메뉴 건너뛰기




Volumn 43, Issue 9, 2011, Pages 2335-2392

An invitation to higher gauge theory

Author keywords

2 category; 2 group; Category; Gerbe; Higher gauge theory; String

Indexed keywords


EID: 80051795956     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-010-1070-9     Document Type: Review
Times cited : (237)

References (96)
  • 1
    • 13244264886 scopus 로고    scopus 로고
    • Nonabelian bundle gerbes, their differential geometry and gauge theory
    • Also available as arXiv:hep-th/0312154
    • Aschieri P., Cantini L., Jurčo B.: Nonabelian bundle gerbes, their differential geometry and gauge theory. Commun. Math. Phys. 254, 367-400 (2005) Also available as arXiv: hep-th/0312154.
    • (2005) Commun. Math. Phys. , vol.254 , pp. 367-400
    • Aschieri, P.1    Cantini, L.2    Jurčo, B.3
  • 2
    • 23044439351 scopus 로고    scopus 로고
    • 8 gauge theory
    • Also available as arXiv:hep-th/0409200
    • 8 gauge theory. JHEP 10, 068 (2004) Also available as arXiv: hep-th/0409200.
    • (2004) Jhep , vol.10 , pp. 068
    • Aschieri, P.1    Jurčo, B.2
  • 3
    • 1542552153 scopus 로고
    • Differential geometry on the space of connections via graphs and projective limits
    • Also available as arXiv:hep-th/9412073
    • Ashtekar A., Lewandowski J.: Differential geometry on the space of connections via graphs and projective limits. J. Geom. Phys. 17, 191-230 (1995) Also available as arXiv: hep-th/9412073.
    • (1995) J. Geom. Phys. , vol.17 , pp. 191-230
    • Ashtekar, A.1    Lewandowski, J.2
  • 4
    • 1542429021 scopus 로고    scopus 로고
    • Four-dimensional BF theory as a topological quantum field theory
    • Baez J.: Four-dimensional BF theory as a topological quantum field theory. Lett. Math. Phys. 38, 129-143 (1996).
    • (1996) Lett. Math. Phys. , vol.38 , pp. 129-143
    • Baez, J.1
  • 5
    • 0032396211 scopus 로고    scopus 로고
    • Spin foam models
    • Also available as arXiv: gr-qc/9709052
    • Baez J.: Spin foam models. Class. Quantum Grav. 15, 1827-1858 (1998) Also available as arXiv: gr-qc/9709052.
    • (1998) Class. Quantum Grav. , vol.15 , pp. 1827-1858
    • Baez, J.1
  • 6
    • 0001903332 scopus 로고    scopus 로고
    • An introduction to spin foam models of BF theory and quantum gravity
    • H. Gausterer and H. Grosse (Eds.), Berlin: Springer
    • Baez J.: An introduction to spin foam models of BF theory and quantum gravity. In: Gausterer, H., Grosse, H. (eds) Geometry and Quantum Physics, pp. 25-93. Springer, Berlin (2000).
    • (2000) Geometry and Quantum Physics , pp. 25-93
    • Baez, J.1
  • 8
    • 18544381081 scopus 로고    scopus 로고
    • Higher dimensional algebra VI: Lie 2-algebras
    • Also available as arXiv:math.0307263
    • Baez J., Crans A.: Higher dimensional algebra VI: Lie 2-algebras. Theory Appl Categories 12, 492-538 (2004) Also available as arXiv: math. 0307263.
    • (2004) Theory Appl Categories , vol.12 , pp. 492-538
    • Baez, J.1    Crans, A.2
  • 9
    • 37849047718 scopus 로고    scopus 로고
    • From loop groups to 2-groups
    • Also available as arXiv:math.QA/0504123
    • Baez J., Crans A., Schreiber U., Stevenson D.: From loop groups to 2-groups. HHA 9, 101-135 (2007) Also available as arXiv: math. QA/0504123.
    • (2007) Hha , vol.9 , pp. 101-135
    • Baez, J.1    Crans, A.2    Schreiber, U.3    Stevenson, D.4
  • 10
    • 39049126362 scopus 로고    scopus 로고
    • Exotic statistics for strings in 4d BF theory
    • Also available as arXiv:gr-qc/0603085
    • Baez J., Crans A., Wise D.: Exotic statistics for strings in 4d BF theory. Adv. Theor. Math. Phys. 11, 707-749 (2007) Also available as arXiv: gr-qc/0603085.
    • (2007) Adv. Theor. Math. Phys. , vol.11 , pp. 707-749
    • Baez, J.1    Crans, A.2    Wise, D.3
  • 11
    • 71249086281 scopus 로고    scopus 로고
    • Categorified symplectic geometry and the classical string
    • Also available as arXiv:0808.0246
    • Baez J., Hoffnung A., Rogers C.: Categorified symplectic geometry and the classical string. Commun. Math. Phys. 293, 701-715 (2010) Also available as arXiv: 0808. 0246.
    • (2010) Commun. Math. Phys. , vol.293 , pp. 701-715
    • Baez, J.1    Hoffnung, A.2    Rogers, C.3
  • 14
    • 18544362027 scopus 로고    scopus 로고
    • Higher dimensional algebra V: 2-groups
    • Also available as arXiv:math.0307200
    • Baez J., Lauda A.: Higher dimensional algebra V: 2-groups. Theory Appl. Categories 12, 423-491 (2004) Also available as arXiv: math. 0307200.
    • (2004) Theory Appl. Categories , vol.12 , pp. 423-491
    • Baez, J.1    Lauda, A.2
  • 15
    • 39049092465 scopus 로고    scopus 로고
    • Quantization of strings and branes coupled to BF theory
    • Also available as arXiv:gr-qc/0605087
    • Baez J., Perez A.: Quantization of strings and branes coupled to BF theory. Adv. Theor. Math. Phys. 11, 1-19 (2007) Also available as arXiv: gr-qc/0605087.
    • (2007) Adv. Theor. Math. Phys. , vol.11 , pp. 1-19
    • Baez, J.1    Perez, A.2
  • 16
    • 80051787829 scopus 로고    scopus 로고
    • Categorified symplectic geometry and the string Lie 2-algebra
    • Available as arXiv: 0901. 4721
    • Baez, J., Rogers, C.: Categorified symplectic geometry and the string Lie 2-algebra. Homol. Homotopy Appl. (to appear). Available as arXiv: 0901. 4721.
    • Homol. Homotopy Appl.
    • Baez, J.1    Rogers, C.2
  • 18
    • 0031572649 scopus 로고    scopus 로고
    • Functional integration on spaces of connections
    • Also available as arXiv:q-alg/9507023
    • Baez J., Sawin S.: Functional integration on spaces of connections. J. Funct. Analysis 150, 1-26 (1997) Also available as arXiv: q-alg/9507023.
    • (1997) J. Funct. Analysis , vol.150 , pp. 1-26
    • Baez, J.1    Sawin, S.2
  • 19
    • 79952799789 scopus 로고    scopus 로고
    • The classifying space of a topological 2-group
    • N. Baas, E. Friedlander, B. Jahren, P. A.Østvær (Eds.), Berlin: Springer
    • Baez J., Stevenson D.: The classifying space of a topological 2-group. In: Baas, N., Friedlander, E., Jahren, B., Østvær, P. A. (eds) Algebraic Topology: The Abel Symposium 2007, Springer, Berlin (2009).
    • (2009) Algebraic Topology: The Abel Symposium 2007
    • Baez, J.1    Stevenson, D.2
  • 21
    • 0011674848 scopus 로고
    • A new approach to strings and superstrings
    • Balachandran A. P., Lizzi F., Sparano G.: A new approach to strings and superstrings. Nucl. Phys. B 277, 359-387 (1986).
    • (1986) Nucl. Phys. B , vol.277 , pp. 359-387
    • Balachandran, A.P.1    Lizzi, F.2    Sparano, G.3
  • 22
    • 34047198210 scopus 로고    scopus 로고
    • Hidden quantum gravity in 3d Feynman diagrams
    • Also available as arXiv:gr-qc/0604016
    • Baratin A., Freidel L.: Hidden quantum gravity in 3d Feynman diagrams. Class. Quant. Grav. 24, 1993-2026 (2007) Also available as arXiv: gr-qc/0604016.
    • (2007) Class. Quant. Grav. , vol.24 , pp. 1993-2026
    • Baratin, A.1    Freidel, L.2
  • 23
    • 34047211307 scopus 로고    scopus 로고
    • Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams
    • Also available as arXiv:hep-th/0611042
    • Baratin A., Freidel L.: Hidden quantum gravity in 4d Feynman diagrams: emergence of spin foams. Class. Quant. Grav. 24, 2027-2060 (2007) Also available as arXiv: hep-th/0611042.
    • (2007) Class. Quant. Grav. , vol.24 , pp. 2027-2060
    • Baratin, A.1    Freidel, L.2
  • 25
    • 33748333184 scopus 로고    scopus 로고
    • Categorical representations of categorical groups
    • Also available as arXiv:math.0407463
    • Barrett J. W., Mackaay M.: Categorical representations of categorical groups. Theory Appl. Categories 16, 529-557 (2006) Also available as arXiv: math. 0407463.
    • (2006) Theory Appl. Categories , vol.16 , pp. 529-557
    • Barrett, J.W.1    Mackaay, M.2
  • 27
    • 77958489862 scopus 로고    scopus 로고
    • Notes on 1- and 2-gerbes
    • Also available as arXiv:math.0611317, J. Baez and P. May (Eds.), Berlin: Springer
    • Breen L.: Notes on 1- and 2-gerbes. In: Baez, J., May, P. (eds) Towards Higher Categories, pp. 193-235. Springer, Berlin (2009) Also available as arXiv: math. 0611317.
    • (2009) Towards Higher Categories , pp. 193-235
    • Breen, L.1
  • 29
    • 28744434776 scopus 로고    scopus 로고
    • Differential geometry of gerbes
    • Available as arXiv:math.AG/0106083
    • Breen L., Messing W.: Differential geometry of gerbes. Adv. Math. 198, 732-846 (2005) Available as arXiv: math. AG/0106083.
    • (2005) Adv. Math. , vol.198 , pp. 732-846
    • Breen, L.1    Messing, W.2
  • 32
    • 84974005606 scopus 로고
    • The geometry of degree-four characteristic classes and of line bundles on loop spaces I
    • Brylinski J.-L., McLaughlin D. A.: The geometry of degree-four characteristic classes and of line bundles on loop spaces I. Duke Math. J. 75, 603-638 (1994).
    • (1994) Duke Math. J. , vol.75 , pp. 603-638
    • Brylinski, J.-L.1    McLaughlin, D.A.2
  • 33
    • 0001620479 scopus 로고    scopus 로고
    • The geometry of degree-four characteristic classes and of line bundles on loop spaces II
    • Brylinski J.-L., McLaughlin D. A.: The geometry of degree-four characteristic classes and of line bundles on loop spaces II. Duke Math. J. 83, 105-139 (1996).
    • (1996) Duke Math. J. , vol.83 , pp. 105-139
    • Brylinski, J.-L.1    McLaughlin, D.A.2
  • 34
    • 4444362828 scopus 로고    scopus 로고
    • Holonomy on D-branes
    • Also available as arXiv:hep-th/0204199
    • Carey A. L., Johnson S., Murray M. K.: Holonomy on D-branes. J. Geom. Phys. 52, 186-216 (2004) Also available as arXiv: hep-th/0204199.
    • (2004) J. Geom. Phys. , vol.52 , pp. 186-216
    • Carey, A.L.1    Johnson, S.2    Murray, M.K.3
  • 38
    • 0002986922 scopus 로고
    • A categorical construction of 4d TQFTs
    • Also available as arXiv: hep-th/9301062, L. Kauffman and R. Baadhio (Eds.), Singapore: World Scientific
    • Crane L., Yetter D.: A categorical construction of 4d TQFTs. In: Kauffman, L., Baadhio, R. (eds) Quantum Topology, pp. 120-130. World Scientific, Singapore (1993) Also available as arXiv: hep-th/9301062.
    • (1993) Quantum Topology , pp. 120-130
    • Crane, L.1    Yetter, D.2
  • 39
    • 29544441862 scopus 로고    scopus 로고
    • Measurable categories and 2-groups
    • Also available as arXiv:math.0305176
    • Crane L., Yetter D. N.: Measurable categories and 2-groups. Appl. Categorical Struct 13, 501-516 (2005) Also available as arXiv: math. 0305176.
    • (2005) Appl. Categorical Struct , vol.13 , pp. 501-516
    • Crane, L.1    Yetter, D.N.2
  • 42
    • 0001411870 scopus 로고
    • Supermembranes: the first fifteen weeks
    • Also available at
    • Duff, M. J.: Supermembranes: the first fifteen weeks. Class. Quantum Grav. 5, 189-205 (1988). Also available at 〈http://ccdb4fs. kek. jp/cgi-bin/img_index?8708425〉.
    • (1988) Class. Quantum Grav. , vol.5 , pp. 189-205
    • Duff, M.J.1
  • 43
    • 0001238925 scopus 로고
    • Group-like structures in categories
    • Eckmann B., Hilton P.: Group-like structures in categories. Math. Ann. 145, 227-255 (1962).
    • (1962) Math. Ann. , vol.145 , pp. 227-255
    • Eckmann, B.1    Hilton, P.2
  • 44
    • 34247244048 scopus 로고    scopus 로고
    • Representation theory of 2-groups on Kapranov and Voevodsky 2-vector spaces
    • Also available as arXiv:math.0408120
    • Elgueta J.: Representation theory of 2-groups on Kapranov and Voevodsky 2-vector spaces. Adv. Math. 213, 53-92 (2007) Also available as arXiv: math. 0408120.
    • (2007) Adv. Math. , vol.213 , pp. 53-92
    • Elgueta, J.1
  • 45
    • 48249083128 scopus 로고    scopus 로고
    • Extended matter coupled to BF theory
    • Also available as arXiv:0709.4235
    • Fairbairn W., Perez A.: Extended matter coupled to BF theory. Adv. Theor. Math. Phys. D 78, 024013 (2008) Also available as arXiv: 0709. 4235.
    • (2008) Adv. Theor. Math. Phys. D , vol.78 , pp. 024013
    • Fairbairn, W.1    Perez, A.2
  • 48
    • 0000973888 scopus 로고    scopus 로고
    • Anomalies in string theory with D-Branes, §6: Additional remarks
    • Also available as arXiv:hep-th/9907189
    • Freed D. S., Witten E.: Anomalies in string theory with D-Branes, §6: Additional remarks. Asian J. Math. 3, 819-852 (1999) Also available as arXiv: hep-th/9907189.
    • (1999) Asian J. Math. , vol.3 , pp. 819-852
    • Freed, D.S.1    Witten, E.2
  • 49
    • 10844256517 scopus 로고    scopus 로고
    • Ponzano-Regge model revisited. I: Gauge fixing, observables and interacting spinning particles
    • Also available as arXiv:hep-th/0401076
    • Freidel L., Louapre D.: Ponzano-Regge model revisited. I: Gauge fixing, observables and interacting spinning particles. Class. Quant. Grav. 21, 5685-5726 (2004) Also available as arXiv: hep-th/0401076.
    • (2004) Class. Quant. Grav. , vol.21 , pp. 5685-5726
    • Freidel, L.1    Louapre, D.2
  • 52
    • 0001755444 scopus 로고
    • Topological actions in two-dimensional quantum field theories
    • G. t'Hooft, A. Jaffe, G. Mack, P. K. Mitter, and R. Stora (Eds.), New York: Plenum
    • Gawedzki K.: Topological actions in two-dimensional quantum field theories. In: t'Hooft, G., Jaffe, A., Mack, G., Mitter, P. K., Stora, R. (eds) Nonperturbative Quantum Field Theory, pp. 101-141. Plenum, New York (1988).
    • (1988) Nonperturbative Quantum Field Theory , pp. 101-141
    • Gawedzki, K.1
  • 53
    • 0036967828 scopus 로고    scopus 로고
    • WZW branes and gerbes
    • Also available as arXiv:hep-th/0205233
    • Gawedzki K., Reis N.: WZW branes and gerbes. Rev. Math. Phys. 14, 1281-1334 (2002) Also available as arXiv: hep-th/0205233.
    • (2002) Rev. Math. Phys. , vol.14 , pp. 1281-1334
    • Gawedzki, K.1    Reis, N.2
  • 54
    • 34250168075 scopus 로고    scopus 로고
    • Available as arXiv: math. 0404003
    • Getzler, E.: Lie theory for nilpotent L8-algebras. Available as arXiv:math.0404003
    • ∞-algebras
    • Getzler, E.1
  • 56
    • 9944229016 scopus 로고    scopus 로고
    • Higher gauge theory-differential versus integral formulation
    • Also available as arXiv:hep-th/0309173
    • Girelli F., Pfeiffer H.: Higher gauge theory-differential versus integral formulation. J. Math. Phys. 45, 3949-3971 (2004) Also available as arXiv: hep-th/0309173.
    • (2004) J. Math. Phys. , vol.45 , pp. 3949-3971
    • Girelli, F.1    Pfeiffer, H.2
  • 57
    • 41549087044 scopus 로고    scopus 로고
    • Topological higher gauge theory-from BF to BFCG theory
    • Also available as arXiv:0708.3051
    • Girelli F., Pfeiffer H., Popescu E. M.: Topological higher gauge theory-from BF to BFCG theory. J. Math. Phys. 49, 032503 (2008) Also available as arXiv: 0708. 3051.
    • (2008) J. Math. Phys. , vol.49 , pp. 032503
    • Girelli, F.1    Pfeiffer, H.2    Popescu, E.M.3
  • 60
    • 38249025705 scopus 로고
    • The combinatorics of n-categorical pasting
    • Johnson M.: The combinatorics of n-categorical pasting. J. Pure Appl. Algebra 62, 211-225 (1989).
    • (1989) J. Pure Appl. Algebra , vol.62 , pp. 211-225
    • Johnson, M.1
  • 61
    • 80053383493 scopus 로고    scopus 로고
    • A 2-categories companion
    • Baez J., May P. (eds), Springer. Also available as arXiv: math. 0702535
    • Lack, S.: A 2-categories companion. In: Baez J., May P. (eds) Towards Higher Categories pp. 105-191. Springer (2009). Also available as arXiv: math. 0702535.
    • (2009) Towards Higher Categories , pp. 105-191
    • Lack, S.1
  • 63
    • 0033243656 scopus 로고    scopus 로고
    • Diffeomorphism invariant quantum field theories of connections in terms of webs
    • Also available as arXiv:gr-qc/9901015
    • Lewandowski J., Thiemann T.: Diffeomorphism invariant quantum field theories of connections in terms of webs. Class. Quant. Grav. 16, 2299-2322 (1999) Also available as arXiv: gr-qc/9901015.
    • (1999) Class. Quant. Grav. , vol.16 , pp. 2299-2322
    • Lewandowski, J.1    Thiemann, T.2
  • 65
    • 0037174517 scopus 로고    scopus 로고
    • Holonomy and parallel transport for Abelian gerbes
    • Also available as arXiv:math.DG/0007053
    • Mackaay M., Picken R.: Holonomy and parallel transport for Abelian gerbes. Adv. Math. 170, 287-339 (2002) Also available as arXiv: math. DG/0007053.
    • (2002) Adv. Math. , vol.170 , pp. 287-339
    • Mackaay, M.1    Picken, R.2
  • 70
    • 0001335921 scopus 로고
    • Remarks on infinite dimensional Lie groups
    • (Les Houches, 1983), North-Holland, Amsterdam
    • Milnor, J.: Remarks on infinite dimensional Lie groups. In: Relativity, Groups and Topology II, (Les Houches, 1983), North-Holland, Amsterdam (1984).
    • (1984) Relativity, Groups and Topology II
    • Milnor, J.1
  • 72
    • 43949143905 scopus 로고    scopus 로고
    • Two-dimensional topological field theories coupled to four-dimensional BF theory
    • Also available as arXiv:0709.4235
    • Montesinos M., Perez A.: Two-dimensional topological field theories coupled to four-dimensional BF theory. Phys. Rev. D 77, 104020 (2008) Also available as arXiv: 0709. 4235.
    • (2008) Phys. Rev. D , vol.77 , pp. 104020
    • Montesinos, M.1    Perez, A.2
  • 73
    • 0001750989 scopus 로고    scopus 로고
    • Bundle gerbes
    • Also available as arXiv: dg-ga/9407015
    • Murray M. K.: Bundle gerbes. J. London Math. Soc. 54, 403-416 (1996) Also available as arXiv: dg-ga/9407015.
    • (1996) J. London Math. Soc. , vol.54 , pp. 403-416
    • Murray, M.K.1
  • 75
    • 0346308628 scopus 로고    scopus 로고
    • Higgs fields, bundle gerbes and string structures
    • Also available as arXiv:math.DG/0106179
    • Murray M. K., Stevenson D.: Higgs fields, bundle gerbes and string structures. Commun. Math. Phys. 243, 541-555 (2003) Also available as arXiv: math. DG/0106179.
    • (2003) Commun. Math. Phys. , vol.243 , pp. 541-555
    • Murray, M.K.1    Stevenson, D.2
  • 76
    • 0346903967 scopus 로고    scopus 로고
    • Higher gauge theory and a non-Abelian generalization of 2-form electromagnetism
    • Also available as arXiv:hep-th/0304074
    • Pfeiffer H.: Higher gauge theory and a non-Abelian generalization of 2-form electromagnetism. Ann. Phys. 308, 447-477 (2003) Also available as arXiv: hep-th/0304074.
    • (2003) Ann. Phys. , vol.308 , pp. 447-477
    • Pfeiffer, H.1
  • 77
    • 0001700234 scopus 로고
    • A 2-categorical pasting theorem
    • Power A. J.: A 2-categorical pasting theorem. J. Algebra 129, 439-445 (1990).
    • (1990) J. Algebra , vol.129 , pp. 439-445
    • Power, A.J.1
  • 80
    • 1842855789 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, Also available at 〈
    • Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004). Also available at 〈http://www. cpt. univ-mrs. fr/~rovelli/book. pdf〉.
    • (2004) Quantum Gravity
    • Rovelli, C.1
  • 84
    • 0001164659 scopus 로고
    • The Lie algebra structure of tangent cohomology and deformation theory
    • Schlessinger M., Stasheff J.: The Lie algebra structure of tangent cohomology and deformation theory. J. Pure Appl. Algebra 38, 313-322 (1985).
    • (1985) J. Pure Appl. Algebra , vol.38 , pp. 313-322
    • Schlessinger, M.1    Stasheff, J.2
  • 87
    • 79958051054 scopus 로고    scopus 로고
    • Parallel transport and functors
    • Also available as arXiv:0705.0452
    • Schreiber U., Waldorf K.: Parallel transport and functors. J. Homotopy Relat. Struct. 4, 187-244 (2009) Also available as arXiv: 0705. 0452.
    • (2009) J. Homotopy Relat. Struct. , vol.4 , pp. 187-244
    • Schreiber, U.1    Waldorf, K.2
  • 90
    • 0013260041 scopus 로고    scopus 로고
    • Ph. D. thesis, University of Adelaide. Also available as arXiv: math. DG/0004117
    • Stevenson, D.: The Geometry of Bundle Gerbes. Ph. D. thesis, University of Adelaide (2000). Also available as arXiv: math. DG/0004117.
    • (2000) The Geometry of Bundle Gerbes
    • Stevenson, D.1
  • 93
    • 0001376821 scopus 로고
    • Geodesic fields in the calculus of variation for multiple integrals
    • Weyl H.: Geodesic fields in the calculus of variation for multiple integrals. Ann. Math. 36, 607-629 (1935).
    • (1935) Ann. Math. , vol.36 , pp. 607-629
    • Weyl, H.1
  • 94
    • 0001592410 scopus 로고
    • Note on a previous paper entitled 'On adding relations to homotopy groups
    • Whitehead J. H. C.: Note on a previous paper entitled 'On adding relations to homotopy groups'. Ann. Math. 47, 806-810 (1946).
    • (1946) Ann. Math. , vol.47 , pp. 806-810
    • Whitehead, J.H.C.1
  • 95
    • 84966252616 scopus 로고
    • Combinatorial homotopy II
    • Whitehead J. H. C.: Combinatorial homotopy II. Bull. Am. Math. Soc. 55, 453-496 (1949).
    • (1949) Bull. Am. Math. Soc. , vol.55 , pp. 453-496
    • Whitehead, J.H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.