Bundle Gerbes and Surface Holonomy

Fuchs, Jürgen; Nikolaus, Thomas; Schweigert, Christoph; Waldorf, Konrad

Bundle Gerbes and Surface Holonomy

Jan 14, 2009

25 pages

e-Print:

0901.2085 [math.DG]

View in:

ADS Abstract Service

pdf

reference search15 citations

Citations per year

Abstract: (arXiv)

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes under descent. Inspired by structures arising in a representation theoretic approach to rational conformal field theories, we introduce geometric structure that is appropriate to define surface holonomy in more general situations: Jandl gerbes for unoriented surfaces, D-branes for surfaces with boundaries, and bi-branes for surfaces with defect lines.

Note:

25 pages

field theory: conformal: rational
surface
holonomy
D-brane
defect

References(28)

Figures(0)

[Al]

Topological Quantization and Cohomology

Orlando Alvarez
(
- UC, Berkeley and
- LBL, Berkeley
)

- Commun.Math.Phys. 100 (1985) 279
•
DOI:
- 10.1007/BF01212452

[ADW]

Geometric quantization of Chern-Simons gauge theory

- J.Diff.Geom. 33 (1991) 3, 787-902

[BK]

Lectures on Tensor Categories and Modular Funtors (American Mathematical Society, Providence)

B. Bakalov
,
A.A. Kirillov

[FFFS]

Correlation functions and boundary conditions in RCFT and three-dimensional topology

Giovanni Felder
(
- Zurich, ETH
)
,
Jurg Frohlich
(
- Zurich, ETH
)
,
Jurgen Fuchs
(
- Zurich, ETH
)
,
Christoph Schweigert
(
- Paris U., VI-VII
)

- Compos.Math. 131 (2002) 189-237
•
e-Print:
- hep-th/9912239
•
DOI:
- 10.1023/A:1014903315415

[FFFS]

TFT construction of RCFT correlators. V. Proof of modular invariance and factorisation

Jens Fjelstad
(
- Hamburg U., Dept. Math.
)
,
Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- Potsdam, Max Planck Inst.
)
,
Christoph Schweigert
(
- Hamburg U., Dept. Math.
)

- Theor.Appl.Categor. 16 (2006) 342-433
•
e-Print:
- hep-th/0503194

[FjFRS2]

Uniqueness of open / closed rational CFT with given algebra of open states

Jens Fjelstad
(
- Cardiff U.
)
,
Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- King's Coll. London, Dept. Math
)
,
Christoph Schweigert
(
- Hamburg U., Dept. Math.
)

- Adv.Theor.Math.Phys. 12 (2008) 6, 1283-1375
•
e-Print:
- hep-th/0612306
•
DOI:
- 10.4310/ATMP.2008.v12.n6.a4

[FHT]

Loop groups and twisted K-theory I

Daniel S. Freed
(
- Texas U., Math Dept.
)
,
Michael J. Hopkins
(
- MIT
)
,
Constantin Teleman
(
- Cambridge U. (main)
)

- J.Topol. 4 (2011) 4, 737-798
•
e-Print:
- 0711.1906
•
DOI:
- 10.1112/jtopol/jtr019

[FrB]

Vertex Algebras and Algebrai Curves, second edition (American Mathematical Society, Providence)

E. Frenkel
,
D. Ben-Zvi

[FRS1]

TFT construction of RCFT correlators 1. Partition functions

Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- Paris U., VI-VII
)
,
Christoph Schweigert
(
- Paris U., VI-VII
)

- Nucl.Phys.B 646 (2002) 353-497
•
e-Print:
- hep-th/0204148
•
DOI:
- 10.1016/S0550-3213(02)00744-7

[FRS2]

TFT construction of RCFT correlators. 2. Unoriented world sheets

Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- Humboldt U., Berlin
)
,
Christoph Schweigert
(
- Aachen, Tech. Hochsch. and
- Hamburg U.
)

- Nucl.Phys.B 678 (2004) 511-637
•
e-Print:
- hep-th/0306164
•
DOI:
- 10.1016/j.nuclphysb.2003.11.026

[FRS3]

TFT construction of RCFT correlators IV: Structure constants and correlation functions

Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- Potsdam, Max Planck Inst.
)
,
Christoph Schweigert
(
- Hamburg U.
)

- Nucl.Phys.B 715 (2005) 539-638
•
e-Print:
- hep-th/0412290
•
DOI:
- 10.1016/j.nuclphysb.2005.03.018

[FRS4]

Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions

- Contemp.Math. 431 (2007) 203-224
•
e-Print:
- math/0511590

[FSW]

Bi-branes: Target space geometry for world sheet topological defects

- J.Geom.Phys. 58 (2008) 576-598
•
e-Print:
- hep-th/0703145
•
DOI:
- 10.1016/j.geomphys.2007.12.009

[Ga1]

Topological actions in two-dimensional quantum field theories, in: Nonperturbative Quantum Field Theory, G 'tHooft, A. Jae, G. Mack, P.K. Mitter, and R. Stora (eds.) New York), p. 101