String theory and CP violation

[bcrowell]

What is wrong with the following reasoning? String theory has diffeomorphism invariance. Since time reversal is a diffeomorphism, string theory is time-reversal invariant. Therefore T and CP violation can't occur in string theory, and string theory can't describe the standard model in the appropriate limit.

 

[humanino]

Several things can go wrong, as symmetries can be broken spontaneously, or dynamically. In some details for a specific construction :
Towards a theory of quark masses, mixings and CP-violation
A recent review can be found in
http://trshare.triumf.ca/~joss/e949/resources/RevModPhys_80_000577-CP_violation.pdf
Rev. Mod. Phys., Vol. 80, No. 2, April–June 2008
Section VII

 

[bcrowell]

Thanks, humanino -- that's very helpful!

Could you, for example, have a classical theory of gravity (say one with the same weak-field limit as GR) that spontaneously broke T or CP symmetry?

[EDIT] WP sort of answered my question. GR has examples of spontaneous symmetry breaking, such as the existence of a preferred frame (the Hubble flow or CMB frame) in cosmological solutions.

 

[humanino]

This is an interesting question. This is in line with what Penrose tries to do : from a classical point of view, he argues that the cosmological time and related entropy issues are visible in the Weyl conformal part of the curvature. His hope is that the ambitwistor "googly" problem will produce CP and T violations eventually. Although he does have the right weak-field limit, I am unsure what has been the progress in the full non-linear graviton case.

 

[bcrowell]

This is an interesting question. This is in line with what Penrose tries to do : from a classical point of view, he argues that the cosmological time and related entropy issues are visible in the Weyl conformal part of the curvature. His hope is that the ambitwistor "googly" problem will produce CP and T violations eventually. Although he does have the right weak-field limit, I am unsure what has been the progress in the full non-linear graviton case.

You're referring to the Weyl curvature hypothesis? I didn't realize that this had anything to do with CP or T...? What is the ambitwistor "googly" problem? Can you point me to a paper on any of this? Thanks!

 

[humanino]

Yes, I am referring to the Weyl curvature hypothesis. It is stated independently of CP or T. However, the proper definition of the graviton relates both in Penrose's twisors, as far as I understand. The best reference I know, you probably already know, it's
http://users.ox.ac.uk/~tweb/00002/index.shtml
Chaos, Solitons and Fractals 10: 581-611.

The ambitwistor formalism consists in an attempt to complexify space-time and treat twistors as "normal" quantum fundamental variables, like position, whose conjugate would be dual twistors.

 

[atyy]

http://prd.aps.org/abstract/PRD/v21/i10/p2742_1
Quantum gravity and time reversibility
Robert M. Wald
The meaning of time-reversal and CPT invariances of a theory is discussed both in the context of theories defined on flat spacetime as well as in general relativity. It is argued that quantum gravity cannot be time-reversal or CPT invariant; that an "arrow of time" must be fundamentally built into the theory. However, a weaker form of CPT invariance could still hold, in which case the fundamental "arrow of time" would not show up in the measurements of observers who perform scattering experiments. Consequences of this weaker hypothesis are explored.

Also interesting, even if not GR-gravity:
http://arxiv.org/abs/hep-th/9307079
White Holes, Black Holes and Cpt in Two Dimensions
Andrew Strominger
It is argued that a unitarity-violating but weakly CPT invariant superscattering matrix exists for leading-order large-N dilaton gravity, if and only if one includes in the Hilbert space Planckian "thunderpop" excitations which create white holes. CPT apparently cannot be realized in a low-energy effective theory in which such states have been integrated out. Rules for computing the leading-large-N superscattering are described in terms of quantum field theory on a single multiply-connected spacetime obtained by sewing the future (past) horizons of the original spacetime with the past (future) horizons of its CPT conjugate. Some difficulties which may arise in going beyond leading order in 1/N are briefly discussed.