Chern-Simons Field Theory| 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
* 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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