Vacuum Polarization by Topological Defects with Finite Core

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Vacuum Polarization by Topological Defects with
Finite Core

• Aram Saharian
• Department of Theoretical Physics, Yerevan State
  University,
• Yerevan, Armenia
• International Centre for Theoretical Physics,
  Trieste, Italy
• __________________________________________________
  ______
• Based on E. R. Bezerra de Mello, V. B. Bezerra,
  A. A. Saharian,
• A. S. Tarloyan, Phys. Rev. D74,
  025017 (2006)
• E. R. Bezerra de Mello, A. A.
  Saharian,
• J. High
  Energy Phys. 10, 049 (2006)
• E. R. Bezerra de Mello, A. A.
  Saharian,
• Phys.
  Rev. D75, 065019, 2007
• A. A. Saharian, A. L.
  Mkhitaryan, arXiv0705.2245 hep-th

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Topological defects

• Investigation of topological defects (monopoles,
  strings, domain walls) is fast developing area,
  which includes various fields of physics, like
  low temperature condensed matter, liquid
  crystals, astrophysics and high energy physics
• Defects are generically predicted to exist in
  most interesting models of particle physics
  trying to describe the early universe
• Detection of such structures in the modern
  universe would provide precious information on
  events in the earliest instants after the Big
  Bang and
• Their absence would force a major revision of
  current physical theories
• Recently a variant of the cosmic string formation
  mechanism is proposed in the framework of brane
  inflation

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Quantum effects induced by topological defects

• In quantum field theory the non-trivial topology
  induced by defects leads to non-zero vacuum
  expectation values for physical observables
  (vacuum polarization)
• Many of treatments of quantum fields around
  topological defects deal mainly with the case of
  idealized defects with the core of zero thickness
• Realistic defects have characteristic core radius
  determined by the symmetry breaking scale at
  which they are formed

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Plan

• Positive frequency Wightman function
• Vacuum expectation values (VEVs) for the field
  ...square and the energy-momentum tensor
• Specific model for the core

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Vacuum polarization by a global monopole with
finite core

• Global monopole is a spherical symmetric
  topological defect created by a phase transition
  of a system composed by a self coupling scalar
  field whose original global O(3) symmetry is
  spontaneously broken to U(1)
• Background spacetime is curved (no summation over
  i)
• Metric inside the core with radius

Line element for (D1)-dim global monopole
Solid angle deficit (1-s2)SD
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Scalar field
Field equation
(units h c 1 are used)
Comprehensive insight into vacuum fluctuations is
given by the Wightman function
Complete set of solutions to the field equation
Vacuum expectation values (VEVs) of the field
square and the energy-momentum tensor
Wightman function determines the response of a
particle detector of the Unruh-deWitt type
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Eigenfunctions
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Exterior Wightman function
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Vacuum expectation values
VEV of the field square
For point-like global monopole and for massless
field
µ - renormalization mass scale
B0 for a spacetime of odd dimension
Part induced by the core
On the core boundary the VEV diverges
At large distances (a/rltlt1) the main contribution
comes from l0 mode and for massless field
For long range effects of the core
appear
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Flower-pot model
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Vacuum expectation values inside the core
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VEVs inside the core Asymptotics
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Fermionic field
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VEV of the EMT and fermionic condensate
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Flower-pot model Exterior region
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Asymptotics
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Vacuum polarization by a cosmic string with
finite core
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Specific models for the string core
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Vacuum densities for Z2 symmetric thick brane
in AdS spacetime
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Wightman function outside the brane
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VEVs outside the brane
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Model with flat spacetime inside the brane
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Interior region
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Brane-induced VEVs in the exterior region
Minimally coupled D 4 massless scalar field
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Parts in the interior VEVs induced by AdS geometry
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Conformally coupled D 4 massless scalar field
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For a general static model of the core with
finite support we have presented the exterior
Wightman function, the VEVs of the field square
and the energy-momentum tensor as the sum
.
zero radius defect part core-induced part The
renormalization procedure for the VEVs of the
field square and the energy-momentum tensor is
the same as that for the geometry of zero radius
defects Core-induced parts are presented in terms
of integrals strongly convergent for strictly
exterior points Core-induced VEVs diverge on the
boundary of the core and to remove these surface
divergences more realistic model with smooth
transition between exterior and interior
geometries has to be considered For a cosmic
string the relative contribution of the
core-induced part at large distances decays
logarithmically and long-range effects of the
core appear In the case of a global monopole
long-range effects appear for special value of
the curvature coupling parameter