Higher Spins Without (Anti-)de Sitter

Can the holographic principle be extended beyond the well-known AdS/CFT correspondence? During the last couple of years, there has been a substantial amount of research trying to find answers for this question. In this work, we provide a review of recent developments of three-dimensional theories of gravity with higher spin symmetries. We focus in particular on a proposed holographic duality involving asymptotically flat spacetimes and higher spin extended bms 3 symmetries. In addition, we also discuss developments concerning relativistic and nonrelativistic higher spin algebras. As a special case, Carroll gravity will be discussed in detail.

Note:

35 pages, 3 figures; Invited contribution to a special issue of Universe on Higher Spin Gauge Theories edited by Andrea Campoleoni and Nicolas Boulanger; v2: corrected minor typos and added references; v3: corrected minor typos, matches published version

higher spin
non-anti-de sitter
flat space
holography
nonrelativistic holography

References(200)

Figures(0)

[1]

AdS dual of the critical O(N) vector model

I.R. Klebanov
(
- Princeton U.
)
,
A.M. Polyakov
(
- Princeton U.
)

- Phys.Lett.B 550 (2002) 213-219
•
e-Print:
- hep-th/0210114
•
DOI:
- 10.1016/S0370-2693(02)02980-5

[2]

Notes on higher spin symmetries

Andrei Mikhailov
(
- Santa Barbara, KITP
)

e-Print:
- hep-th/0201019

[3]

Massless higher spins and holography

E. Sezgin
(
- Texas A-M
)
,
P. Sundell
(
- Uppsala U., Inst. Theor. Phys.
)

- Nucl.Phys.B 644 (2002) 303-370,
- Nucl.Phys.B 660 (2003) 403-403 (erratum)
•
e-Print:
- hep-th/0205131
•
DOI:
- 10.1016/S0550-3213(02)00739-3

[4]

On the Gravitational Interaction of Massless Higher Spin Fields

E.S. Fradkin
(
- Lebedev Inst.
)
,
Mikhail A. Vasiliev
(
- Lebedev Inst.
)

- Phys.Lett.B 189 (1987) 89-95,
- Phys. Lett. B189 ( 1987) 89-95
•
DOI:
- 10.1016/0370-2693(87)91275-5

[5]

Cubic Interaction in Extended Theories of Massless Higher Spin Fields

E.S. Fradkin
(
- Lebedev Inst.
)
,
Mikhail A. Vasiliev
(
- Lebedev Inst.
)

- Nucl.Phys.B 291 (1987) 141-171
•
DOI:
- 10.1016/0550-3213(87)90469-X

[6]

Consistent equation for interacting gauge fields of all spins in (3+1)-dimensions

Mikhail A. Vasiliev
(
- Lebedev Inst.
)

- Phys.Lett.B 243 (1990) 378-382,
- Phys. Lett. B243 (1990) 378-382 and Moscow Inst. Phys. Acad. Sci. - 90-029 (90,rec.Jul.) 11 p
•
DOI:
- 10.1016/0370-2693(90)91400-6

[7]

String Lessons for Higher-Spin Interactions

A. Sagnotti
(
- Pisa, Scuola Normale Superiore and
- INFN, Pisa
)
,
M. Taronna
(
- Pisa, Scuola Normale Superiore and
- INFN, Pisa
)

- Nucl.Phys.B 842 (2011) 299-361
•
e-Print:
- 1006.5242
•
DOI:
- 10.1016/j.nuclphysb.2010.08.019

[8]

Holography, Unfolding and Higher-Spin Theory

Mikhail A. Vasiliev
(
- Lebedev Inst.
)

- J.Phys.A 46 (2013) 214013
•
e-Print:
- 1203.5554
•
DOI:
- 10.1088/1751-8113/46/21/214013

[9]

Elements of Vasiliev Theory

V.E. Didenko
(
- Lebedev Inst.
)
,
E.D. Skvortsov
(
- Lebedev Inst. and
- Potsdam, Max Planck Inst.
)

- Lect.Notes Phys. 1028 (2024) 269-456
•
e-Print:
- 1401.2975
•
DOI:
- 10.1007/978-3-031-59656-8_3

[10]

Higher Spin Gauge Theory and Holography: The Three-Point Functions

- JHEP 09 (2010) 115
•
e-Print:
- 0912.3462
•
DOI:
- 10.1007/JHEP09(2010)115

[11]

Higher Spins in AdS and Twistorial Holography

Simone Giombi
(
- Harvard U.
)
,
Xi Yin
(
- Harvard U., Phys. Dept. and
- Princeton, Inst. Advanced Study
)

- JHEP 04 (2011) 086
•
e-Print:
- 1004.3736
•
DOI:
- 10.1007/JHEP04(2011)086

[12]

$AdS_4/CFT_3$ Construction from Collective Fields

Robert de Mello Koch
(
- Witwatersrand U.
)
,
Antal Jevicki
(
- Brown U.
)
,
Kewang Jin
(
- Brown U.
)
,
Joao P. Rodrigues
(
- Witwatersrand U.
)

- Phys.Rev.D 83 (2011) 025006
•
e-Print:
- 1008.0633
•
DOI:
- 10.1103/PhysRevD.83.025006

[13]

On Higher Spin Gauge Theory and the Critical O(N) Model

- Phys.Rev.D 85 (2012) 086005
•
e-Print:
- 1105.4011
•
DOI:
- 10.1103/PhysRevD.85.086005

[14]

Holographic dual of free field theory

Michael R. Douglas
(
- SUNY, Stony Brook
)
,
Luca Mazzucato
(
- SUNY, Stony Brook
)
,
Shlomo S. Razamat
(
- SUNY, Stony Brook
)

- Phys.Rev.D 83 (2011) 071701
•
e-Print:
- 1011.4926
•
DOI:
- 10.1103/PhysRevD.83.071701

[15]

The Higher Spin/Vector Model Duality

- J.Phys.A 46 (2013) 214003
•
e-Print:
- 1208.4036
•
DOI:
- 10.1088/1751-8113/46/21/214003

[16]

Higher Spin Interactions from Conformal Field Theory: The Complete Cubic Couplings

- Phys.Rev.Lett. 116 (2016) 18, 181602
•
e-Print:
- 1603.00022
•
DOI:
- 10.1103/PhysRevLett.116.181602

[17]

Constraining Conformal Field Theories with A Higher Spin Symmetry

- J.Phys.A 46 (2013) 214011
•
e-Print:
- 1112.1016
•
DOI:
- 10.1088/1751-8113/46/21/214011

[18]

Constraining conformal field theories with a slightly broken higher spin symmetry

- Class.Quant.Grav. 30 (2013) 104003
•
e-Print:
- 1204.3882
•
DOI:
- 10.1088/0264-9381/30/10/104003

[19]

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