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Notes on higher-spin diffeomorphisms

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 Added by Xavier Bekaert
 Publication date 2021
  fields
and research's language is English




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Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined.

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126 - M. Beccaria , A.A. Tseytlin 2015
We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the physical ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has a Weyl-invariant action in curved background and corresponds to partially massless field in AdS_5. We discuss in detail the special case of s=2 (or conformal graviton), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.
We briefly review the concepts of generalized zero curvature conditions and integrability in higher dimensions, where integrability in this context is related to the existence of infinitely many conservation laws. Under certain assumptions, it turns out that these conservation laws are, in fact, generated by a class of geometric target space transformations, namely the volume-preserving diffeomorphisms. We classify the possible conservation laws of field theories for the case of a three-dimensional target space. Further, we discuss some explicit examples.
58 - Karl Landsteiner 2016
Chiral anomalies give rise to dissipationless transport phenomena such as the chiral magnetic and vortical effects. In these notes I review the theory from a quantum field theoretic, hydrodynamic and holographic perspective. A physical interpretation of the otherwise somewhat obscure concepts of consistent and covariant anomalies will be given. Vanishing of the CME in strict equilibrium will be connected to the boundary conditions in momentum space imposed by the regularization. The role of the gravitational anomaly will be explained. That it contributes to transport in an unexpectedly low order in the derivative expansion can be easiest understood via holography. Anomalous transport is supposed to play also a key role in understanding the electronics of advanced materials, the Dirac- and Weyl (semi)metals. Anomaly related phenomena such as negative magnetoresistivity, anomalous Hall effect, thermal anomalous Hall effect and Fermi arcs can be understood via anomalous transport. Finally I briefly review a holographic model of Weyl semimetal which allows to infer a new phenomenon related to the gravitational anomaly: the presence of odd viscosity.
In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional Anti de Sitter group using an ambient space formalism.
We analyze the properly normalized three-point correlator of two protected scalar operators and one higher spin twist-two operator in N=4 super Yang-Mills, in the limit of large spin j. The relevant structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. We show that crossing symmetry of the four point correlator plus a judicious guess for the perturbative structure of the three-point correlator, allow to make a prediction for the structure constant at all loops in perturbation theory, up to terms that remain finite as the spin becomes large. Furthermore, the expression for the structure constant allows to propose an expression for the all loops four-point correlator G(u,v), in the limit u,v -> 0. Our predictions are in perfect agreement with the large j expansion of results available in the literature.
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