We construct Gepner models in terms of coset conformal field theories and compute their twisted equivariant K-theories. These classify the -brane charges on the associated geometric backgrounds and therefore agree with the topological K-theories. We show this agreement for various cases, in particular, the Fermat quintic.
REFERENCES
1.
R.
Minasian
and G. W.
Moore
, “-theory and Ramond-Ramond charge
,” J. High Energy Phys.
11
, 002
(1997
).2.
3.
4.
A.
Recknagel
and V.
Schomerus
, “-branes in Gepner models
,” Nucl. Phys. B
531
, 185
(1998
).5.
6.
A.
Recknagel
, “On permutation branes
,” Fortschr. Phys.
51
, 824
(2003
).7.
I.
Brunner
and M. R.
Gaberdiel
, “Matrix factorisations and permutation branes
,” J. High Energy Phys.
07
, 012
(2005
).8.
I.
Brunner
and M. R.
Gaberdiel
, “The matrix factorisations of the -model
,” J. Phys. A
38
, 7901
(2005
).9.
H.
Enger
, A.
Recknagel
, and D.
Roggenkamp
, “Permutation branes and linear matrix factorisations
,” hep-th/0508053.10.
S.
Fredenhagen
and T.
Quella
, “Generalised permutation branes
,” J. High Energy Phys.
11
, 004
(2005
).11.
C.
Caviezel
, S.
Fredenhagen
, and M. R.
Gaberdiel
, “The RR charges of A-type Gepner models
,” hep-th/0511078.12.
S.
Fredenhagen
and V.
Schomerus
, “Branes on group manifolds, gluon condensates, and twisted K-theory
,” J. High Energy Phys.
04
, 007
(2001
).13.
P.
Bouwknegt
and V.
Mathai
, “D-branes, B-fields and twisted K-theory
,” J. High Energy Phys.
0003
, 007
(2000
).14.
P.
Bouwknegt
, A. L.
Carey
, V.
Mathai
, M. K.
Murray
, and D.
Stevenson
, “Twisted K-theory and K-theory of bundle gerbes
,” Commun. Math. Phys.
228
, 17
(2002
).15.
J. M.
Maldacena
, G. W.
Moore
, and N.
Seiberg
, “Geometrical interpretation of -branes in gauged WZW models
,” J. High Energy Phys.
07
, 046
(2001
).16.
J. M.
Maldacena
, G. W.
Moore
, and N.
Seiberg
, “-brane instantons and K-theory charges
,” J. High Energy Phys.
11
, 062
(2001
).17.
18.
S.
Fredenhagen
, “Organizing boundary rg flows
,” Nucl. Phys. B
660
, 436
(2003
).19.
20.
M. R.
Gaberdiel
and T.
Gannon
, “The charges of a twisted brane
,” J. High Energy Phys.
01
, 018
(2004
).21.
M. R.
Gaberdiel
and T.
Gannon
, “-brane charges on non-simply connected groups
,” J. High Energy Phys.
04
, 030
(2004
).22.
V.
Braun
and S.
Schafer-Nameki
, “Supersymmetric WZW models and twisted K-theory of
,” hep-th/0403287.23.
24.
M. R.
Gaberdiel
, T.
Gannon
, and D.
Roggenkamp
, “The -branes of
,” J. High Energy Phys.
07
, 015
(2004
).25.
M. R.
Gaberdiel
, T.
Gannon
, and D.
Roggenkamp
, “The coset -branes of
,” J. High Energy Phys.
10
, 047
(2004
).26.
S.
Schafer-Nameki
, “K-theoretical boundary rings in coset models
,” Nucl. Phys. B
706
, 531
(2005
).27.
D. S.
Freed
, “The Verlinde algebra is twisted equivariant K-theory
,” Turkish J. Math.
25
, 159
(2001
).28.
D. S.
Freed
, M. J.
Hopkins
, and C.
Teleman
, “Twisted equivariant K-theory with complex coefficients
,” http://arXiv.org/abs/math.AT/0206257. Volume 3 contains relevant changes.29.
D. S.
Freed
, M. J.
Hopkins
, and C.
Teleman
, “Twisted K-theory and loop group representations
,” http://arXiv.org/abs/math.AT/0312155.30.
V.
Braun
, “K-theory torsion,” hep-th/0005103.31.
I.
Brunner
and J.
Distler
, “Torsion D-branes in nongeometrical phases
,” Adv. Theor. Math. Phys.
5
, 265
(2002
).32.
I.
Brunner
, J.
Distler
, and R.
Mahajan
, “Return of the torsion -branes
,” Adv. Theor. Math. Phys.
5
, 311
(2002
).33.
I.
Brunner
, M. R.
Douglas
, A. E.
Lawrence
, and C.
Romelsberger
, “-branes on the quintic
,” J. High Energy Phys.
08
, 015
(2000
).34.
M. R.
Gaberdiel
and S.
Schafer-Nameki
, “-branes in an asymmetric orbifold
,” Nucl. Phys. B
B654
, 177
(2003
).35.
A.
Kapustin
and L.
Rozansky
, “On the relation between open and closed topological strings
,” Commun. Math. Phys.
252
, 393
(2004
).36.
F.
Gliozzi
, J.
Scherk
, and D. I.
Olive
, “Supersymmetry, supergravity theories and the dual spinor model
,” Nucl. Phys. B
122
, 253
(1977
).37.
D.
Gepner
, “Space-time supersymmetry in compactified string theory and superconformal models
,” Nucl. Phys. B
296
, 757
(1988
).38.
D.
Gepner
and Z.-a.
Qiu
, “Modular invariant partition functions for parafermionic field theories
,” Nucl. Phys. B
285
423
, (1987
).39.
Z.-a.
Qiu
, “Modular invariant partition functions for superconformal field theories
,” Phys. Lett. B
198
, 497
(1987
).40.
S.
Fredenhagen
and V.
Schomerus
, “On boundary RG-flows in coset conformal field theories
,” Phys. Rev. D
67
, 085001
(2003
).41.
C.
Teleman
, “K-theory and the moduli space of bundles on a surface and deformations of the Verlinde algebra
,” in Topology, Geometry and Quantum Field Theory
, Vol. 308
of London Math. Soc. Lecture Note Ser. (Cambridge University Press
, Cambridge, 2004
), pp. 358
–378
.42.
K.
Wendland
, “Moduli spaces of unitary conformal field theories
.” Ph.D. thesis, Friedrich-Wilhelms Universität Bonn
, 2000
.43.
A.
Kapustin
and Y.
Li
, “-branes in topological minimal models: The Landau-Ginzburg approach
,” J. High Energy Phys.
07
, 045
(2004
).44.
I.
Brunner
, K.
Hori
, K.
Hosomichi
, and J.
Walcher
, “Orientifolds of Gepner models
,” hep-th/0401137.45.
E.
Witten
, “Phases of theories in two dimensions
,” Nucl. Phys. B
403
, 159
(1993
).46.
D.
Orlov
, “Triangulated categories of singularities and -branes in Landau-Ginzburg models
,” math.AG/0302304.47.
48.
H.
Knörrer
, “Cohen-Macaulay modules on hypersurface singularities. I
,” Invent. Math.
88
, 153
(1987
).49.
J.
Walcher
, “Stability of Landau-Ginzburg branes
,” J. Math. Phys.
46
, 082305
(2005
).50.
W.
Nahm
and K.
Wendland
, “A hiker’s guide to . Aspects of superconformal field theory with central charge
,” Commun. Math. Phys.
216
, 85
(2001
).51.
K.
Wendland
, “Orbifold constructions of K3: A link between conformal field theory and geometry
,” in Orbifolds in Mathematics and Physics, Madison, WI, 2001, Vol. 310
of Contemp. Math. (Amer. Math. Soc.
, Providence, RI
, 2002
), pp. 333
–358
.52.
W.
Nahm
and K.
Wendland
, “Mirror symmetry on Kummer type K3 surfaces
,” Commun. Math. Phys.
243
, 557
(2003
).53.
J.
Fuchs
, A.
Klemm
, C.
Scheich
, and M. G.
Schmidt
, “Spectra and symmetries of Gepner models compared to Calabi- Yau compactifications
,” Ann. Phys.
204
, 1
(2004
).© 2006 American Institute of Physics.
2006
American Institute of Physics
You do not currently have access to this content.