Orbit method quantization of the AdS$_2$ superparticle - INSPIRE

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Orbit method quantization of the AdS $_2$ superparticle

Martin Heinze
(
- Hamburg U., Inst. Theor. Phys. II
)
,
Ben Hoare
(
- Humboldt U., Berlin
)
,
George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst. and
- Tbilisi State U.
)
,
Luka Megrelidze
(
- Ilia State U.
)

Apr 16, 2015

17 pages

Published in:

J.Phys.A 48 (2015) 31, 315403

Published: Jul 20, 2015

e-Print:

1504.04175 [hep-th]

DOI:

10.1088/1751-8113/48/31/315403

Report number:

FUT-PH-03-15,
HU-EP-15-15,
ZMP-HH-15-5

View in:

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Abstract: (IOP)

We consider the Hamiltonian reduction and canonical quantization of a massive AdS(2) superparticle realized on the coset

\mathrm{OSP}(1| 2)/

SO(1,1). The phase space of the massive superparticle is represented as a coadjoint orbit of a timelike element of

{\mathfrak{osp}}(1| 2)

. This orbit has a well defined symplectic structure and the

\mathrm{OSP}(1| 2)

symmetry is realized as the Poisson bracket algebra of the Noether charges. We then construct canonical coordinates given by one bosonic and one fermionic oscillator, whose quantization leads to the Holstein–Primakoff type realization of

{\mathfrak{osp}}(1| 2)

. We also perform a similar analysis and discuss new features and inconsistencies in the massless case.

Note:

19 pages; v2: typos corrected, references added, matches published version

AdS/CFT correspondence
superparticle
coset superspace
AdS $_2$
OSP (1∣2)
geometric quantization
quantization: canonical
charge: Noether
sparticle
orbit

References(64)

Figures(0)

[1]

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

[1]

Anti-de Sitter space and holography

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Adv.Theor.Math.Phys. 2 (1998) 253-291
•
e-Print:
- hep-th/9802150
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a2

[1]

Gauge theory correlators from noncritical string theory

S.S. Gubser
(
- Princeton U.
)
,
Igor R. Klebanov
(
- Princeton U.
)
,
Alexander M. Polyakov
(
- Princeton U.
)

- Phys.Lett.B 428 (1998) 105-114
•
e-Print:
- hep-th/9802109
•
DOI:
- 10.1016/S0370-2693(98)00377-3

[2]

Type IIB superstring action in AdS(5) x S**5 background

R.R. Metsaev
(
- Lebedev Inst.
)
,
Arkady A. Tseytlin
(
- Lebedev Inst. and
- Imperial Coll., London and
- Santa Barbara, KITP
)

- Nucl.Phys.B 533 (1998) 109-126
•
e-Print:
- hep-th/9805028
•
DOI:
- 10.1016/S0550-3213(98)00570-7

[3]

Foundations of the AdS $_{5} \times S^{5}$ Superstring. Part I

- J.Phys.A 42 (2009) 254003
•
e-Print:
- 0901.4937
•
DOI:
- 10.1088/1751-8113/42/25/254003

[3]

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

[4]

Hidden Symmetries of the AdS $_5 \times S^5$ Superstring

Iosif Bena
(
- UCLA
)
,
Joseph Polchinski
(
- Santa Barbara, KITP
)
,
Radu Roiban
(
- UC, Santa Barbara
)

- Phys.Rev.D 69 (2004) 046002
•
e-Print:
- hep-th/0305116
•
DOI:
- 10.1103/PhysRevD.69.046002

[5]

TBA and Y-system for planar AdS(4)/CFT(3)

Diego Bombardelli
(
- INFN, Bologna and
- Bologna U.
)
,
Davide Fioravanti
(
- INFN, Bologna and
- Bologna U.
)
,
Roberto Tateo
(
- Turin U. and
- INFN, Turin
)

- Nucl.Phys.B 834 (2010) 543-561
•
e-Print:
- 0912.4715
•
DOI:
- 10.1016/j.nuclphysb.2010.04.005

[5]

Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory: TBA and excited states

Nikolay Gromov
(
- DESY and
- Hamburg U., Inst. Theor. Phys. II and
- St. Petersburg, INP
)
,
Vladimir Kazakov
(
- Ecole Normale Superieure
)
,
Andrii Kozak
(
- Ecole Normale Superieure
)
,
Pedro Vieira
(
- Potsdam, Max Planck Inst.
)

- Lett.Math.Phys. 91 (2010) 265-287
•
e-Print:
- 0902.4458
•
DOI:
- 10.1007/s11005-010-0374-8

[5]

Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory

Nikolay Gromov
(
- St. Petersburg, INP and
- Hamburg U., Inst. Theor. Phys. II and
- DESY
)
,
Vladimir Kazakov
(
- Paris U., VI-VII and
- Ecole Normale Superieure
)
,
Pedro Vieira
(
- Porto U. and
- Potsdam, Max Planck Inst.
)

- Phys.Rev.Lett. 103 (2009) 131601
•
e-Print:
- 0901.3753
•
DOI:
- 10.1103/PhysRevLett.103.131601

[5]

Quantum Spectral Curve for Planar $\mathcal{N} = 4$ Super-Yang-Mills Theory

Nikolay Gromov
(
- King's Coll. London, Dept. Math and
- St. Petersburg, INP
)
,
Vladimir Kazakov
(
- Paris U., VI-VII and
- Ecole Normale Superieure
)
,
Sebastien Leurent
(
- Imperial Coll., London
)
,
Dmytro Volin
(
- Nordita and
- Royal Inst. Tech., Stockholm and
- Stockholm U.
)

- Phys.Rev.Lett. 112 (2014) 1, 011602
•
e-Print:
- 1305.1939
•
DOI:
- 10.1103/PhysRevLett.112.011602

[6]

Exact Spectrum of Planar ${\cal N}=4$ Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling

Nikolay Gromov
(
- DESY and
- Hamburg U., Inst. Theor. Phys. II and
- St. Petersburg, INP
)
,
Vladimir Kazakov
(
- Ecole Normale Superieure and
- Paris U., VI-VII
)
,
Pedro Vieira
(
- Potsdam, Max Planck Inst. and
- Porto U.
)

- Phys.Rev.Lett. 104 (2010) 211601
•
e-Print:
- 0906.4240
•
DOI:
- 10.1103/PhysRevLett.104.211601

[6]

Konishi operator at intermediate coupling

Sergey Frolov
(
- Trinity Coll., Dublin
)

- J.Phys.A 44 (2011) 065401
•
e-Print:
- 1006.5032
•
DOI:
- 10.1088/1751-8113/44/6/065401

[6]

Orbit method quantization of the AdS $_2$ superparticle

Martin Heinze
(
- Hamburg U., Inst. Theor. Phys. II
)
,
Ben Hoare
(
- Humboldt U., Berlin
)
,
George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst. and
- Tbilisi State U.
)
,
Luka Megrelidze
(
- Ilia State U.
)

- J.Phys.A 48 (2015) 31, 315403
•
e-Print:
- 1504.04175
•
DOI:
- 10.1088/1751-8113/48/31/315403

[6]

Scaling dimensions from the mirror TBA

Sergey Frolov
(
- Hamilton Math. Inst., Dublin
)

- J.Phys.A 45 (2012) 305402
•
e-Print:
- 1201.2317
•
DOI:
- 10.1088/1751-8113/45/30/305402

[7]

The Mass Spectrum of Chiral N=2 D=10 Supergravity on S**5

H.J. Kim
(
- SUNY, Stony Brook
)
,
L.J. Romans
(
- Caltech
)
,
P. van Nieuwenhuizen
(
- SUNY, Stony Brook
)

- Phys.Rev.D 32 (1985) 389
•
DOI:
- 10.1103/PhysRevD.32.389

[7]

The Spectrum of the s**5 Compactification of the Chiral N=2, D=10 Supergravity and the Unitary Supermultiplets of U(2, 2/4)

M. Gunaydin
(
- Caltech
)
,
N. Marcus
(
- UC, Berkeley
)

- Class.Quant.Grav. 2 (1985) L11
•
DOI:
- 10.1088/0264-9381/2/2/001

[8]

Exact Quantization of a Superparticle in AdS(5) x S**5

Tetsuo Horigane
(
- Tokyo U., Komaba
)
,
Yoichi Kazama
(
- Tokyo U., Komaba
)

- Phys.Rev.D 81 (2010) 045004
•
e-Print:
- 0912.1166
•
DOI:
- 10.1103/PhysRevD.81.045004

[9]

Light cone gauge formulation of IIB supergravity in AdS(5) x S**5 background and AdS / CFT correspondence

R.R. Metsaev
(
- Lebedev Inst.
)

- Phys.Lett.B 468 (1999) 65-75
•
e-Print:
- hep-th/9908114
•
DOI:
- 10.1016/S0370-2693(99)01063-1

[10]

Light cone superstring in AdS space-time

R.R. Metsaev
(
- Ohio State U. and
- Lebedev Inst.
)
,
Charles B. Thorn
(
- Florida U.
)
,
Arkady A. Tseytlin
(
- Ohio State U.
)

- Nucl.Phys.B 596 (2001) 151-184
•
e-Print:
- hep-th/0009171
•
DOI:
- 10.1016/S0550-3213(00)00712-4

[11]

Spacecone quantization of AdS superparticle

W. Siegel
(
- SUNY, Stony Brook
)

e-Print:
- 1005.5049

[12]

Strings in flat space and pp waves from 4 = super Yang-Mills J High Energy Phys. JHEP04013

Berenstein D
,
Maldacena J. M
,
Nastase H

[13]

A Semiclassical limit of the gauge / string correspondence

S.S. Gubser
(
- Princeton U.
)
,
I.R. Klebanov
(
- Princeton U.
)
,
Alexander M. Polyakov
(
- Princeton U.
)

- Nucl.Phys.B 636 (2002) 99-114
•
e-Print:
- hep-th/0204051
•
DOI:
- 10.1016/S0550-3213(02)00373-5

[14]

Semiclassical quantization of rotating superstring in AdS5 × S5 J. High Energy Phys. JHEP06007

Frolov S
,
Tseytlin A. A

[15]

Multispin string solutions in AdS(5) x S**5

S. Frolov
(
- Ohio State U. and
- Steklov Math. Inst., Moscow
)
,
Arkady A. Tseytlin
(
- Ohio State U. and
- Imperial Coll., London and
- Lebedev Inst.
)

- Nucl.Phys.B 668 (2003) 77-110
•
e-Print:
- hep-th/0304255
•
DOI:
- 10.1016/S0550-3213(03)00580-7

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