Higher Spin Theory; Conformal Field Theory; String Theory
Oblak Blagoje (2017), Berry Phases on Virasoro Orbits, in Journal of High Energy Physics
, 1710, 114.
Ferreira Kevin (2017), Even spin N = 4 holography, in Journal of High Energy Physics
, 1709, 110.
Eberhardt Lorenz, Gaberdiel Matthias, Li Wei (2017), A holographic dual for string theory on AdS3 × S3 × S3 × S1, in Journal of High Energy Physics
, 1708, 111.
Ferreira Kevin, Gaberdiel Matthias, Jottar Juan (2017), Higher spins on AdS3 from the world-sheet, in Journal of High Energy Physics
, 1707, 131.
Gaberdiel Matthias, Gopakumar Rajesh, Hull Chris (2017), Stringy AdS3 from the Worldsheet, in Journal of High Energy Physics
, 1707, 90.
Gaberdiel Matthias, Gopakumar Rajesh, Li Wei, Peng Cheng (2017), Higher Spins and Yangian Symmetries, in Journal of High Energy Physics
, 1704, 152.
Eberhardt Lorenz, Gaberdiel Matthias, Gopakumar Rajesh, Li Wei (2017), BPS spectrum on AdS3×S3×S3×S1, in Journal of High Energy Physics
, 1703, 124.
Gaberdiel Matthias, Keller Christoph, Paul Hynek (2017), Mathieu Moonshine and Symmetry Surfing, in Journal of Physics A
, 50, 474002.
Datta Shouvik, Gaberdiel Matthias, Li Wei, Peng Cheng (2016), Twisted sectors from plane partitions, in Journal of High Energy Physics
, 1609, 138.
One of the most important topics in string theory in recent years has been the AdS/CFT correspondence. In its original form it relates string theory on a 5-dimensional Anti-de Sitter background to N=4 superconformal Yang-Mills theory in 4 dimensions. This duality is of great importance since it allows one to gain insight into quantum gravity on the one hand, and into strongly coupled (gauge) theories on the other. Unfortunately, however, a real understanding of why this correspondence works and which ingredients are crucial for its functioning is still missing. This is an important question given that for many interesting applications of the AdS/CFT correspondence, say to QCD or condensed matter physics, other versions of the duality (that cannot be directly justified from string theory) seem to be relevant. In order to gain insight into this problem it is instructive to consider the limit in which the conformal field theory is weakly coupled. In that case, the dual string theory is believed to possess a consistent higher spin subsector that should be dual to the nearly free field theory. This special case is of quite some interest since both sides of the duality are then weakly coupled, and hence one may hope to find a perturbative proof of the AdS/CFT correspondence in this regime. It may also allow one to get a glimpse of the large symmetry that is believed to underlie string theory.About five years ago I made (together with Rajesh Gopakumar) a concrete proposal for such a duality. It relates a specific higher spin theory on AdS3 to a 't Hooft like large N limit of a family of 2-dimensional minimal model conformal field theories. By now substantial support for this proposal has been obtained, and recently the precise connection with string theory has been understood. This has opened the door for a number of interesting problems: in particular, it should be possible to exhibit in detail the structure of the symmetry algebra underlying string theory at its most symmetrical point (the tensionless point), to understand the constraints of this symmetry for various aspects of the theory, and to unravel the relation of these symmetries to the integrable structure that is, for example, visible in the spin-chain approach. Finally, since the duality is also understood in detail at finite N, the 2d CFT makes concrete predictions for quantum gravity effects in AdS3, which it would be very interesting to understand from a perturbative quantum gravity point of view. All of these directions (as well as others in this area) will be pursued. In 2010, Eguchi, Ooguri, and Tachikawa observed that the first few Fourier coefficients of the elliptic genus of K3 can be written in terms of dimensions of Mathieu M24 representations. (The Mathieu group M24 is one of the sporadic finite simple groups.) In previous work I have given very convincing evidence that this observation is true for all Fourier coefficients, and it would be very interesting to understand the microscopic origin of this fact.