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\ XV, 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].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 6 may 2021