo
(
- Ferrara U. and
- INFN, Ferrara
)
,
Martina Gerbino
(
- Ferrara U. and
- INFN, Ferrara
)
,
Giulia Gubitosi
(
- Naples U. and
- INFN, Naples
)

et al.

- JCAP 03 (2023) 018
•
e-Print:
- 2212.04867
•
DOI:
- 10.1088/1475-7516/2023/03/018

[7]

Reexamining aspects of spacetime-symmetry breaking with CMB polarization

- Phys.Rev.D 109 (2024) 1, 015032
•
e-Print:
- 2311.16368
•
DOI:
- 10.1103/PhysRevD.109.015032

[8]

PARITY VIOLATION IN METRIC TORSION THEORIES OF GRAVITATION

- Phys.Rev.D 22 (1980) 1915-1921
•
DOI:
- 10.1103/PhysRevD.22.1915

[9]

Some Properties of O(32) Superstrings

Edward Witten
(
- Princeton U.
)

- Phys.Lett.B 149 (1984) 351-356,
- IN *DINE, M. (ED.): STRING THEORY IN FOUR DIMENSIONS* 43-48. (PHYS. LETT. B149 (1984) 351-356) AND PREPRINT - WITTEN, E. (REC.NOV.84) 12 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0370-2693(84)90422-2

[10]

Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory

Michael B. Green
(
- Queen Mary, U. of London and
- Caltech
)
,
John H. Schwarz
(
- Caltech
)

- Phys.Lett.B 149 (1984) 117-122,
- In *Schwarz, J.H. (ed.): Superstrings, Vol. 2*, 1007-1012,
- In *Ferrara, S. (ed.): Supersymmetry, Vol. 2*, 1300-1305,
- In *Appelquist, T. (ed.) et al.: Modern Kaluza-Klein theories*, 608-613,
- In *Salam, A. (ed.), Sezgin, E. (ed.): Supergravities in diverse dimensions, vol. 2* 1146-1151,
- In *Bohm, A. et al.: Dynamical groups and spectrum generating algebras, vol. 2* 912-917,
- In *Froggatt, C.D., Nielsen, H.B.: Origin of symmetries* 450-455
•
DOI:
- 10.1016/0370-2693(84)91565-X