BF Theory| 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(B ∧ F) .
@ 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 EPJC(16)-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 CMP(20)-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: General relativity
is not a topological theory, but one can write down its action as that of
a BF theory (B ∧ F, with B = e ∧
e) with an added term of the type *B ∧ F,
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 (B ∧ F + \(1\over2\)b φabcd Bab ∧ Bcd) 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];
Gonzalez et al PRD(18)-a1806
[polynomial in the B field, (complex) general relativity and anti-self-dual gravity].
@ 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 [and matter fields];
Celada & Montesinos CQG(12)-a1209 [Lorentz-covariant Hamiltonian analysis];
Berra-Montiel et al CQG(19)-a1901 [polysymplectic formulation];
Montesinos & Celada PRD(20)-a1912 [canonical analysis with no second-class constraints].
@ 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];
Oliveira a1801-PhD [BFCG theory, categorical generalization];
Celada et al a2010,
Montesinos et al GRG(21) [in n dimensions, canonical].
> 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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