Isometry Group Orbit Quantization of Spinning Strings in AdS$_{3} \times$ S$^3$ - INSPIRE

DataBETA

Isometry Group Orbit Quantization of Spinning Strings in AdS $_{3} \times$ S $^3$

Martin Heinze
(
- Humboldt U., Berlin
)
,
George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst. and
- Unlisted, GE
)
,
Luka Megrelidze
(
- Ilia State U.
)

Oct 13, 2014

16 pages

Published in:

J.Phys.A 48 (2015) 12, 125401

Published: Mar 6, 2015

e-Print:

1410.3428 [hep-th]

DOI:

10.1088/1751-8113/48/12/125401

Report number:

HU-EP-14-39,
NORDITA-2014-113

View in:

reference search11 citations

Citations per year

Abstract: (IOP)

Describing the bosonic AdS

_{3}\,\times \,

S(3) particle and string in SU(1,1) × SU(2) group variables, we provide a Hamiltonian treatment of the isometry group orbits of solutions via analysis of the pre-symplectic form. For the particle we obtain a one-parameter family of orbits parameterized by creation–annihilation variables, which leads to the Holstein–Primakoff realization of the isometry group generators. The scheme is then applied to spinning string solutions characterized by one winding number in AdS(3) and two winding numbers in S(3). We find a two-parameter family of orbits, where quantization again provides the Holstein–Primakoff realization of the symmetry generators with an oscillator-type energy spectrum. Analyzing the minimal energy at strong coupling, we verify the spectrum of short strings at special values of winding numbers.

Note:

17 pages, v2: references changed, typos corrected, published in JPhysA

group: isometry
string: spin
orbit: quantization
group: SU(2)
anti-de Sitter
strong coupling
energy spectrum
Hamiltonian
oscillator
SU(1,1)

References(51)

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

[2]

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

[2]

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

[3]

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

[3]

Quantum spectral curve for arbitrary state/operator in AdS $_{5}$ /CFT $_{4}$

Nikolay Gromov
(
- King's Coll. London, Dept. Math and
- St. Petersburg, INP
)
,
Vladimir Kazakov
(
)
,
Sébastien Leurent
(
- Bourgogne U.
)
,
Dmytro Volin
(
- Nordita and
- Trinity Coll., Dublin and
- Stockholm U. (main)
)

- JHEP 09 (2015) 187
•
e-Print:
- 1405.4857
•
DOI:
- 10.1007/JHEP09(2015)187

[3]

Quantum Spectral Curve of the $\mathcal N=$ 6 Supersymmetric Chern-Simons Theory

Andrea Cavaglià
(
- Turin U. and
- INFN, Turin
)
,
Davide Fioravanti
(
- INFN, Bologna and
- Bologna U.
)
,
Nikolay Gromov
(
- King's Coll. London, Dept. Math and
- St. Petersburg, INP
)
,
Roberto Tateo
(
- Turin U. and
- INFN, Turin
)

- Phys.Rev.Lett. 113 (2014) 2, 021601
•
e-Print:
- 1403.1859
•
DOI:
- 10.1103/PhysRevLett.113.021601

[4]

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

[5]

Strings in flat space and pp waves from N=4 superYang-Mills

- JHEP 04 (2002) 013
•
e-Print:
- hep-th/0202021
•
DOI:
- 10.1088/1126-6708/2002/04/013

[5]

Semiclassical quantization of rotating superstring in AdS(5) x S**5

S. Frolov
(
- Ohio State U.
)
,
Arkady A. Tseytlin
(
- Ohio State U. and
- Imperial Coll., London
)

- JHEP 06 (2002) 007
•
e-Print:
- hep-th/0204226
•
DOI:
- 10.1088/1126-6708/2002/06/007

[6]

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

[7]

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

[7]

Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions

A.A. Tseytlin
(
- Imperial Coll., London
)

- Lett.Math.Phys. 99 (2012) 103-125
•
e-Print:
- 1012.3986
•
DOI:
- 10.1007/s11005-011-0466-0

[7]

Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5

Tristan McLoughlin
(
- Potsdam, Max Planck Inst.
)

- Lett.Math.Phys. 99 (2012) 127-148
•
e-Print:
- 1012.3987
•
DOI:
- 10.1007/s11005-011-0510-0

[8]

On the Spectrum of the $AdS_{5}$ x $S^{5}$ String at large $\lambda$

Filippo Passerini
(
- Humboldt U., Berlin
)
,
Jan Plefka
(
- Humboldt U., Berlin
)
,
Gordon W. Semenoff
(
- British Columbia U.
)
,
Donovan Young
(
- Copenhagen U.
)

- JHEP 03 (2011) 046
•
e-Print:
- 1012.4471
•
DOI:
- 10.1007/JHEP03(2011)046

[9]

Bosonic String Quantization in Static Gauge

George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst. and
- Tbilisi State U.
)
,
Jan Plefka
(
- Humboldt U., Berlin
)
,
Jonas Pollok
(
- Humboldt U., Berlin
)

- J.Phys.A 45 (2012) 485401
•
e-Print:
- 1207.4368
•
DOI:
- 10.1088/1751-8113/45/48/485401

[10]

Static gauge and energy spectrum of single-mode strings in AdS $_{5} ×$ S $^{5}$

Sergey Frolov
(
)
,
Martin Heinze
(
- Humboldt U., Berlin
)
,
George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst.
)
,
Jan Plefka
(
- Humboldt U., Berlin
)

- J.Phys.A 47 (2014) 085401
•
e-Print:
- 1310.5052
•
DOI:
- 10.1088/1751-8113/47/8/085401

[11]

Semiclassical quantization of circular strings in de Sitter and anti-de Sitter space-times

- Phys.Rev.D 51 (1995) 6917-6928
•
e-Print:
- hep-th/9410219
•
DOI:
- 10.1103/PhysRevD.51.6917

[11]

Circular semiclassical string solutions on AdS(5) x S(5)

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

- Nucl.Phys.B 648 (2003) 203-214
•
e-Print:
- hep-th/0209047
•
DOI:
- 10.1016/S0550-3213(02)00966-5

[12]

Path Integral Quantization of the Coadjoint Orbits of the Virasoro Group and 2D Gravity

- Nucl.Phys.B 323 (1989) 719-733
•
DOI:
- 10.1016/0550-3213(89)90130-2

[13]

Oscillator quantization of the massive scalar particle dynamics on ads spacetime

- Phys.Lett.B 625 (2005) 117-126
•
e-Print:
- hep-th/0507031
•
DOI:
- 10.1016/j.physletb.2005.08.059

[14]

Coordinate representation of particle dynamics in AdS and in generic static spacetimes

Harald Dorn
(
- Humboldt U., Berlin
)
,
George Jorjadze
(
- Humboldt U., Berlin and
- Razmadze Math. Inst.
)
,
Chrysostomos Kalousios
(
- Humboldt U., Berlin
)
,
Jan Plefka
(
- Humboldt U., Berlin
)

- J.Phys.A 44 (2011) 095402
•
e-Print:
- 1011.3416
•
DOI:
- 10.1088/1751-8113/44/9/095402

[15]

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

[16]

IIB supergravity and various aspects of light cone formalism in AdS space-time

R.R. Metsaev
(
- Lebedev Inst.
)

e-Print:
- hep-th/0002008

[16]

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

[16]

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

1-25 of 51
1
2
3
25 / page