SU2 U1 and the nature of light

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SU(2) U(1) and the nature of light
COSMO 2005 31 August 2005 Bonn
Ralf Hofmann Universitäten Frankfurt/Heidelberg
hep-th/0504064 Int. J. Mod. Phys. A 20, 4123
(2005), hep-th/0507033 hep hep-th/0507122,
hep-ph/0508176, hep-th/0508212
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Outline
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Motivation for
SU(2) U(1)
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WMAP 1-year release of temperature map
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temperature-polarization cross correlation at
large angles
?
power spectrum of TE cross correlation excess
compared to primordial prediction ! (reionization
versus mobile electric monopoles at
)
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more motivation

• Universes equation of state
• (slowly rolling Planck-scale axion)

• nontrivial ground state physics related to
• physics of photon propagation?
• (invisible
  ether)
• intergalactic magnetic fields ?
• (condensed, electrically charged monopoles)

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SU(2) Yang-Mills thermodynamics, nonperturbatively
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SU(2) Yang-Mills thermodynamics
at large temperatures spatial coarse-graining
over both
topological fluctuations (large, topology
changing quantum fluctuations, calorons)
plane-wave fluctuations (small quantum
fluctuations, perturbation theory)

• induce magnetic monopole constituents in calorons
• induce interactions between monopoles
• after coarse-graining
• pure-gauge configuration

• provide spatial correlations to resolve the
  infrared catastrophe
• after coarse-graining
• inert adjoint scalar with dependent
  modulus
• quasiparticle masses by Higgs mechanism

Polyakov 1974,Nahm 1980, Lee Lu 1998, Kraan
van Baal 1998, Brower et al. 1998, Diakonov et a.
2004, Ilgenfritz et al. 2005,
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SU(2) Yang-Mills thermodynamics phase diagram
confining
preconfining
deconfining
ground state CVL condensate
(spin-1/2) excitation
single and self-intersecting CVLs

ground state monopole condensate plus
collapsing, closed magnetic flux lines (CVL)
(spin-1)
excitation massive, dual mode apparent
gauge-symmetry breaking
ground state short-lived (attracting) BPS
monopoles and antimonopoles (
) plus dilute, screened
BPS monopoles and antimonopoles (spin-1)
excitations two massive modes one massless
mode apparent gauge-symmetry breaking

Hage-dorn
2nd order
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microscopics of ground-state dynamics
deconfining phase
inert adjoint scalar after spatial
coarse-graining
pure gauge after spatial
coarse-graining
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quasiparticle excitations after spatial
coarse-graining
Yang-Mills scale
quasiparticle mass
effective gauge coupling
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one-loop evolution of with temperature
monopole condensation, decoupling of
magnetic-charge conserving atrractor
SU(2)
SU(3)
magnetic charge of isolated monopole after
screening
monopoles mobile close to phase transition CMB
gets polarized at large angles !
mass of isolated monopole after screening
quasiparticle mass
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pressure at one-loop
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energy density at one-loop
today
small correction to dark-energy content of the
Universe (Planck-scale axion)
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electric-magnetic coincidence
at
electric coupling , magnetic
coupling (dynamically stabilized)

• free photon gas (no screening,
  decoupled )
• 2. (i) not yet a coupling of the photon to the
  monopole condensate
• (ii) photon massless,
• (iii) rest-frame of heat bath not visible in
  single photon propagation (invisible ether),
• (iv) superconductivity of ground state
  (intergalactic magnetic fields ?) barely visible

coincide!
(neither dynamical magnetic charges (screening)
nor condensed electric charges (photon mass)
measureable)
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CMB fluctuations at large angles as radiative
corrections
dominant diagram
subject to compositeness constraints
(plane-wave quantum fluctuations softer than
, harder fluctuations integrated out into
)
radiative corrections to pressure at most 0.2
Herbst, RH, Rohrer 2004
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dominant correction
for
dipole contribution in temperature map of CMB
(computed with upper bound for modulus when
! )
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kinematical plus dynamical generation of dipole
anisotropy ?

• solar system moves w.r.t. CMB rest frame
• km/s
  Peebles Wilkinson 1968
• horizon-volume of solar system moves into
  regions which,
• formerly, were causally disconnected

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Summary and Outlook
Universe today possibly dynamically stabilized at
boundary between deconfining and preconfining
phase of SU(2) Yang-Mills theory of scale
invisible ether structureless condensate of
electric monopoles
(electric-magnetic concidence)
after jump to preconfining phase Universes
ground state
visibly superconducting
monopole condensate small correction to
Universes dark-
energy content
large-angle part of CMB power spectra radiative
corrections in
deconfining
phase of
(mobile and dilute
monopoles)
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Summary and Outlook
future work

• computation of two-loop correction to pressure
  in an FRW background
• at low
• computation of various thermal two-point
  correlators in Minkowski
• space and FRW background with or without axion
  background
• polarization power spectra and CP
  violation
• rate of axion rolling necessary for jump to
  preconfining phase
• (violation of thermal equilibrium)

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(No Transcript)
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Typical situation in thermal perturbation theory
taken from Kajantie et al. 2002
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SU(2)
taken from van Baal Kraan 1998
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Does fluctuate?
quantum mechanically
No !
compositeness scale
thermodynamically
No !
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Thermodynamical self-consistency
pressure (one-loop)
however Higgs-induced masses and ground-state
pressure both - dependent
- derivatives involve also implicit dependences
relations between thermod.quantities
violated
.
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Relaxation to the minima