Chern-Simons Field Theory  

In General > s.a. topological field theories / 3D manifolds; Chern-Simons Function; graph invariants.
* Idea: A topological field theory with action given by

\[S^~_{\rm CS} = {\textstyle{1\over2}\int_M} {\rm tr}[A \wedge {\rm d}A + {\textstyle{2\over3}}\,A \wedge A \wedge A]\,.\]

* Use in gauge theories: One can define a state which satisfies \((E \pm {\rm i}B)\, \psi = 0\), the exponential (Kodama) state

\[ \psi^{~}_{CS} = \exp\{\pm\, 2\pi\, S^~_{\rm CS}/g^2\}\,.\]

@ General references: Jackiw ln(89); Dijkgraaf & Witten CMP(90); Kanno LMP(90); Van Baal APPB(90); Grossmann pr(90); Deser mp/98-in [mathematics and physics]; Zanelli AIP(08)-a0805 [uses]; Freed a0808-conf, BAMS(09) [remarks]; Alekseev & Mnëv CMP(11) [1D toy version]; Pisarski a2103 [history, Jackiw].
@ Books: Dunne 95 [self-dual]; Hu 01 [Jones, Gromov-Floer, Donaldson, etc].
@ Hamiltonian formulation: Banerjee & Chakraborty AP(96) [and fermions]; Kim et al JPA(99)ht/98 [symplectic structure, constraints]; Escalante & Carbajal AP(11)-a1107 [and Pontrjagin theory].
@ Loops / braids: Awada MPLA(89), CMP(90); Smolin MPLA(89); Guadagnini PLB(90), et al NPB(90), NPB(90).
@ Symmetries: Kim et al MPLA(98)ht [Lagrangian approach]; Borowiec et al JPA(98) [and conservation].
@ Solutions: Duval & Horvathy in(97)ht/03 [applications, vortices]; Ivanova & Popov JNMP(00)ht/99 [and symmetries]; Horvathy & Zhang PRP(09) [vortices].
@ With matter / sources: Boyanovsky PRD(90); Kohler CQG(95) [point particles as defects]; Giombi et al EPJC(12)-a1110 [vector fermions].

Quantization > s.a. quantization of first-class constraints.
@ General references: Dunne et al AP(89) [Schrödinger representation]; Dunne & Trugenberger MPLA(89) [on Σg × \(\mathbb R\)]; Danielsson PLB(89); Elitzur et al NPB(89); Killingback PLB(89); Ogura PLB(89) [path integral]; Murayama ZPC(90); Labastida et al NPB(91); Witten CMP(91) [complex group]; Buffenoir & Roche CMP(96)qa/95 [combinatorial]; Guo & Zhao CTP(98)ht [quantization of coefficient]; Gukov CMP(05)ht/03 [SL(2, \(\mathbb C\))]; Meusburger & Schroers ATMP(03)ht, NPB(05)ht/03 [group G × g*]; Constantinidis et al CQG(10)-a0907 [canonical, loop quantization]; Guadagnini JPA(11) [perturbative equivalence of the path-integral formalism and the field operator approach].
@ With sources: Buffenoir & Roche ht/05.
@ Kodama state: Oda ht/03; Corichi & Cortez PRD(04)ht/03.

Chern-Simons Modified Gravity > s.a. 3D gravity; Topologically-Massive Gravity.
* Motivation: One of the possible low-energy consequences of string theory is the addition of a Chern-Simons term to the standard Einstein-Hilbert action of general relativity.
@ Reviews: Zanelli ht/05-ln, Hassaine & Zanelli 16 [Chern-Simons (super)gravity]; Alexander & Yunes PRP(09)-a0907; Bergshoeff et al LNP(15)-a1402.
@ General references: Alexander & Yunes PRD(08)-a0805 [and fermions]; Bonora et al CQG(11)-a1105 [and spherical symmetry]; Zanelli CQG(12)-a1208 [CS forms in gravitation theories]; Díaz et al JPA(12)-a1311 [generalized action]; Delsate et al PRD(15)-a1407 [dynamical Chern-Simons gravity, initial-value formulation]; > s.a. parity [violation]; sources of gravitational radiation and space-based detectors.
@ Black holes: Quinzacara & Salgado PRD(12)-a1401 [spherical]; Vincent CQG(14) [rotating, vs Kerr black holes]; Cárdenas-Avendaño et al CQG(18) [fourth constant of motion]; > s.a. black-hole perturbations; black-hole phenomenology.
@ Other phenomenology: Smith et al PRD(08) [effects on bodies orbiting the Earth]; Konno et al PRD(08) [flat rotation curves]; Garfinkle et al PRD(10)-a1007 [linear stability and speed of gravitational waves]; Bhattacharyya & Shankaranarayanan PRD(19)-a1812 [gravitational wave polarization]; > s.a. modified newtonian gravity [post-Newtonian formalism].

Related Topics > s.a. anomaly; bundle [gerbes]; particle statistics; solitons.
@ On manifolds with boundary: Park NPB(99)ht/98; Gallardo & Montesinos JPA(11)-a1008 [formulation as boundary field theory]; > s.a. gauge theories.
@ And knots / links: Witten NPB(89) [and integrable lattice models]; Leal ht/99-conf; Buniy & Kephart ht/06 [Wilson lines and higher-order invariants]; > s.a. knot invariants; knots in physics.
@ Maxwell-Cherm-Simons theory: Kant & Klinkhamer NPB(05)ht [in curved spacetime]; Blasi et al CQG(10)-a1002 [with boundary].
@ And 3-manifold theory: Freed & Gompf PRL(91); Ivanova & Popov ht/01-proc [and cohomology].
@ Higher-dimensional: Bañados et al NPB(96) [D > 2+1]; Smolin ht/97 [11D, from M-theory]; Barcelos-Neto & Marino EPL(02)ht/01 [generalized]; Mišković et al PLB(05)ht [5D, canonical formalism]; Izaurieta et al PLB(09)-a0905 [5D, and gravity]; Gallot et al JMP(13)-a1207 [abelian, and their link invariants]; Camarero et al NPB(17)-a1706 [and supergravity]; Tchrakian a1712-conf [in all dimensions].
@ Discrete: Hu & Sant'Anna IJTP(04) [on a discrete space]; Sun et al PRB(15)-a1502 [on arbitrary graphs].
@ Deformations: Bimonte et al PLB(97); Mukherjee & Saha MPLA(06) [non-commutative]; Meusburger & Schroers NPB(09)-a0805 [generalized, and \(\kappa\)-Poincaré symmetry]; Kupriyanov EPJC(19)-a1905 [non-commutative].
@ Other generalizations: Lemes et al PRD(99) [perturbed]; Edelstein & Zanelli JPCS(06)ht [Chern-Simons-like (super)gravity in odd dimensions]; Brito et al PLB(08)-a0709 [with Lorentz-breaking term]; Engquist & Hohm FdP(08)-a0804 [higher-spin theories]; Bandres et al JHEP(08)-a0807 [ABJM theory]; Willison & Zanelli a0810 [on a cell complex]; Kulshreshtha et al PS(09) [Chern-Simons-Higgs theory]; D'Adda et al PLB(17)-a1609 [quaternion-based]; Cremonini & Grassi a1912 [super-Chern-Simons theory].
@ Other topics: Labastida & Ramallo PLB(89), PLB(89) [operator formalism]; Killingback CQG(90) [non-semisimple]; Müller-Hoissen NPB(90); Sonnenschein PRD(90); Park & Park PRD(98), IJMPA(09) [gauge-invariant]; Khare in(00)ht/99 [2+1 fractional statistics]; Muslih NPPS(02)ht [Hamilton-Jacobi]; Borowiec et al IJGMP(06) [covariant Lagrangian].

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