On the Integrability of Planar $N=2$ Superconformal Gauge Theories - INSPIRE

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On the Integrability of Planar $N=2$ Superconformal Gauge Theories

Abhijit Gadde
(
- YITP, Stony Brook and
- Caltech
)
,
Pedro Liendo
(
- YITP, Stony Brook
)
,
Leonardo Rastelli
(
- YITP, Stony Brook
)
,
Wenbin Yan
(
- YITP, Stony Brook and
- Caltech
)

Nov, 2012

18 pages

Published in:

JHEP 08 (2013) 015

Published: 2013

e-Print:

1211.0271 [hep-th]

DOI:

10.1007/JHEP08(2013)015

Report number:

YITP-SB-12-38

View in:

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Abstract: (Springer)

We study the integrability properties of planar superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2, 1|2) sector, which exists in any superconformal gauge theory, may be integrable to all loops. We summarize the known results in the literature that are consistent with this conjecture.

Note:

20 pages, 1 figure. v2: minor changes, JHEP version

Supersymmetric gauge theory
1/N Expansion
Integrable Field Theories
gauge field theory: conformal
spin: chain
operator: dilation
magnon: scattering
integrability
quantum chromodynamics
Yang-Baxter equation

References(43)

Figures(2)

[1]

Review of AdS/CFT Integrability: An Overview

Niklas Beisert
(
- Potsdam, Max Planck Inst.
)
,
Changrim Ahn
(
- Ewha Women's U., Seoul
)
,
Luis F. Alday
(
- Oxford U. and
- Princeton, Inst. Advanced Study
)
,
Zoltan Bajnok
(
- Hungarian Acad. Sci., Budapest
)
,
James M. Drummond
(
- CERN and
- Annecy, LAPTH
)

et al.

- Lett.Math.Phys. 99 (2012) 3-32
•
e-Print:
- 1012.3982
•
DOI:
- 10.1007/s11005-011-0529-2

[2]

Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models

L.N. Lipatov
(
- St. Petersburg, INP and
- INFN, Padua
)

- JETP Lett. 59 (1994) 596-599,
- Pisma Zh.Eksp.Teor.Fiz. 59 (1994) 571-574
•
e-Print:
- hep-th/9311037

[3]

High-energy QCD as a completely integrable model

L.D. Faddeev
(
- Steklov Math. Inst., St. Petersburg and
- Helsinki U.
)
,
G.P. Korchemsky
(
- SUNY, Stony Brook
)

- Phys.Lett.B 342 (1995) 311-322
•
e-Print:
- hep-th/9404173
•
DOI:
- 10.1016/0370-2693(94)01363-H

[4]

Bethe ansatz for QCD pomeron

G.P. Korchemsky
(
- SUNY, Stony Brook
)

- Nucl.Phys.B 443 (1995) 255-304
•
e-Print:
- hep-ph/9501232
•
DOI:
- 10.1016/0550-3213(95)00099-E

[5]

Integrability of three particle evolution equations in QCD

- Phys.Rev.Lett. 81 (1998) 2020-2023
•
e-Print:
- hep-ph/9805225
•
DOI:
- 10.1103/PhysRevLett.81.2020

[6]

Baryon distribution amplitudes in QCD

Vladimir M. Braun
(
- Nordita
)
,
Sergey E. Derkachov
(
- St. Petersburg Inst. Tech.
)
,
G.P. Korchemsky
(
- Orsay, LPT
)
,
A.N. Manashov
(
- St. Petersburg State U.
)

- Nucl.Phys.B 553 (1999) 355-426
•
e-Print:
- hep-ph/9902375
•
DOI:
- 10.1016/S0550-3213(99)00265-5

[7]

Renormalization of twist - three operators and integrable lattice models

Andrei V. Belitsky
(
- Regensburg U.
)

- Nucl.Phys.B 574 (2000) 407-447
•
e-Print:
- hep-ph/9907420
•
DOI:
- 10.1016/S0550-3213(00)00003-1

[8]

One-loop QCD spin chain and its spectrum

Niklas Beisert
(
- Potsdam, Max Planck Inst. and
- Princeton U. and
- Santa Barbara, KITP
)
,
Gabriele Ferretti
(
- Goteborg, ITP
)
,
Rainer Heise
(
- Goteborg, ITP
)
,
Konstantin Zarembo
(
- Uppsala U., Inst. Theor. Phys. and
- Moscow, ITEP
)

- Nucl.Phys.B 717 (2005) 137-189
•
e-Print:
- hep-th/0412029
•
DOI:
- 10.1016/j.nuclphysb.2005.04.004

[9]

Quantum integrability in superYang-Mills theory on the light cone

Andrei V. Belitsky
(
- Maryland U.
)
,
Sergey E. Derkachov
(
- Orsay, LPT and
- St. Petersburg State U.
)
,
G.P. Korchemsky
(
- Orsay, LPT
)
,
A.N. Manashov
(
- Ruhr U., Bochum and
- St. Petersburg State U.
)

- Phys.Lett.B 594 (2004) 385-401
•
e-Print:
- hep-th/0403085
•
DOI:
- 10.1016/j.physletb.2004.04.092

[10]

Dilatation operator in (super-)Yang-Mills theories on the light-cone

A.V. Belitsky
(
- Arizona State U.
)
,
Sergey E. Derkachov
(
- Orsay, LPT and
- St. Petersburg State U.
)
,
G.P. Korchemsky
(
- Orsay, LPT
)
,
A.N. Manashov
(
- Regensburg U. and
- St. Petersburg State U.
)

- Nucl.Phys.B 708 (2005) 115-193
•
e-Print:
- hep-th/0409120
•
DOI:
- 10.1016/j.nuclphysb.2004.11.034

[11]

Integrability in Yang-Mills theory on the light cone beyond leading order

- Phys.Rev.Lett. 94 (2005) 151603
•
e-Print:
- hep-th/0412054
•
DOI:
- 10.1103/PhysRevLett.94.151603

[12]

Integrability of two-loop dilatation operator in gauge theories

- Nucl.Phys.B 735 (2006) 17-83
•
e-Print:
- hep-th/0509121
•
DOI:
- 10.1016/j.nuclphysb.2005.11.015

[13]

Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM

G.P. Korchemsky
(
- Saclay, SPhT
)

- Lett.Math.Phys. 99 (2012) 425-453
•
e-Print:
- 1012.4000
•
DOI:
- 10.1007/s11005-011-0516-7

[14]

The Bethe ansatz for N=4 superYang-Mills

- JHEP 03 (2003) 013
•
e-Print:
- hep-th/0212208
•
DOI:
- 10.1088/1126-6708/2003/03/013

[15]

The Dilatation operator of conformal N=4 superYang-Mills theory

- Nucl.Phys.B 664 (2003) 131-184
•
e-Print:
- hep-th/0303060
•
DOI:
- 10.1016/S0550-3213(03)00406-1

[16]

The complete one loop dilatation operator of N=4 superYang-Mills theory

Niklas Beisert
(
- Potsdam, Max Planck Inst.
)

- Nucl.Phys.B 676 (2004) 3-42
•
e-Print:
- hep-th/0307015
•
DOI:
- 10.1016/j.nuclphysb.2003.10.019

[17]

The su(2|3) dynamic spin chain

Niklas Beisert
(
- Potsdam, Max Planck Inst.
)

- Nucl.Phys.B 682 (2004) 487-520
•
e-Print:
- hep-th/0310252
•
DOI:
- 10.1016/j.nuclphysb.2003.12.032

[18]

N=4 SYM to two loops: Compact expressions for the non-compact symmetry algebra of the su(1,1|2) sector

Benjamin I. Zwiebel
(
- Princeton U.
)

- JHEP 02 (2006) 055
•
e-Print:
- hep-th/0511109
•
DOI:
- 10.1088/1126-6708/2006/02/055

[19]

Superspace calculation of the three-loop dilatation operator of N=4 SYM theory

Christoph Sieg
(
- Bohr Inst.
)

- Phys.Rev.D 84 (2011) 045014
•
e-Print:
- 1008.3351
•
DOI:
- 10.1103/PhysRevD.84.045014

[20]

From Scattering Amplitudes to the Dilatation Generator in N=4 SYM

Benjamin I. Zwiebel
(
- Caltech
)

- J.Phys.A 45 (2012) 115401
•
e-Print:
- 1111.0083
•
DOI:
- 10.1088/1751-8113/45/11/115401

[21]

Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills

Joseph A. Minahan
(
- Uppsala U., Inst. Theor. Phys.
)

- Lett.Math.Phys. 99 (2012) 33-58
•
e-Print:
- 1012.3983
•
DOI:
- 10.1007/s11005-011-0522-9

[22]

Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory

C. Sieg
(
)

- Lett.Math.Phys. 99 (2012) 59-84
•
e-Print:
- 1012.3984
•
DOI:
- 10.1007/s11005-011-0508-7

[23]

Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries

Konstantinos Zoubos
(
- Bohr Inst.
)

- Lett.Math.Phys. 99 (2012) 375-400
•
e-Print:
- 1012.3998
•
DOI:
- 10.1007/s11005-011-0515-8

[24]

The Veneziano Limit of N = 2 Superconformal QCD: Towards the String Dual of N = 2 SU(N(c)) SYM with N(f) = 2 N(c)

Abhijit Gadde
(
- YITP, Stony Brook
)
,
Elli Pomoni
(
- YITP, Stony Brook
)
,
Leonardo Rastelli
(
- YITP, Stony Brook
)

e-Print:
- 0912.4918

[25]

Spin Chains in $\mathcal{N}$ =2 Superconformal Theories: From the $\mathbb{Z}_{2}$ Quiver to Superconformal QCD

Abhijit Gadde
(
- YITP, Stony Brook
)
,
Elli Pomoni
(
- YITP, Stony Brook
)
,
Leonardo Rastelli
(
- YITP, Stony Brook
)

- JHEP 06 (2012) 107
•
e-Print:
- 1006.0015
•
DOI:
- 10.1007/JHEP06(2012)107

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