Topological Defects| Topological Defects |
In General > s.a. defects / einstein-cartan theory;
quantum systems; solitons; torsion.
* Origin: They may form whenever
a symmetry breaking phase transition occurs.
* Examples: Vortex lines in type II
superconductors or liquid helium; Declination lines in liquid crystals; Phase transitions
in the early universe; Kinks in φ4 theory
and Sine-Gordon solitons as domain walls in 1+1 dimensions.
* Classification: To study the kinds
of defects that a field can have, consider the field as a map φ:
M 3\ X → V, where
M 3 is a connected, orientable, compact
3-manifold, X a set of defects, and V a topological space;
Then φ cannot have
(i) point defects if π2(M 3\ X) = 0;
(ii) line defects if π1(M 3\ X) = 0;
(iii) wall defects if π0(M 3\ X) = 0.
@ General references: Hindmarsh & Rajantie PRL(00) [formation, in U(1) gauge theory];
Blasone et al mp/04-en [in quantum field theory];
Vitiello a0807
[in quantum field theory, fractals and coherent states];
del Campo & Zurek IJMPA(14) [symmetry breaking and universality];
Ang & Prakash a1810 [classification].
@ And Lorentz symmetry breaking: Lubo PRD(05)hp/04;
Seifert proc(14)-a1403.
Cosmological Defects, Theory
> s.a. cosmic strings; monopoles.
* Hybrid defects: Various types
of composite topological defects are possible; For example, monopoles tied to
strings can form "dumbbells" and "necklaces".
@ General references: Kibble JPA(76)
+ commentary Hindmarsh JPA(16)-a1612;
Vilenkin in(97)ap/96;
París & Roca NPB(98)ht/97 [effective dynamics],
ht/98 [supersymmetric];
Olasagasti PRD(01) [gravitational field];
Borsanyi & Hindmarsh PRD(08) [semiclassical decay];
Avelino & Sousa PRD(16)-a1511,
Martins & Cabral PRD(16)-a1602,
Avelino a2001 [models of network evolution];
Mukhopadhyay et al a2009 [formation, density estimates].
@ Domain walls: Chamblin & Eardley PLB(00)ht/99 [punctures];
Cvetič & Wang PRD(00)ht/99 [in d dimensions];
Bento & Lemos PRD(01)gq [and gravitational radiation];
Pogosian & Vachaspati PRD(03)ht/02;
Vachaspati ht/02-ln;
Argüelles & Grandi G&C(17)-a1008 [in Hořava gravity];
Pospelov et al PRL(13)-a1205
+ Phy(13)
[terrestrial experiments to detect wall-crossing events using magnetic-field detectors];
> s.a. Cosmic Balloons; cosmological acceleration.
@ Domain wall neworks: Avelino et al PLB(05) [evolution, simulations],
PRD(06) [junctions and dynamics];
Eto et al PRD(07);
Menezes PhD(07)-a0808 [and cosmological acceleration];
Sousa & Avelino PRD(10)-a1101 [PRS algorithm],
a1507/PRD [and cmb anisotropies].
@ Textures: Turok PRL(89);
Spergel & Turok SA(92)mar;
Durrer & Zhou PRL(95) [structure formation];
Garcia de Andrade gq/99 [teleparallel];
Lichtensteiger & Durrer PRD(99)ap [static];
Chakraborty & Rahaman NCB(00) [gravitational fields];
Speight LMP(05) [homotopy classification];
Cruz et al Sci(07)-a0710
+ pw(07)oct [and cmb];
Feeney et al PRL(12)
+ news ucl(12)jun [no evidence in the cmb].
@ Necklaces: Berezinsky & Vilenkin PRL(97)ap [and UHECR];
Siemens et al NPB(01);
Kibble & Vachaspati JPG(15)-a1506 [monopoles tied to strings].
@ In lattice theories: Davis et al JHEP(00)hl [lattice gauge theory];
> s.a. ising models.
@ Related topics: Carroll & Trodden PRD(98)ht/97 [Dirichlet];
Cho & Vilenkin PRD(99),
PRD(99)gq/98 [vacuumless];
Kholodenko JGP(00) [2+1 dimensions];
Aharonov & Reznik PRL(00) [local/non-local duality];
Bowick et al JHEP(03) [of various dimensions];
Stoica AIP(07)-a0708 [and brane inflation];
Zhang et al JCAP(15)-a1501 [spontaneous nucleation in the multiverse].
Cosmological Defects, Phenomenology
> s.a. sources of gravitational radiation;
supermassive black holes.
* Motivation: In models with large
extra dimensions, topological defects provide a mechanism by which (3+1)-dimensional
branes appear in a higher-dimensional bulk.
@ General references:
Vachaspati hp/97-ln [formation],
98,
ap/99-ln,
hp/01-ln;
Jiang & Duan JMP(00)ht/99 [classification];
Kibble cm/02-ln;
Sakellariadou hp/02-ln;
Rajantie CP(03)ap;
Nitta PRD(12)-a1205 [defect formation from defect-antidefect annihilations];
Mukhopadhyay et al a2004 [formation from the quantum vacuum].
@ Detection: Pustelny et al a1303
+ news tr(13)mar [GNOME, Global Network of Optical Magnetometers for Exotic physics].
@ Large-scale structure: Durrer et al PRP(02)ap/01;
Bevis et al PRD(04)ap [WMAP].
@ Cosmological phase transitions:
Lilley & Ferrera PRD(01) [first-order];
Stephens PhD(00)hp/01;
Meierovich PRD(10)-a1009 [vector order parameter];
> s.a. phase transitions.
@ And cmb anisotropy:
Riazuelo et al PRD(00)ap/99;
Bouchet et al PRD(02);
Fraisse ap/05/PRL [bounds from WMAP data];
Lizarraga et al PRD(14)-a1408 [in both temperature and polarization].
@ Domain walls: Friedland et al PRD(03)ap/02,
Avelino et al PRD(06) [as dark energy];
Pospelov et al PRL(13)-a1205 [constraints];
Dai et al a2105 [interaction with macroscopic classical objects].
@ Other effects: Marques & Bezerra PRD(02) [H atom energy levels];
Moss & Pogosian PRL(14)-a1403 [cmb polarization and BICEP2].
In Solid State Physics and Other Fields
> s.a. defects; Order [topological order].
@ General references: Gómez-Ruiz et al PRL(20) [counting statistics of topological defects].
@ Defects in the lab: Zurek PRP(96)cm;
Vachaspati CP(98)hp;
Kibble PhyC(02)cm/01-proc,
cm/02-ln,
PT(07)sep.
@ Liquid crystals: Sci < 1996 [simulations];
Ray & Srivastava PRD(04)ht/01 [correlations].
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