Logarithmic conformal field theory through nilpotent conformal dimensions

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFT's such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor.

Note:

17 pages, Latex

11.25.Hf
Conformal field theory
field theory: conformal
dimension: 2
supersymmetry: superfield
n-point function: correlation function
tensor: energy-momentum
analytic properties

References(23)

Figures(0)

Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory

A.A. Belavin
(
- Landau Inst.
)
,
Alexander M. Polyakov
(
- Landau Inst.
)
,
A.B. Zamolodchikov
(
- CERN and
- Landau Inst.
)

- Nucl.Phys.B 241 (1984) 333-380,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 5-52. (NUCL. PHYS. B241 (1984) 333-380) AND CERN GENEVA - TH. 3827 (84,REC.JUN.) 71 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0550-3213(84)90052-X

Logarithmic operators in conformal field theory

V. Gurarie
(
- Princeton U.
)

- Nucl.Phys.B 410 (1993) 535-549
•
e-Print:
- hep-th/9303160
•
DOI:
- 10.1016/0550-3213(93)90528-W

Quantum field theory for the multivariable Alexander-Conway polynomial

L. Rozansky
(
- Northwestern U.
)
,
H. Saleur
(
- Yale U.
)

- Nucl.Phys.B 376 (1992) 461-509
•
DOI:
- 10.1016/0550-3213(92)90118-U

S and T matrices for the superU(1,1) WZW model: Application to surgery and three manifolds invariants based on the Alexander-Conway polynomial

L. Rozansky
(
- Texas U.
)
,
H. Saleur
(
- Yale U.
)

- Nucl.Phys.B 389 (1993) 365-423
•
e-Print:
- hep-th/9203069
•
DOI:
- 10.1016/0550-3213(93)90326-K

Logarithmic operators and hidden continuous symmetry in critical disordered models

- Nucl.Phys.B 466 (1996) 444-462,
- In *Shifman, M. (ed.) et al.: From fields to strings, vol. 3* 2223-2245
•
e-Print:
- hep-th/9511134
•
DOI:
- 10.1016/0550-3213(96)00118-6

- Phys.Lett.B 402 2

The Logarithmic conformal field theories

M.R. Rahimi Tabar
(
- IPM, Tehran and
- Iran U. Sci. Tech.
)
,
A. Aghamohammadi
(
- IPM, Tehran and
- Azzahra U.
)
,
M. Khorrami
(
- IPM, Tehran and
- Tehran U. and
- IASBS, Zanjan
)

- Nucl.Phys.B 497 (1997) 555-566
•
e-Print:
- hep-th/9610168
•
DOI:
- 10.1016/S0550-3213(97)00230-7

Logarithmic correlations in quenched random magnets and polymers

John L. Cardy
(
- Oxford U.
)

e-Print:
- cond-mat/9911024

Quenched averaged correlation functions of the random magnets

M. Reza Rahimi Tabar
(
- Iran U. Sci. Tech. and
- IPM, Tehran
)

- Nucl.Phys.B 588 (2000) 630-637
•
e-Print:
- cond-mat/0002309
•
DOI:
- 10.1016/S0550-3213(00)00474-0

On modular invariant partition functions of conformal field theories with logarithmic operators

Michael A.I. Flohr
(
- Madrid, IMAFF
)

- Int.J.Mod.Phys.A 11 (1996) 4147-4172
•
e-Print:
- hep-th/9509166
•
DOI:
- 10.1142/S0217751X96001954

On fusion rules in logarithmic conformal field theories

Michael A.I. Flohr
(
- Princeton, Inst. Advanced Study
)

- Int.J.Mod.Phys.A 12 (1997) 1943-1958
•
e-Print:
- hep-th/9605151
•
DOI:
- 10.1142/S0217751X97001225

Singular vectors in logarithmic conformal field theories

Michael A.I. Flohr
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 514 (1998) 523-552
•
e-Print:
- hep-th/9707090
•
DOI:
- 10.1016/S0550-3213(97)00012-6

Nonunitary conformal field theory and logarithmic operators for disordered systems

Z. Maassarani
(
- Saclay
)
,
D. Serban
(
- Saclay
)

- Nucl.Phys.B 489 (1997) 603-625
•
e-Print:
- hep-th/9605062
•
DOI:
- 10.1016/S0550-3213(97)00014-X

Conformal algebras of 2-D disordered systems

- J.Phys.A 35 (2002) L377-L384
•
e-Print:
- cond-mat/9911392
•
DOI:
- 10.1088/0305-4470/35/27/101

Symplectic fermions

Horst G. Kausch
(
- Durham U., Dept. of Math.
)

- Nucl.Phys.B 583 (2000) 513-541
•
e-Print:
- hep-th/0003029
•
DOI:
- 10.1016/S0550-3213(00)00295-9

Singletons and logarithmic CFT in AdS / CFT correspondence

Ian I. Kogan
(
- Oxford U.
)

- Phys.Lett.B 458 (1999) 66-72
•
e-Print:
- hep-th/9903162
•
DOI:
- 10.1016/S0370-2693(99)00576-6

The Large $N$ limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
- Adv.Theor.Math.Phys. 2 (1998) 231-252
•
e-Print:
- hep-th/9711200
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a1

Null vectors in logarithmic conformal field theory

Michael Flohr
(
- Hannover U.
)

- PoS tmr2000 (2000) 044
•
e-Print:
- hep-th/0009137
•
DOI:
- 10.22323/1.006.0044

Boundary logarithmic conformal field theory

Ian I. Kogan
(
- Oxford U.
)
,
John F. Wheater
(
- Oxford U.
)

- Phys.Lett.B 486 (2000) 353-361
•
e-Print:
- hep-th/0003184
•
DOI:
- 10.1016/S0370-2693(00)00767-X

Origin of logarithmic operators in conformal field theories

Ian I. Kogan
(
- Oxford U.
)
,
Alex Lewis
(
- Oxford U.
)

- Nucl.Phys.B 509 (1998) 687-704
•
e-Print:
- hep-th/9705240
•
DOI:
- 10.1016/S0550-3213(97)00666-4

Logarithmic operators and dynamical extension of the symmetry group in the bosonic SU(2)-0 and SUSY SU(2)-2 WZNW models

- Nucl.Phys.B 489 (1997) 469-484
•
e-Print:
- hep-th/9606138
•
DOI:
- 10.1016/S0550-3213(97)00011-4

Conformal Invariance and Surface Critical Behavior

John L. Cardy
(
- Boston U.
)

- Nucl.Phys.B 240 (1984) 514-532
•
DOI:
- 10.1016/0550-3213(84)90241-4

Logarithmic conformal field theories near a boundary

S. Moghimi-Araghi
(
- Sharif U. of Tech.
)
,
S. Rouhani
(
- Sharif U. of Tech. and
- IPM, Tehran
)

- Lett.Math.Phys. 53 (2000) 49-57
•
e-Print:
- hep-th/0002142
•
DOI:
- 10.1023/A:1026519016890