From superYang-Mills theory to QCD: Planar equivalence and its implications

We review and extend our recent work on the planar (large N) equivalence between gauge theories with varying degree of supersymmetry. The main emphasis is made on the planar equivalence between N=1 gluodynamics (super-Yang-Mills theory) and a non-supersymmetric orientifold field theory. We outline an orientifold large N expansion, analyze its possible phenomenological consequences in one-flavor massless QCD, and make a first attempt at extending the correspondence to three massless flavors. An analytic calculation of the quark condensate in one-flavor QCD starting from the gluino condensate in N=1 gluodynamics is thoroughly discussed. We also comment on a planar equivalence involving N=2 supersymmetry, on chiral rings in non-supersymmetric theories, and on the origin of planar equivalence from an underlying, non-tachyonic type-0 string theory. Finally, possible further directions of investigation, such as the gauge/gravity correspondence in large-N orientifold field theory, are briefly discussed.

Note:

To be published in the Ian Kogan memorial collection 'From Fields to Strings: Circumnavigating Theoretical Physics', World Scientific, 2004 •
106 pages, LaTex. 15 figures. v2:minor changes, refs. added. To be published in the Ian Kogan Memorial Collection "From Fields to Strings: Circumnavigating Theoretical Physics," World Scientific, 2004

gauge field theory: SU(N)
supersymmetry: superfield
supersymmetry: superspace
expansion 1/N
vacuum state
orbifold
orientifold
Feynman graph: planar
fermion: flavor
energy

References(142)

Figures(8)

[1]

Supersymmetry and supergravity

J. Bagger
,
J. Wess

[2]

The Power of holomorphy: Exact results in 4-D SUSY field theories

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

- PASCOS 1994:0357-369
•
e-Print:
- hep-th/9408013

[2]

The Power of duality: Exact results in 4-D SUSY field theory

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

- Int.J.Mod.Phys.A 16 (2001) 4365-4376,
- PASCOS/Hopkins 1995:0183-198,
- In *Bergstroem, L. (ed.) et al.: The Oskar Klein memorial lectures, vol. 3* 43-57,
- Prog.Theor.Phys.Suppl. 123 (1996) 337-347,
- In *Seoul 1996, Current topics in physics, vol. 1* 106-120
•
e-Print:
- hep-th/9506077
•
DOI:
- 10.1142/S0217751X01005705

[3]

Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory

- Nucl.Phys.B 426 (1994) 19-52,
- Nucl.Phys.B 430 (1994) 485-486 (erratum)
•
e-Print:
- hep-th/9407087
•
DOI:
- 10.1016/0550-3213(94)90124-4

[3]

Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD

- Nucl.Phys.B 431 (1994) 484-550
•
e-Print:
- hep-th/9408099
•
DOI:
- 10.1016/0550-3213(94)90214-3

[4]

Vortices and Quark Confinement in Nonabelian Gauge Theories

S. Mandelstam
(
- UC, Berkeley
)

- Phys.Rept. 23 (1976) 245-249,
- In *Gervais, J.L. (Ed.), Jacob, M. (Ed.): Non-linear and Collective Phenomena In Quantum Physics*, 12-16
•
DOI:
- 10.1016/0370-1573(76)90043-0

[5]

G. ’t Hooft, inCarg ́ese Summer School Lecture Notes on Fundamental Interactions, NATO Adv. Study Inst

Series B

[5]

: Phys., Vol. 85

M.L. ́evy

[5]

Topology of the Gauge Condition and New Confinement Phases in Nonabelian Gauge Theories

Gerard 't Hooft
(
- Caltech
)

- Nucl.Phys.B 190 (1981) 455-478
•
DOI:
- 10.1016/0550-3213(81)90442-9

[6]

Exact results in non-supersymmetric large N orientifold field theories

A. Armoni
(
- CERN
)
,
M. Shifman
(
- CERN and
- Minnesota U., Theor. Phys. Inst.
)
,
G. Veneziano
(
- CERN
)

- Nucl.Phys.B 667 (2003) 170-182
•
e-Print:
- hep-th/0302163
•
DOI:
- 10.1016/S0550-3213(03)00538-8

[7]

SUSY relics in one flavor QCD from a new 1/N expansion

A. Armoni
(
- CERN
)
,
M. Shifman
(
- CERN and
- Minnesota U., Theor. Phys. Inst.
)
,
G. Veneziano
(
- CERN
)

- Phys.Rev.Lett. 91 (2003) 191601
•
e-Print:
- hep-th/0307097
•
DOI:
- 10.1103/PhysRevLett.91.191601

[8]

QCD quark condensate from SUSY and the orientifold large N expansion

A. Armoni
(
- CERN
)
,
M. Shifman
(
- Minnesota U., Theor. Phys. Inst.
)
,
G. Veneziano
(
- CERN and
- Santa Barbara, KITP
)

- Phys.Lett.B 579 (2004) 384-390
•
e-Print:
- hep-th/0309013
•
DOI:
- 10.1016/j.physletb.2003.10.094

[9]

4-D conformal theories and strings on orbifolds

Shamit Kachru
(
- UC, Berkeley and
- LBL, Berkeley and
- Santa Barbara, KITP
)
,
Eva Silverstein
(
- SLAC and
- Santa Barbara, KITP
)

- Phys.Rev.Lett. 80 (1998) 4855-4858
•
e-Print:
- hep-th/9802183
•
DOI:
- 10.1103/PhysRevLett.80.4855

[10]

On conformal field theories in four-dimensions

Albion E. Lawrence
(
- Harvard U.
)
,
Nikita Nekrasov
(
- Moscow, ITEP and
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U.
)

- Nucl.Phys.B 533 (1998) 199-209
•
e-Print:
- hep-th/9803015
•
DOI:
- 10.1016/S0550-3213(98)00495-7

[11]

String expansion as large N expansion of gauge theories

Michael Bershadsky
(
- Harvard U.
)
,
Zurab Kakushadze
(
- Harvard U. and
- Northeastern U.
)
,
Cumrun Vafa
(
- Harvard U.
)

- Nucl.Phys.B 523 (1998) 59-72
•
e-Print:
- hep-th/9803076
•
DOI:
- 10.1016/S0550-3213(98)00272-7

[12]

A Planar Diagram Theory for Strong Interactions

Gerard 't Hooft
(
- CERN
)

- Nucl.Phys.B 72 (1974) 461,
•
DOI:
- 10.1016/0550-3213(74)90154-0

[13]

Large N limit of orbifold field theories

Michael Bershadsky
(
- Harvard U.
)
,
Andrei Johansen
(
- Harvard U.
)

- Nucl.Phys.B 536 (1998) 141-148
•
e-Print:
- hep-th/9803249
•
DOI:
- 10.1016/S0550-3213(98)00526-4

[14]

Gauge theories from orientifolds and large N limit

Zurab Kakushadze
(
- Harvard U. and
- Northeastern U.
)

- Nucl.Phys.B 529 (1998) 157-179
•
e-Print:
- hep-th/9803214
•
DOI:
- 10.1016/S0550-3213(98)00366-6

[14]

On large N gauge theories from orientifolds

Zurab Kakushadze
(
- Harvard U. and
- Northeastern U.
)

- Phys.Rev.D 58 (1998) 106003
•
e-Print:
- hep-th/9804184
•
DOI:
- 10.1103/PhysRevD.58.106003

[15]

Duality of nonsupersymmetric large N gauge theories

Martin Schmaltz
(
- Boston U.
)

- Phys.Rev.D 59 (1999) 105018
•
e-Print:
- hep-th/9805218
•
DOI:
- 10.1103/PhysRevD.59.105018

[16]

Nonsupersymmetric large N gauge theories from type 0 brane configurations

Adi Armoni
(
- Tel Aviv U.
)
,
Barak Kol
(
- Tel Aviv U.
)

- JHEP 07 (1999) 011
•
e-Print:
- hep-th/9906081
•
DOI:
- 10.1088/1126-6708/1999/07/011

[17]

On methods for extracting exact nonperturbative results in nonsupersymmetric gauge theories

Matthew J. Strassler
(
- Pennsylvania U.
)

e-Print:
- hep-th/0104032

[18]

Testing nonperturbative orbifold conjecture

- Phys.Rev.D 67 (2003) 022003
•
e-Print:
- hep-th/0208073
•
DOI:
- 10.1103/PhysRevD.67.022003

[19]

Comments on condensates in nonsupersymmetric orbifold field theories

David Tong
(
- MIT, LNS
)

- JHEP 03 (2003) 022
•
e-Print:
- hep-th/0212235
•
DOI:
- 10.1088/1126-6708/2003/03/022

[20]

Constraints on Supersymmetry Breaking

Edward Witten
(
- Princeton U.
)

- Nucl.Phys.B 202 (1982) 253,
- IN *FERRARA, S. (ED.): SUPERSYMMETRY, VOL. 1*, 490-553. (NUCL. PHYS. B202 (1982) 253-316) AND PREPRINT - WITTEN, E. (REC.MAR.82) 111 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(82)90071-2

1-25 of 142
1
2
3
4
5
6
25 / page