BF Theory  

In General > s.a. branes; lattice gauge theory; yang-mills gauge theory.
* Idea: A topological gauge theory, used as model for gravity, with variables a connection Aai and a Lie-elgebra valued 2-form Babi, and action

S = M tr(BF) .

@ General references: Broda in(05)ht [summary].
@ Spin-foam models: Baez LMP(96)qa/95; Baez LNP(00)gq/99; Maran gq/03, gq/03, PRD(04)gq.
@ Discretized: Kawamoto et al NPB(00)ht/99 [4D]; Oriti & Williams PRD(01)gq/00 [and Barrett-Crane model]; Mnev ht/06 [simplicial].
@ Connections: Cattaneo et al JMP(95), CMP(99)m.DG/98; Cattaneo et al LMP(00)m.QA [Wilson loops].
@ Canonical-symplectic form: Mondragón & Montesinos JMP(06)gq/04, Montesinos CQG(06)gq [4D, covariant]; Durka et al PRD(10)-a0912, Durka & Kowalski-Glikman CQG(10)-a1003 [SO(4,1) constrained, and Holst formulation of gravity]; Escalante & Rubalcava-García IJGMP(12)-a1107 [Dirac constraint analysis].
@ Related topics: Waelbroeck CMP(95)gq/93 [flat spacetimes]; Cattaneo et al JMP(95), NPB(95) [knots]; Freidel & Krasnov CQG(99)ht/98 [volume].
@ Massive: Landim & Almeida PLB(01)ht/00 [topological mass, D dimensions]; Landim PLB(02) [D dimensions]; Bizdadea & Saliu a1511 [Abelian, gauge-invariant].
@ With other fields: Leitgeb et al NPB(99)ht [2D with matter]; Bizdadea et al IJMPA(06)-a0704 [3-form gauge fields]; Fairbairn & Pérez PRD(08)-a0709 [extended matter].
@ For Husain-Kuchař model: Barbero & Villaseñor PRD(01)gq/00; Montesinos & Velázquez AIP(09)-a0812.
@ Other versions: Husain & Major NPB(97)gq, Momen PLB(97)ht/96 [bounded regions]; Ikeda JHEP(00)ht, JHEP(01)ht [deformation]; Diakonov & Petrov G&C(02)ht/01 [Yang-Mills and string theory]; Blasi et al NPB(06) [non-commutative, 2D]; Borowiec et al IJGMP(06) [covariant, Lagrangian]; Cattaneo et al a1701 [cellular BF theory].

And Gravity > s.a. first-order actions; 3D gravity; canonical general relativity, connection and other formulations; gravity theories; Simplicity Constraints.
* Idea: Gravity is not a topological theory, but one can write down its action as that of a BF theory (BF, with B = ee) with an added term of the type *BF, with a coefficient that corresponds to the Immirzi parameter.
* Motivation: It is taken as a starting point for spin-foam formulations of quantum gravity.
* Plebański action: For complex general relativity one can write down a modified BF action,

S(A, B, φ) = M (BF + \(1\over2\)b φabcd BabBcd) d4x .

@ General references: Freidel & Speziale Sigma(12)-a1201 [rev]; Cattaneo & Schiavina JMP(16)-a1509; Celada et al CQG(16)-a1610 [rev].
@ Plebański action: Reisenberger CQG(99)gq/98 [complex general relativity]; Buffenoir et al CQG(04) [Hamiltonian analysis]; Ita HJ-a0804, HJ-a0901, a0911-proc, IJMPD(12)-a0705v4, MPLA(12)-a0710v4 [instanton representetation]; Alexandrov CQG(12)-a1202 [degenerate sector, and its spin-foam quantization]; González et al a1204 [gauge and spacetime connections].
@ Modified Plebański action: in Maran gq/05 [SO(4, \(\mathbb C\)) theory]; Krasnov CQG(08)gq/07; Krasnov & Shtanov CQG(08)-a0705; Krasnov CQG(09)-a0811 [without simplicity constraint]; Ramírez & Rosales IJMPA(12)-a0910 [supergravity extension]; Gielen & Oriti CQG(10)-a1004; Gielen JPCS(11)-a1011 [with linear constraints].
@ With arbitrary Immirzi parameter: Holst PRD(96)gq/95 [for Barbero Hamiltonian]; Capovilla et al CQG(01)gq; Montesinos & Velázquez PRD(10)-a1002 [and cosmological constant]; Dupuis & Livine CQG(11)-a1006 [simplicity constraints and coherent intertwiners]; Durka & Kowalski-Glikman PRD(11)-a1103 [Noether charges and AdS-Schwarzschild black-hole entropy]; Montesinos & Velázquez Sigma(11)-a1111 [different forms], PRD(12)-a1112 [with Immirzi parameter and matter fields]; Celada & Montesinos CQG(12)-a1209 [Lorentz-covariant Hamiltonian analysis].
@ With cosmological constant: Miković JPCS(06)gq/05 [as deformed SO(4,1) theory]; de Gracia et al a1702 [Hamilton-Jacobi analysis].
@ Related topics: Constantinidis et al JHEP(02)ht/01 [symmetries and gravity]; Canfora NPB(05)ht [and large-N expansion]; Miković Sigma(06)ht-proc [quantum gravity as broken phase of BF theory]; Cuesta & Montesinos PRD(07); Bonzom CQG(09)-a0903 [and area-angle Regge calculus]; Krasnov IJMPA(09)-a0907 [with potential term for B field]; Mielke PLB(10) [spontaneously broken topological BF theory]; Dupuis & Livine CQG(11)-a1104 [holomorphic simplicity constraints and spin-foam models].
> Related topics: see holography; spherical symmetry.

Quantized > s.a. 2D quantum gravity; Feynman Diagram; loop quantum gravity [BF state].
* Idea: The transition amplitude for the 3D BF theory with cosmological constant is given by the Turaev-Viro state-sum invariant.
@ General references: Cattaneo & Rossi CMP(01)m.QA/00 [n-dimensional, Batalin-Vilkovisky]; Bonzom & Smerlak PRL(12)-a1201 ["cellular quantization" and spin-foam gravity]; Escalante & Cavildo-Sánchez a1607 [Faddeev-Jackiw quantization].
@ Loop quantum gravity approach: Bi & Gegenberg CQG(94)gq/93; Constantinidis et al CQG(12)-a1203 [2D, coupled to topological matter]; Bonzom & Livine JMP(12); Bonzom et al PRD(14)-a1403 [SU(2) BF theory with a (negative) cosmological constant].

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