In this talk, I explain mechanism for generating massless, partially massless and massive higher spin fields in d-dimensional anti-de Sitter space.I start from massless higher spin fields in (d+1)-dimensional anti-de Sitter space and Kaluza-Klein compactify to d-dimesional anti-de Sitter space on an interval (AdS waveguide).I demonstrate that, to obtain partially massless higher spin fields, boundary conditions at the end of interval must involve spectrum-dependent, equivalently, higher-derivative boundary conditions. If time permits, I also demonstrate how the partially massless Higgs mechanism works from the viewpoint of dual CFT.
Overview of recent progress on non-perturbative aspects of higher spin theories in three dimensions with emphasis on black holes.
The two main results that will be discussed are:
1) novel properties of extremal and susy solutions, and
2) Lorentzian features of eternal higher spin black holes.
We consider a tree-level meromorphic, unitary and crossing symmetric scattering amplitude. We set up bootstrap equations and use them together with unitarity to constrain the asymptotic form of the leading Regge trajectory.
We review the construction of invariant functionals and conserved charges in nonlinear HS theory. In context of AdS/CFT correspondence we discuss a proposal for boundary correlation functions defined via an invariant functional 4-form. The construction of HS conserved charges is tested on some HS black hole solutions leading to a standard ADM values at lowest level in perturbation theory.
We place new constraints on the landscape of 2d conformal field theories with higher spin currents, and on higher spin theories in AdS_3, using Lorentzian bootstrap methods. We show that unitary 2d CFTs with large central charge, light primary operators and a finite tower of higher spin currents cannot exist, and likewise for their putative AdS_3 dual theories of higher spin gravity. Theories with infinite towers of currents evade this conclusion, consistent with a potential embedding into string theory.
The vector space of Killing tensors forms a module of the Lie algebra of global symmetries. Since the classification of global reducibility parameters is generically easier than the classification of global symmetries, this fact can be used to constrain the latter when knowing the former. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal.
Review of some recent work (arXiv:1603.06273 with D. Ponomarev) on computation of simple scattering amplitudes in flat space higher spin theory.
We will describe recent work on Large N Vector model correspondence
involving the 1 dimensional Sachdev-Ye-Kitaev model and its AdS2 dual.
After a review of holographic features of general relativity in 3 and 4 dimensions, I will show how to derive the transformation laws of the Bondi mass and angular momentum aspects under finite supertranslations, superrotations and complex Weyl rescalings.
Gaberdiel and Gopakumar recently proposed that the tensionless limit of string theory on $AdS_3 \times S^3 \times T^4$ takes the form of a higher spin theory with a gauge algebra that is called the `higher spin square'. Here we will couple a bulk matter field to the higher spin square gauge theory and show that its particle spectrum accounts for the entire untwisted sector of the dual symmetric orbifold CFT.
We construct asymptotic charges for both bosonic and fermionic free higher-spin fields on anti de Sitter backgrounds of any dimension. We work within the Hamiltonian setup: we first revisit the Hamiltonian presentation of Fronsdal's action and then we provide boundary conditions on fields and explicit expressions for the charges.
Metro Line U6 to "Klinikum Großhadern"
Stop: Giselastraße
We provide manifestly duality-symmetric formulations of linearized gravity and higher spin gauge fields. This requires introducing appropriate prepotentials and leads to a loss of manifest spacetime covariance. The prepotentials intriguingly exhibit higher spin Weyl symmetry for all spins. The analysis is motivated by the study of the conjectured hidden symmetries of gravity (such as E(10)), which have duality buit in.
We show that the most general cubic action for a set of even and odd forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H is given by a natural generalization of the Frobenius-Chern-Simons (FCS) model proposed in arXiv:505.04957 as a minimal bosonic 4D higher spin gravity theory. The result is a cubic FCS action for a superconnection valued in H X F where F is a Z2-graded quasi-Frobenius algebra. Unital element not necessary of the general model is subsequently introduced. An example of such a model is given based on Clifford algebra C_2n and it is shown to provide a nontrivial FCS extension of the bosonic Konstein--Vasiliev model with gauge algebra hu (2^(n-1),0).
The standard bosonic higher spin algebra in d dimensional anti-deSitter space AdS_d is given by the enveloping algebra of SO(d-1,2) quotiented by its Joseph ideal which defines its minimal unitary representation (minrep). The quasiconformal method provides us with a unified approach to minreps of non-compact groups and leads to realizations for which the Joseph ideal vanishes identically as operators. Hence the quasiconformal realization of the enveloping algebra of the minrep of SO(d-1,2) yields directly the bosonic higher spin algebra in AdS_d. There exists a one-to-one correspondence between the minrep of SO(d-1,2) and its deformations and massless conformal fields in d-dimensional Minkowski spacetimes. The enveloping algebras of the deformed minreps lead to novel deformed higher spin algebras in AdS_d. Furthermore, the quasiconformal approach allows one to define supersymmetric extensions of higher spin algebras and their deformations. I will review the quasiconformal approach to the unitary realizations and classification of higher spin algebras , their deformations and supersymmetric extensions in all dimensions.
Employing the conjectured duality between higher-spin theories in AdS and free CFTs, we present the complete holographically reconstructed cubic action of the minimal higher-spin theory in any dimension. The action we find is the unique solution one would obtain from solving the Noether procedure up to the quartic order.
Employing the conjectured duality between higher-spin theories on AdS and free CFTs, we extract the quartic self-interaction of the bulk scalar from the conformal block expansion of the dual CFT correlator. To this end, we demonstrate techniques to establish conformal partial wave expansions of four-point Witten diagrams. Implications for the (non-)locality of the quartic interaction are briefly discussed.
In this talk we derive a field redefinition that brings current
interactions in the zero-form sector of the nonlinear HS equations
in $AdS_4$ to the standard local form. It is demonstrated that the
cubic vertex resulting from the nonlinear higher-spin interactions
is independent of the free phase parameter in the system. Proper
holographic dependence on the the phase parameter is shown to
result from the phase-dependent boundary conditions.