Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFrom Higher Spins to Strings: A Primer
187
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A contribution to the collection of reviews Introduction to Higher Spin Theory edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincare-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasilievs equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the central on-mass-shell theorem. These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.
rate research
Read More
A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the $B_p$--models. The cases of $B_1$ and its infinite graded-symmetric product $sym,(times B_1)^infty$ correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particle $B_2$--higher-spin theory is conjectured to be associated with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be dual to the rank-$p$ boundary tensor sigma-models. $B_p$ higher-spin models with $pgeq 2$ possess two coupling constants responsible for higher-spin interactions in $AdS$ background and stringy/tensor effects, respectively. The brane-like idempotent extension of the Coxeter higher-spin theory is proposed allowing to unify in the same model the fields supported by space-times of different dimensions. Consistency of the holographic interpretation of the boundary matrix-like model in the $B_2$-higher-spin model is shown to demand $Ngeq 4$ SUSY, suggesting duality with the $N=4$ SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations.
At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height $h_i$ by columns of height $D-2-h_i$, where $D$ is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of $D-2$ extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in $D=5$ and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in $D=3$.
We establish the elliptic blowup equations for E-strings and M-strings and solve elliptic genera and refined BPS invariants from them. Such elliptic blowup equations can be derived from a path integral interpretation. We provide toric hypersurface construction for the Calabi-Yau geometries of M-strings and those of E-strings with up to three mass parameters turned on, as well as an approach to derive the perturbative prepotential directly from the local description of the Calabi-Yau threefolds. We also demonstrate how to systematically obtain blowup equations for all rank one 5d SCFTs from E-string by blow-down operations. Finally, we present blowup equations for E-M and M string chains.
We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit system manifest. In this approach, physical systems are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive systems can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk--boundary correspondence.
Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-$n$ field for each spin-$n$). For this reason they are sometimes referred to as the generalized Riemann tensors. In this article, a method for deriving these curvature tensors from first principles is presented; the derivation is completed without any a priori knowledge of the existence of the Riemann tensors or the curvature tensors of higher-spin gauge theories. To perform this derivation, a recently developed procedure for deriving exactly gauge invariant Lagrangian densities from quadratic combinations of $N$ order of derivatives and $M$ rank of tensor potential is applied to the $N = M = n$ case under the spin-$n$ gauge transformations. This procedure uniquely yields the Lagrangian for classical electrodynamics in the $N = M = 1$ case and the Lagrangian for higher derivative gravity (`Riemann and `Ricci squared terms) in the $N = M = 2$ case. It is proven here by direct calculation for the $N = M = 3$ case that the unique solution to this procedure is the spin-3 curvature tensor and its contractions. The spin-4 curvature tensor is also uniquely derived for the $N = M = 4$ case. In other words, it is proven here that, for the most general linear combination of scalars built from $N$ derivatives and $M$ rank of tensor potential, up to $N=M=4$, there exists a unique solution to the resulting system of linear equations as the contracted spin-$n$ curvature tensors. Conjectures regarding the solutions to the higher spin-$n$ $N = M = n$ are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
