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Register a new userConformal higher-spin symmetries in twistor string theory
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Authors
D.V. Uvarov
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It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains $psl(4|4,mathbb R)$ superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to $SL(4|4,mathbb R)$ one.
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We consider the conformal higher spin (CHS) theory in d=4 that contains the s=1 Maxwell vector, s=2 Weyl graviton and their higher spin s=3,4,... counterparts with higher-derivative box^s kinetic terms. The interacting action for such theory can be found as the coefficient of the logarithmically divergent part in the induced action for sources coupled to higher spin currents in a free complex scalar field model. We explicitly determine some cubic and quartic interaction vertices in the CHS action from scalar loop integrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11 -> 11, 22 -> 22 and 11 -> 22 and find that after summing up all the intermediate CHS exchanges they vanish. This generalises the vanishing of the scattering amplitude for external conformal scalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896. This vanishing should generalise to all scattering amplitudes in the CHS theory and as in the conformal scalar scattering case should be a consequence of the underlying infinite dimensional higher spin symmetry that extends the standard conformal symmetry.
This paper is a supplement to and extension of arXiv:1903.01399. In the internal twistor space of the 4D Vasilievs higher-spin gravity, we study the star-product eigenfunctions of number operators with generic complex eigenvalues. In particular, we focus on a set of eigenfunctions represented by formulas with generalized Laguerre functions. This set of eigenfunctions can be written as linear combinations of two subsets of eigenfunctions, one of which is closed under the star-multiplication with the creation operator to a generic complex power -- and the other similarly with the annihilation operator. The two subsets intersect when the left and the right eigenvalues differ by an integer. We further investigate how star-multiplications with both the creation and annihilation operators together may change such eigenfunctions and briefly discuss some problems that we are facing in order to use these eigenfunctions as the initial data to construct solutions to Vasilievs equations.
We discuss the problem of consistent description of higher spin massive fields coupled to external gravity. As an example we consider massive field of spin 2 in arbitrary gravitational field. Consistency requires the theory to have the same number of degrees of freedom as in flat spacetime and to describe causal propagation. By careful analysis of lagrangian structure of the theory and its constraints we show that there exist at least two possibilities of achieving consistency. The first possibility is provided by a lagrangian on specific manifolds such as static or Einstein spacetimes. The second possibility is realized in arbitrary curved spacetime by a lagrangian representing an infinite series in curvature. In the framework of string theory we derive equations of motion for background massive spin 2 field coupled to gravity from the requirement of quantum Weyl invariance. These equations appear to be a particular case of the general consistent equations obtained from the field theory point of view.
In this paper, we examine the conditions under which a higher-spin string theory can be quantised. The quantisability is crucially dependent on the way in which the matter currents are realised at the classical level. In particular, we construct classical realisations for the $W_{2,s}$ algebra, which is generated by a primary spin-$s$ current in addition to the energy-momentum tensor, and discuss the quantisation for $sle8$. From these examples we see that quantum BRST operators can exist even when there is no quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find that there can be several inequivalent ways of quantising a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already-known $W$ strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalisations lead us to examine the whether classical BRST operators for $W_{2,{nover 2}}$ ($n$ odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.
We argue that CP is a gauge symmetry in string theory. As a consequence, CP cannot be explicitly broken either perturbatively or non-pertubatively; there can be no non-perturbative CP-violating parameters. String theory is thus an example of a theory where all $theta$ angles arise due to spontaneous CP violation, and are in principle calculable.
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