Catastrophes and the Classification of Conformal Theories

Vafa, Cumrun; Warner, Nicholas P.

doi:10.1016/0370-2693(89)90473-5

Catastrophes and the Classification of Conformal Theories

Cumrun Vafa
(
- Harvard U.
)
,
Nicholas P. Warner
(
- MIT
)

Nov, 1988

8 pages

Published in:

Phys.Lett.B 218 (1989) 51-58

Published: 1989

DOI:

10.1016/0370-2693(89)90473-5

Report number:

HUTP-88-A037

View in:

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Abstract: (Elsevier)

Using ideas from renormalization group theory we show that the study of catastrophes (singularities) is a powerful tool in the classification of conformal theories. The results are most powerful when applied to N =2 superconformal models. The ideas are illustrated by considering some examples including the minimal superconformal models.

FIELD THEORY: CONFORMAL
FIELD THEORY: TWO-DIMENSIONAL
RENORMALIZATION GROUP
SUPERSYMMETRY
field theory: scalar
MATHEMATICAL METHODS

References(25)

Figures(0)

Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- JETP Lett. 43 (1986) 730-732,
- Pisma Zh.Eksp.Teor.Fiz. 43 (1986) 565-567

Renormalization Group and Perturbation Theory Near Fixed Points in Two-Dimensional Field Theory

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- Sov.J.Nucl.Phys. 46 (1987) 1090,
- Yad.Fiz. 46 (1987) 1819-1831

Conformal Symmetry and Multicritical Points in Two-Dimensional Quantum Field Theory. (In Russian)

A.B. Zamolodchikov
(
- Moscow, ITEP
)

- Sov.J.Nucl.Phys. 44 (1986) 529-533,
- Yad.Fiz. 44 (1986) 821-827

- Phys.Scripta 15 191

Conditions of Weyl Invariance of Two-dimensional $\sigma$ Model From Equations of Stationarity of 'Central Charge' Action

Arkady A. Tseytlin
(
- Lebedev Inst.
)

- Phys.Lett.B 194 (1987) 63
•
DOI:
- 10.1016/0370-2693(87)90770-2

Zamolodchikov's C Theorem and String Effective Actions

- Phys.Lett.B 212 (1988) 33-40
•
DOI:
- 10.1016/0370-2693(88)91231-2

$c$ Theorem and the Topology of 2- $d$ Qfts

Cumrun Vafa
(
- Harvard U.
)

- Phys.Lett.B 212 (1988) 28-32
•
DOI:
- 10.1016/0370-2693(88)91230-0

Perturbative Evaluation of the Conformal Anomaly at New Critical Points with Applications to Random Systems

A.W.W. Ludwig
(
- UC, Santa Barbara
)
,
John L. Cardy
(
- UC, Santa Barbara
)

- Nucl.Phys.B 285 (1987) 687-718
•
DOI:
- 10.1016/0550-3213(87)90362-2

(2, 0) Supersymmetry and Space-Time Supersymmetry in the Heterotic String Theory

Ashoke Sen
(
- SLAC
)

- Nucl.Phys.B 278 (1986) 289-308
•
DOI:
- 10.1016/0550-3213(86)90214-2

Heterotic String Theory on Calabi-yau Manifolds in the Green-schwarz Formalism

Ashoke Sen
(
- SLAC
)

- Nucl.Phys.B 284 (1987) 423-448
•
DOI:
- 10.1016/0550-3213(87)90043-5

Phenomenology and Conformal Field Theory Or Can String Theory Predict the Weak Mixing Angle?

Tom Banks
(
- UC, Santa Cruz
)
,
Lance J. Dixon
(
- SLAC
)
,
Daniel Friedan
(
- Chicago U., EFI and
- Chicago U.
)
,
Emil J. Martinec
(
- Chicago U., EFI and
- Chicago U.
)

- Nucl.Phys.B 299 (1988) 613-626
•
DOI:
- 10.1016/0550-3213(88)90551-2

Quantum Geometry of Bosonic Strings

Alexander M. Polyakov
(
- Landau Inst.
)

- Phys.Lett.B 103 (1981) 207-210,
- In *Schwarz, J.H. (ed.): Superstrings, Vol. 1*, 287-290,
•
DOI:
- 10.1016/0370-2693(81)90743-7

Theory of Strings with Boundaries: Fluctuations, Topology, and Quantum Geometry

Orlando Alvarez
(
- Cornell U., LNS
)

- Nucl.Phys.B 216 (1983) 125-184
•
DOI:
- 10.1016/0550-3213(83)90490-X

Nonlocal Current Algebra and $N=2$ Superconformal Field Theory in Two-dimensions

Zong-an Qiu
(
- Princeton, Inst. Advanced Study
)

- Phys.Lett.B 188 (1987) 207-213
•
DOI:
- 10.1016/0370-2693(87)90008-6

Modular Invariant Partition Functions for $N=2$ Superconformal Field Theories

Zong-an Qiu
(
- Princeton, Inst. Advanced Study
)

- Phys.Lett.B 198 (1987) 497-502
•
DOI:
- 10.1016/0370-2693(87)90906-3

Space-Time Supersymmetry in Compactified String Theory and Superconformal Models

Doron Gepner
(
- Princeton U.
)

- Nucl.Phys.B 296 (1988) 757,
•
DOI:
- 10.1016/0550-3213(88)90397-5

Exactly Solvable String Compactifications on Manifolds of SU(N) Holonomy

Doron Gepner
(
- Princeton U.
)

- Phys.Lett.B 199 (1987) 380-388,
- In *Schellekens, A.N. (ed.): Superstring construction* 403-411. (Phys. Lett. B199 (1987) 380-388) and Princeton Univ. - PUPT-1066 (87,rec.Oct.) 19 p. (see Book Index)
•
DOI:
- 10.1016/0370-2693(87)90938-5

- Nucl.Phys.B 296 380

- Phys.Lett.B 185 92

Modular invariance in superconformal models

David Kastor
(
- Chicago U., EFI and
- Chicago U.
)

- Nucl.Phys.B 280 (1987) 304-320,
- Nucl.Phys.B 280 (1987) 304-320
•
DOI:
- 10.1016/0550-3213(87)90150-7

Two-dimensional critical systems labelled by Dynkin diagrams

Vincent Pasquier
(
- Saclay
)

- Nucl.Phys.B 285 (1987) 162-172
•
DOI:
- 10.1016/0550-3213(87)90332-4

Modular invariant partition functions in two dimensions

- Nucl.Phys.B 280 (1987) 445-465,
- Nucl.Phys.B 280 (1987) 445-465
•
DOI:
- 10.1016/0550-3213(87)90155-6

The ADE Classification of Minimal and A1(1) Conformal Invariant Theories

- Commun.Math.Phys. 113 (1987) 1
•
DOI:
- 10.1007/BF01221394

Strings on Orbifolds

- Nucl.Phys.B 261 (1985) 678-686,
•
DOI:
- 10.1016/0550-3213(85)90593-0

Strings on Orbifolds. 2.

- Nucl.Phys.B 274 (1986) 285-314,
- In *Schellekens, A.N. (ed.): Superstring construction* 181-210. (Nucl. Phys. B274 (1986) 285-314) and Preprint - Dixon, L.J. (86,rec.Mar.) 55 p. (see Book Index)
•
DOI:
- 10.1016/0550-3213(86)90287-7