406
A. Castro
expect that the intertwining of the two copies of sl(2) will produce interesting
features. For example, we should be able to probe if the global conditions on the
|U states are enhanced to the Virasoro conditions on the Ishibashi state [60, 61], or
something completely different, such as the conditions proposed in [62]. We leave
these questions for future work.
Another natural direction forward is to use our construction to build probes in
SL(N) × SL(N) Chern–Simons theory, and hence generalize (42) beyond pure
AdS 3 gravity. This would provide a unique way to build local probes in higher spin
gravity. A discussion of Ishibashi states for W 3 algebra was done in [63], which is
a natural starting point for future investigations.
Bibliography
1. A. Achucarro, P.K. Townsend, Extended supergravities in d = (2+1) as Chern–Simons theories.
Phys. Lett. B229, 383–387 (1989)
2. E. Witten, (2+1)-Dimensional gravity as an exactly soluble system. Nucl. Phys. B311, 46
(1988)
3. S. Prokushkin, M.A. Vasiliev, 3-D higher spin gauge theories with matter, in Proceedings of the
31st International Symposium Ahrenshoop Theory of Elementary Particles, Buckow, Germany,
2–6 Sept 1997 (1998)
4. S. Prokushkin, M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D
AdS space-time. Nucl. Phys. B545, 385 (1999)
5. M. Henneaux, S.J. Rey, Nonlinear W inf inity as asymptotic symmetry of three-dimensional
higher spin anti-de sitter gravity. JHEP 1012, 007 (2010)
6. A. Campoleoni, S. Fredenhagen, S. Pfenninger, S. Theisen, Asymptotic symmetries of threedimensional gravity coupled to higher-spin fields. JHEP 1011, 007 (2010)
7. A. Campoleoni, S. Fredenhagen, S. Pfenninger, Asymptotic W-symmetries in threedimensional higher-spin gauge theories. JHEP 1109, 113 (2011)
8. M.R. Gaberdiel, T. Hartman, Symmetries of holographic minimal models. JHEP 1105, 031
(2011)
9. M.R. Gaberdiel, R. Gopakumar, Minimal model holography. J.Phys. A46, 214002 (2013)
10. M.R. Gaberdiel, R. Gopakumar, String theory as a higher spin theory. JHEP 09, 085 (2016)
11. M. Gutperle, P. Kraus, Higher spin black holes. JHEP 1105, 022 (2011)
12. A. Achúcarro, P. Townsend, A Chern–Simons action for three-dimensional anti-de Sitter
supergravity theories. Phys. Lett. B 180(1–2), 89–92 (1986)
13. M. Blencowe, A consistent interacting massless higher spin field theory in D = (2+1). Class.
Quant. Grav. 6, 443 (1989)
14. X. Bekaert, S. Cnockaert, C. Iazeolla, M.A. Vasiliev, Nonlinear higher spin theories in
various dimensions, in Proceedings of the 1st Solvay Workshop, Higher Spin Gauge Theories,
Brussels, Belgium, 12–14 May, 2004 (2004), pp. 132–197
15. M. Ammon, M. Gutperle, P. Kraus, E. Perlmutter, Black holes in three dimensional higher spin
gravity: a review. J. Phys. A46, 214001 (2013)
16. A. Castro, E. Llabrés, Unravelling holographic entanglement entropy in higher spin theories.
JHEP 1503, 124 (2015)
17. M. Bañados, R. Canto, S. Theisen, Higher spin black holes in three dimensions: remarks on
asymptotics and regularity. Phys. Rev. D94(2), 024002 (2016)
18. A. Castro, N. Iqbal, E. Llabrés: Eternal higher spin black holes: a thermofield interpretation.
JHEP 08, 022 (2016)
A. Castro
expect that the intertwining of the two copies of sl(2) will produce interesting
features. For example, we should be able to probe if the global conditions on the
|U states are enhanced to the Virasoro conditions on the Ishibashi state [60, 61], or
something completely different, such as the conditions proposed in [62]. We leave
these questions for future work.
Another natural direction forward is to use our construction to build probes in
SL(N) × SL(N) Chern–Simons theory, and hence generalize (42) beyond pure
AdS 3 gravity. This would provide a unique way to build local probes in higher spin
gravity. A discussion of Ishibashi states for W 3 algebra was done in [63], which is
a natural starting point for future investigations.
Bibliography
1. A. Achucarro, P.K. Townsend, Extended supergravities in d = (2+1) as Chern–Simons theories.
Phys. Lett. B229, 383–387 (1989)
2. E. Witten, (2+1)-Dimensional gravity as an exactly soluble system. Nucl. Phys. B311, 46
(1988)
3. S. Prokushkin, M.A. Vasiliev, 3-D higher spin gauge theories with matter, in Proceedings of the
31st International Symposium Ahrenshoop Theory of Elementary Particles, Buckow, Germany,
2–6 Sept 1997 (1998)
4. S. Prokushkin, M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D
AdS space-time. Nucl. Phys. B545, 385 (1999)
5. M. Henneaux, S.J. Rey, Nonlinear W inf inity as asymptotic symmetry of three-dimensional
higher spin anti-de sitter gravity. JHEP 1012, 007 (2010)
6. A. Campoleoni, S. Fredenhagen, S. Pfenninger, S. Theisen, Asymptotic symmetries of threedimensional gravity coupled to higher-spin fields. JHEP 1011, 007 (2010)
7. A. Campoleoni, S. Fredenhagen, S. Pfenninger, Asymptotic W-symmetries in threedimensional higher-spin gauge theories. JHEP 1109, 113 (2011)
8. M.R. Gaberdiel, T. Hartman, Symmetries of holographic minimal models. JHEP 1105, 031
(2011)
9. M.R. Gaberdiel, R. Gopakumar, Minimal model holography. J.Phys. A46, 214002 (2013)
10. M.R. Gaberdiel, R. Gopakumar, String theory as a higher spin theory. JHEP 09, 085 (2016)
11. M. Gutperle, P. Kraus, Higher spin black holes. JHEP 1105, 022 (2011)
12. A. Achúcarro, P. Townsend, A Chern–Simons action for three-dimensional anti-de Sitter
supergravity theories. Phys. Lett. B 180(1–2), 89–92 (1986)
13. M. Blencowe, A consistent interacting massless higher spin field theory in D = (2+1). Class.
Quant. Grav. 6, 443 (1989)
14. X. Bekaert, S. Cnockaert, C. Iazeolla, M.A. Vasiliev, Nonlinear higher spin theories in
various dimensions, in Proceedings of the 1st Solvay Workshop, Higher Spin Gauge Theories,
Brussels, Belgium, 12–14 May, 2004 (2004), pp. 132–197
15. M. Ammon, M. Gutperle, P. Kraus, E. Perlmutter, Black holes in three dimensional higher spin
gravity: a review. J. Phys. A46, 214001 (2013)
16. A. Castro, E. Llabrés, Unravelling holographic entanglement entropy in higher spin theories.
JHEP 1503, 124 (2015)
17. M. Bañados, R. Canto, S. Theisen, Higher spin black holes in three dimensions: remarks on
asymptotics and regularity. Phys. Rev. D94(2), 024002 (2016)
18. A. Castro, N. Iqbal, E. Llabrés: Eternal higher spin black holes: a thermofield interpretation.
JHEP 08, 022 (2016)