String Axions: The Very Basics Johar M. Ashfaque University of Liverpool
April 20, 2014
Johar M. Ashfaque
Mathematical Physics
Introduction
What follows is a very basic introduction to axions.
Johar M. Ashfaque
Mathematical Physics
References
F. Wilczek Problem of Strong P and T Invariance in the Presence of Instantons Phys.Rev.Lett. 40 (1978) 279 L.J. Rosenberg, Searching for the Axion, http://www.slac. stanford.edu/econf/C040802/papers/MOT002.PDF R.D. Peccei, H. R. Quinn, CP Conservation in the Presence of Pseudoparticles, Phys.Rev.Lett. 38 (1977) 1440 S. Weinberg, A new light boson?, Phys.Rev.Lett. 40 (1978) 223
Johar M. Ashfaque
Mathematical Physics
The CPT Theorem
Any local relativistic quantum field theory must also be invariant under the composition of the discrete symmetries CPT, where C is charge conjugation, P is parity reflection and T is time reversal.
Johar M. Ashfaque
Mathematical Physics
U(1)A Symmetry
U(1)A symmetry is not a true symmetry of QCD.
Johar M. Ashfaque
Mathematical Physics
Strong CP Problem
NEDM ⇒ θ be small. Experimental bound to date is ∼ 2.9 × 10−26 e cm. Why θ ∼ 10−9 and does not take the values between 0 and 2π?
Johar M. Ashfaque
Mathematical Physics
U(1)PQ Symmetry
θG G where G is the gluon field strength with its dual given by G and θ = θ + arg det M with M being the quark mass matrix.
Johar M. Ashfaque
Mathematical Physics
Axions
PQ symmetry requires a new light, weakly coupled particle called the axion (Weinberg, Wilczek). Axions are pseudo-Goldstone bosons and are the only solution to strong CP problem compatible with CP violation.
Johar M. Ashfaque
Mathematical Physics
Axions in String Theory
Axions are pseudoscalar fields enjoying PQ shift symmetries of the form a 7→ a + αfa where a is the axion field, fa is the decay constant with α being an arbitrary constant. Axions arise in string compactifications from the integration of p-form gauge potentials over p-cycles of the compact space. The continuous shift symmetry holds to all orders in perturbation theory but is broken by instanton effects.
Johar M. Ashfaque
Mathematical Physics
Sakharov Criteria
Particle physics can produce matter/anti-matter asymmetry in the early universe if there is Baryon Number Violation CP and C Violation Departure from Thermal Equilibrium.
Johar M. Ashfaque
Mathematical Physics