Tests for c theorems in 4-D

A proof for a non-perturbative C-theorem in four dimensions, capturing the irreversibility of the renormalization group flow in the space of unitary quantum field theories, has not been accomplished, yet. We test the conjectured C-theorems using the exact results recently obtained in N=1 supersymmetric gauge theories. We find that the flow towards the infrared region is consistent with the main proposals for a C-theorem.

11.30.Pb
11.10.-z
Quantum field theory
Supersymmetry
renormalization group: C-theorem
renormalization group: transformation
gauge field theory: SU(N)
gauge field theory: Sp(N)
gauge field theory: SO(N)
supersymmetry: superfield

References(28)

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

e-Print:
- cond-mat/9302009

The Thermodynamics of quantum systems and generalizations of Zamolodchikov's C theorem

- Nucl.Phys.B 400 (1993) 525-546
•
e-Print:
- cond-mat/9301009
•
DOI:
- 10.1016/0550-3213(93)90414-K

Is There a c Theorem in Four-Dimensions?

John L. Cardy
(
- UC, Santa Barbara
)

- Phys.Lett.B 215 (1988) 749-752
•
DOI:
- 10.1016/0370-2693(88)90054-8

Derivation of a Four-dimensional $c$ Theorem

H. Osborn
(
- Cambridge U.
)

- Phys.Lett.B 222 (1989) 97-102
•
DOI:
- 10.1016/0370-2693(89)90729-6

Analogs for the $c$ Theorem for Four-dimensional Renormalizable Field Theories

I. Jack
(
- CERN
)
,
H. Osborn
(
- Cambridge U.
)

- Nucl.Phys.B 343 (1990) 647-688,
- Nucl. Phys. B343 (1990) 647-688 and Cambridge Univ. - DAMTP 90-02 (90,rec.Apr.) 37 p
•
DOI:
- 10.1016/0550-3213(90)90584-Z

C theorem and spectral representation

Andrea Cappelli
(
- INFN, Florence
)
,
Daniel Friedan
(
- Rutgers U., Piscataway
)
,
Jose I. Latorre
(
- Barcelona U.
)

- Nucl.Phys.B 352 (1991) 616-670
•
DOI:
- 10.1016/0550-3213(91)90102-4

A new c theorem in four-dimensions

G.M. Shore
(
- CERN
)

- Phys.Lett.B 253 (1991) 380-390
•
DOI:
- 10.1016/0370-2693(91)91736-F

The C(F) theorem

G.M. Shore
(
- CERN
)

- Phys.Lett.B 256 (1991) 407-415
•
DOI:
- 10.1016/0370-2693(91)91783-R

Renormalization group patterns and C theorem in more than two-dimensions

Andrea Cappelli
(
- CERN
)
,
Jose Ignacio Latorre
(
- CERN
)
,
Xavier Vilasis-Cardona
(
- Barcelona U.
)

- Nucl.Phys.B 376 (1992) 510-538
•
e-Print:
- hep-th/9109041
•
DOI:
- 10.1016/0550-3213(92)90119-V

Exact results on the space of vacua of four-dimensional SUSY gauge theories

Nathan Seiberg
(
- Rutgers U., Piscataway
)

- Phys.Rev.D 49 (1994) 6857-6863
•
e-Print:
- hep-th/9402044
•
DOI:
- 10.1103/PhysRevD.49.6857

Electric - magnetic duality in supersymmetric nonAbelian gauge theories

N. Seiberg
(
- Rutgers U., Piscataway and
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 435 (1995) 129-146
•
e-Print:
- hep-th/9411149
•
DOI:
- 10.1016/0550-3213(94)00023-8

Lectures on supersymmetric gauge theories and electric-magnetic duality

- Nucl.Phys.B Proc.Suppl. 45BC (1996) 1-28,
- Subnucl.Ser. 34 (1997) 237-299,
- ,
- ,
- ,
•
e-Print:
- hep-th/9509066
•
DOI:
- 10.1016/0920-5632(95)00626-5