Translational symmetry breaking in field theories and the cosmological constant

Translational symmetry breaking in field theories and the cosmological constant

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q¯q and q¯F(2n)q. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.

1-9

Evans, Nick

33dfbb52-64dd-4c1f-9cd1-074faf2be4b3

Morris, Tim R.

a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Scott, Marc

4a6abe2e-59fb-4a70-8452-7c13bd0c5ce2

22 January 2016

Evans, Nick

33dfbb52-64dd-4c1f-9cd1-074faf2be4b3

Morris, Tim R.

a9927d31-7a12-4188-bc35-1c9d3a03a6a6

Scott, Marc

4a6abe2e-59fb-4a70-8452-7c13bd0c5ce2

Evans, Nick, Morris, Tim R. and Scott, Marc
(2016)
Translational symmetry breaking in field theories and the cosmological constant.
*Physical Review D*, 93 (2), .
(doi:10.1103/PhysRevD.93.025019).

## Abstract

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q¯q and q¯F(2n)q. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.

Text

** __soton.ac.uk_UDE_PersonalFiles_Users_skr1c15_mydocuments_eprints_PHYSICS_morris_1507.02965v2.pdf
- Accepted Manuscript**
## More information

Accepted/In Press date: 4 January 2016

Published date: 22 January 2016

Organisations:
Theoretical Partical Physics Group

## Identifiers

Local EPrints ID: 397592

URI: https://eprints.soton.ac.uk/id/eprint/397592

ISSN: 1550-7998

PURE UUID: 16443521-f22f-44e4-b95c-5adbdb2bd4b6

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Date deposited: 04 Jul 2016 12:26

Last modified: 20 Jul 2019 01:27

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## Contributors

Author:
Marc Scott

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