The D1D5P system has a large set of BPS states at its orbifold point. Perturbing away from this 'free' point leads to some states joining up into long supermultiplets and lifting, while other states remain BPS. We consider the simplest orbifold which exhibits this lift: that with $N=2$ copies of the free $c=6$ CFT. We write down the number of lifted and unlifted states implied by the index at all levels upto $6$. We work to second order in the perturbation strength $λ$. For levels upto $4$, we find the wavefunctions of the lifted states, their supermultiplet structure and the value of the lift. All states that are allowed to lift by the index are in fact lifted at order $O(λ^2)$. We observe that the unlifted states in the untwisted sector have an antisymmetry between the copies in the right moving Ramond ground state sector, and extend this observation to find classes of states for arbitrary $N$ that will remain unlifted to $O(λ^2)$.
We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where one copy of the seed CFT has been excited with a left-moving superconformal primary. Despite being BPS at the orbifold point, such states can `lift' as the theory is deformed away from this point in moduli space. We compute this lifting at second order in the deformation parameter for arbitrary left-moving dimension $h$ of this class of states. This result displays an interesting universality since the lifting does not depend on the details of the superconformal primary; it depends only on the dimension. In the …
The D1D5 CFT has a large set of states that are supersymmetric at the `free' orbifold point in moduli space. When we perturb away from this point, some of these states join into long multiplets and lift in energy, while others remain supersymmetric. The count of unlifted states can be bounded below by an index, but the index does not yield the pattern of lifting; i.e., which states join into a long multiplet and how much this multiplet lifts. In this paper we consider the simple case of the D1D5 CFT where the orbifold CFT is a sigma model with targets space $(T^4)^2/S_2$ and consider states at…
We consider states of the D1-D5 CFT where only the left-moving sector is excited. As we deform away from the orbifold point, some of these states will remain BPS while others can `lift'. The lifting can be computed by a path integral containing two twist deformations; however, the relevant 4-point amplitude cannot be computed explicitly in many cases. We analyze an older proposal by Gava and Narain where the lift can be computed in terms of a finite number of 3-point functions. A direct Hamiltonian decomposition of the path integral involves an infinite number of 3-point functions, as well the…
We consider states of the D1-D5 CFT where only the left-moving sector is excited. As we deform away from the orbifold point, some of these states will remain BPS while others can `lift'. We compute this lifting for a particular family of D1-D5-P states, at second order in the deformation off the orbifold point. We note that the maximally twisted sector of the CFT is special: the covering surface appearing in the correlator can only be genus one while for other sectors there is always a genus zero contribution. We use the results to argue that fuzzball configurations should be studied for the f…
Higher spin gravity in three dimensions has explicit black holes solutions, carrying higher spin charge. We compute the free energy of a charged black hole from the holographic dual, a 2d CFT with extended conformal symmetry, and find exact agreement with the bulk thermodynamics. In the CFT, higher spin corrections to the free energy can be calculated at high temperature from correlation functions of W-algebra currents.
We consider the D1-D5 CFT near the orbifold point, specifically the computation of correlators involving twist sector fields using covering surface techniques. As is well known, certain twists introduce spin fields on the cover. Here we consider the bosonization of fermions to facilitate computations involving the spin fields. We find a set of cocycle operators that satisfy constraints coming from various $SU(2)$ symmetries, including the $SU(2)_L\times SU(2)_R$ R-symmetry. Using these cocycles, we consider the correlator of four spin fields on the cover, and show that it is invariant under al…
I take steps toward the construction of a CFT dual to Vasiliev's higher spin gravity in three dimensional de Sitter space. There are two main claims. The first is that higher spin de Sitter symmetries are related to extended Virasoro symmetries, as in AdS; this is verified explicitly for the case of W_3 asymptotic symmetry. The associated chiral algebra has imaginary central charge. The second (conjectural) claim, inspired by work of Gaberdiel and Gopakumar in AdS_3/CFT_2, is that an appropriate CFT can be identified as an exotic non-unitary WZW coset model at complex level.
We study the radial quantization of the 3d O(N) vector model. We calculate the higher spin charges whose commutation relations give the higher spin algebra. The Fock states of higher spin gravity in AdS_{4} are realized as the states in the 3d CFT. The inner products between these states encode dynamical information. The construction of bulk operators from CFT is discussed as well. This serves as the simplest explicit demonstration of the CFT definition for the quantum gravity.
We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on the spacelike boundary of dS at future timelike infinity. The CFT is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT flows under a double-trace deformation to an interacting CFT in the IR. We argue that both CFTs are dual to Vasiliev dS gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and bound…
The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.
We study a certain class of nonextremal D1D5 geometries and their ergoregion emission. Using a detailed CFT computation and the formalism developed in arXiv:0906.2015 [hep-th], we compute the full spectrum and rate of emission from the geometries and find exact agreement with the gravity answer. Previously, only part of the spectrum had been reproduced using a CFT description. We close with a discussion of the context and significance of the calculation.
In a class of 2D CFTs with higher spin symmetry, we compute thermal two-point functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge. These are shown to agree with the same quantity calculated holographically using scalar fields propagating in a charged black hole background of 3D higher spin gravity. This match serves as further evidence for the duality between W_N minimal models at large central charge and 3D higher spin gravity. It also supports a recent prescription for computing boundary correlators of multi-trace scalar primary …
We analyze how deforming symmetric product orbifolds of two-dimensional $\mathcal{N}=2$ conformal field theories by an exactly marginal operator lifts higher spin currents present at the orbifold point. We find on the one hand that these currents are universally lifted regardless of the underlying CFT. On the other hand the details of the lifting are surprisingly non-universal, with dependence on the central charge of the underlying CFT and the specific marginal operator in use. In the context of the AdS/CFT correspondence, our results illustrate the mechanism by which the stringy spectrum tur…
We investigate generic n-point correlation functions of conformal field theories (CFTs), with $T\bar{T}$ and $J\bar{T}$ deformations, in terms of the perturbative CFT approach. We systematically obtain the first order correction to the generic correlation functions of CFTs with $T\bar{T}$ or $J\bar{T}$ deformation. We compute the out-of-time ordered correlation function (OTOC) in the Ising model with $T\bar{T}$ or $J\bar{T}$ deformation, which confirms that these deformations do not change the integrable property up to the first order level.
We formulate a first quantized construction of the AdS_{d+1}/CFT_d correspondence using the bi-local representation of the free d-dimensional large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity provides a scheme where the AdS spacetime (and higher-spin fields) are given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher-spin AdS particle model is shown to emerge from the collective bi-particle system of Minkowski particles through a canonical transformation. …
We study Vasiliev's system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.
Large-$N$, $ε$-expansion or the conformal bootstrap allow one to make sense of some of conformal field theories in non-integer dimension, which suggests that AdS/CFT may also extend to fractional dimensions. It was shown recently that the sphere free energy and the $a$-anomaly coefficient of the free scalar field can be reproduced as a one-loop effect in the dual higher-spin theory in a number of integer dimensions. We extend this result to all integer and also to fractional dimensions. Upon changing the boundary conditions in the higher-spin theory the sphere free energy of the large-$N$ Wils…
All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), …
We continue our study of the worldsheet theory of superstrings on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ in the tensionless limit arXiv:1911.00378. We consider the theory on higher genus surfaces. We give evidence that the worldsheet correlators localise on certain worldsheets that cover the boundary of $\mathrm{AdS}_3$ holomorphically. This simplifies the string moduli space integral dramatically to a finite sum. This property shows that the higher genus corrections of the string worldsheet reproduce the structure of the $1/N$ corrections in the dual symmetric orbifold CFT $…
We shortly review the bi-local, collective dipole mechanism to a construction of Higher Spin AdS Gravity from the O(N) vector field theory. We also make some comments regarding an exact nonlinear comparison and in this regard we present a bi-local (symmetric) gauge description of Vasiliev's theory.
We investigate the AdS/CFT correspondence for higher-derivative gravity systems, and develop a formalism in which the generating functional of the boundary field theory is given as a functional that depends only on the boundary values of bulk fields. We also derive a Hamilton-Jacobi-like equation that uniquely determines the generating functional, and give an algorithm calculating the Weyl anomaly. Using the expected duality between a higher-derivative gravity system and N=2 superconformal field theory in four dimensions, we demonstrate that the resulting Weyl anomaly is consistent with the fi…
We find a simple relation between a free higher spin field partition function on thermal quotient of AdS(d+1) and the partition function of the associated d-dimensional conformal higher spin field on thermal quotient of AdS(d). Starting with a conformal higher spin field defined on AdS(d) one may also associate to it another conformal field in d-1 dimensions, thus "iterating" AdS/CFT. We observe that in the case of d=4 this iteration leads to a "trivial" 3d higher spin conformal theory with parity-even non-local action: it describes zero total number of dynamical degrees of freedom and the cor…
We study possible CFT duals of supersymmetric five dimensional black rings in the presence of supersymmetric higher derivative corrections to the N=2 supergravity action. A Virasoro algebra associated to an asymptotic symmetry group of solutions is defined by using the Kerr/CFT approach. We find the central charge and compute the microscopic entropy which is in precise agreement with the macroscopic entropy. Although apparently related to a different aspect of the near-horizon geometry and a different Virasoro algebra, we find that the c-extremization method leads to the same central charge an…
N-point correlation functions of conserved currents and weight-two scalar operators of the three-dimensional free fermion vector model are found as invariants of the higher-spin symmetry in four-dimensional AdS. These are the correlators of the unbroken Vasiliev higher-spin theory. The results extend the recent work arXiv:1210.7963 and are complementary to arXiv:1301.3123 where the correlators were computed entirely on the boundary.
Two and three-point functions of primary fields in four dimensional CFT have a simple space-time dependences factored out from the combinatoric structure which enumerates the fields and gives their couplings. This has led to the formulation of two dimensional topological field theories with $so(4,2)$ equivariance which are conjectured to be equivalent to higher dimensional conformal field theories. We review this CFT4/TFT2 construction in the simplest possible setting of a free scalar field, which gives an algebraic construction of the correlators in terms of an infinite dimensional $so(4,2)$ …
The full list of conserved conformal higher spin currents built from massless scalar and spinor fields is presented. It is shown that, analogously to the relationship between usual conformal and AdS symmetries, the set of the conformal higher spin symmetry parameters associated with the conformal conserved currents in d dimensions is in the one-to-one correspondence with the result of the dimensional reduction of the usual (i.e., non-conformal) higher spin symmetry parameters in d+1 dimensions.
We find black hole solutions of D=3 higher-spin gravity in the hs[λ] + hs[λ] Chern-Simons formulation. These solutions have a spin-3 chemical potential, and carry nonzero values for an infinite number of charges of the asymptotic W_{\infty}[λ] symmetry. Applying a previously developed set of rules for ensuring smooth solutions, we compute the black hole partition function perturbatively in the chemical potential. At λ=0, 1 we compare our result against boundary CFT computations involving free bosons and fermions, and find perfect agreement. For generic λ we expect that our gravity result will …
We conjecture that the level k U(N) Chern-Simons theory coupled to free anticommuting scalar matter in the fundamental is dual to non-minmal higher-spin Vasiliev gravity in dS4 with parity-violating phase \theta0 = πN/2k and Neumann boundary conditions for the scalar. Related conjectures are made for fundamental commuting spinor matter and critical theories. This generalizes a recent conjecture relating the minimal Type A Vasiliev theory in dS4 to the Sp(N) model with fundamental real anti-commuting scalars.
Vasiliev's higher spin supergravity theory on three dimensional anti-de Sitter space is studied and, in particular, the partition function is computed at one loop level. The dual conformal field theory is proposed to be the N=(2,2) CP^N Kazama-Suzuki model in two dimensions. The proposal is based on symmetry considerations and comparison of the bulk partition function with the conformal field theory. Our findings suggest that the theory is strong-weak self-dual.
We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with $\mathcal{W}_N$ symmetry in the "irrational" regime, where $c>N-1$ and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when $c>N-1$. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large $c$, this implies that the…
We demonstrate how three-point correlation functions of the free scalar U(N) model involving two scalar operators and one spin-$s$ conserved current organize themselves into corresponding AdS amplitudes involving two scalar and one spin-$s$ bulk to boundary propagators, coupled via the bulk gauge invariant interaction vertex. Our analysis relies on the general program advocated in hep-th/0308184 and some features of the embedding space formalism also play an important role.
The deformation operator of the D1D5 orbifold CFT, a twist 2 operator, drives the CFT towards the black hole dual and its physics is key to understanding thermalization in the D1D5 system. To further study this deformation, we extend previous work on the effect of twist 2 operators to a method that works for higher orders, in the continuum limit. Our component twist method works by building higher twist operators out of twist 2 operators together with knowledge of Bogoliubov transformations. Consequently, this method sidesteps limitations in Lunin-Mathur technology by avoiding lifts to the cov…
In these lectures we give an overview of the duality between gravitational theories of massless higher spin fields in AdS and large N vector models. We first review the original higher spin/vector model duality conjectured by Klebanov and Polyakov, and then discuss its generalizations involving vector models coupled to Chern-Simons gauge fields. We proceed to review some aspects of the theory of massless higher spins, starting with the Fronsdal equations for free fields and moving on to the fully non-linear Vasiliev equations in four dimensions. We end by reviewing some recent tests of the hig…
We discuss fermionic higher spin gauge symmetry breaking in AdS space from a holographic perspective. Analogously to the recently discussed bosonic case, the higher spin Goldstino mode responsible for the symmetry breaking has a non-vanishing mass in the limit in which the gauge symmetry is restored. This result is precisely in agreement with the AdS/CFT correspondence, which implies that N=4 SYM at vanishing coupling constant is dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, the current conservation condition becomes anomalous…
We study the uniqueness of higher-spin algebras which are at the core of higher-spin theories in AdS and of CFTs with exact higher-spin symmetry, i.e. conserved tensors of rank greater than two. The Jacobi identity for the gauge algebra is the simplest consistency test that appears at the quartic order for a gauge theory. Similarly, the algebra of charges in a CFT must also obey the Jacobi identity. These algebras are essentially the same. Solving the Jacobi identity under some simplifying assumptions spelled out, we obtain that the Eastwood-Vasiliev algebra is the unique solution for d=4 and …
We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5d superconformal algebra F(4) with the even subalgebra SO(5,2) X SU(2). The minrep of F(4) describes…
We follow to Witten proposal in the calculation of conformal anomaly from d+1-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a description in terms of above d+1-dimensional higher derivative gravity which includes not only Einstein term and cosmological constant but also curvature squared terms. The explicit expression for two-dimensional and four-dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagra…
We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite t'Hooft coupling. More concretely, we obtain a formula for $\langle j_s j_{\tilde{0}} j_{\tilde{0}} j_{\tilde{0}} \rangle$, where $j_s$ is a higher spin current and $j_{\tilde{0}}$ is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all…
We derive a holographic relation for the dS static patch with the dual field theory defined on the observer horizon. The starting point is the duality of higher-spin theory on AdS_4 and the O(N) vector model. We build on a similar analytic continuation as used recently to obtain a realization of dS/CFT, and adapt it to the static patch. The resulting duality relates higher-spin theory on the dS_4 static patch to a cut-off CFT on the cylinder RxS^2. The construction permits a derivation of the finite thermodynamic entropy associated to the horizon of the static patch from the dual field theory.…
Department of Physics, Nagoya University（名古屋大学物理系）；Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理中心）
We consider free fermion and free boson CFTs in two dimensions, deformed by a chemical potential $μ$ for the spin-three current. For the CFT on the infinite spatial line, we calculate the finite temperature entanglement entropy of a single interval perturbatively to second order in $μ$ in each of the theories. We find that the result in each case is given by the same non-trivial function of temperature and interval length. Remarkably, we further obtain the same formula using a recent Wilson line proposal for the holographic entanglement entropy, in holomorphically factorized form, associated t…
Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is the first computation of a correlator in 3D higher spin gravity whose functional form is not fixed by conformal invariance. In the bulk we make use of elegant methods to solve the scalar field equation using only matrix manipulations, while on the CFT side we employ the Coulomb gas representation. Comparison is made in the semiclassical limit, in which the …
In this paper we use the spinor-helicity formalism to calculate 3-point functions involving scalar operators and spin-$s$ conserved currents in general 3d CFTs. In spinor-helicity variables we notice that the parity-even and the parity-odd parts of a correlator are related. Upon converting spinor-helicity answers to momentum space, we show that correlators involving spin-$s$ currents can be expressed in terms of some simple conformally invariant conserved structures. This in particular allows us to understand and separate out contact terms systematically, especially for the parity-odd case. We…
We study the role of higher derivative terms (Riemann curvature squared ones) in thermodynamics of SCFTs via AdS/CFT correspondence. Using IIB string effective action (d5 AdS gravity) with such HD terms deduced from heterotic string via duality we calculate strong coupling limit of ${\cal N}=2$ SCFT free energy with the account of next to leading term in large $N$ expansion. It is compared with perturbative result following from boundary QFT. Considering modification of such action where HD terms form Weyl squared tensor we found (strong coupling limit) free energy in such theory. It is intere…
We consider the question of loop corrections (i.e. 1/N) in the vector model/higher spin duality following the recent work of Giombi and Klebanov. The purpose of this paper is to gain further more precise comparison between the two sides of the duality. For CFTs given by 3d O(N) or U(N) vector models we evaluate the leading and one loop partition functions in a variety of geometries. Our calculations are performed in the scheme of collective field theory which was seen in earlier studies to represent a bulk description of Vasiliev higher spin theory. The calculations presented provide data for …
In recent literature one-loop tests of the higher-spin AdS$_{d+1}$/CFT$_d$ correspondences were carried out. Here we extend these results to a more general set of theories in $d>2$. First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of $N$ free fermion fields. In addition to the case of $N$ Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic, and Majorana-Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories,…
The general model of higher derivative (HD) gravity is considered. The search of brane-world cosmology in such theory is presented when bulk is d5 AdS and boundary is spherical, hyperbolic or flat (single) brane. It is found the wide range of theory parameters where such cosmology may be realized. Special attention is paid to the version of HD theory representing SG dual of ${\cal N}=2$ $Sp(N)$ SCFT (in next-to-leading order of large $N$ expansion). In particular, it is shown that inflationary brane Universe does not occur for SG dual while hyperbolic brane occurs (which was not possible in le…
Within the classical approximation we calculate the static $Q\bar Q$ potential via the AdS/CFT relation for nonzero temperature and arbitrary internal orientation of the quarks. We use a higher order curvature corrected target space background. For timelike Wilson loops there arises a critical line in the orientation-distance plane which is shifted to larger distances relative to the calculation with uncorrected background. Beyond that line there is no $Q\bar Q$-force. The overall vanishing of the force for antipodal orientation known from zero tempera ture remains valid. The spacelike Wilson …
In a conformal field theory with weakly broken higher spin symmetry, the leading order anomalous dimensions of the broken currents can be efficiently determined from the structure of the classical non-conservation equations. We apply this method to the explicit example of $O(N)$ invariant scalar field theories in various dimensions, including the large $N$ critical $O(N)$ model in general $d$, the Wilson-Fisher fixed point in $d=4-ε$, cubic scalar models in $d=6-ε$ and the nonlinear sigma model in $d=2+ε$. Using information from the $d=4-ε$ and $d=2+ε$ expansions, we obtain some estimates for …
We extend and refine recent results on Renyi entropy in two-dimensional conformal field theories at large central charge. To do so, we examine the effects of higher spin symmetry and of allowing unequal left and right central charges, at leading and subleading order in large total central charge. The result is a straightforward generalization of previously derived formulae, supported by both gravity and CFT arguments. The preceding statements pertain to CFTs in the ground state, or on a circle at unequal left- and right-moving temperatures. For the case of two short intervals in a CFT ground s…
What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large $N$, $4d$ CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in $1/N$ for large, but finite, coupling. In the language of Regge theory, we show…
The method of large spin perturbation theory allows to analyse conformal field theories (CFT) by turning the crossing equations into an algebraic problem. We apply this method to a generic CFT with weakly broken higher spin (HS) symmetry, to the first non-trivial order in the breaking parameter. We show that the spectrum of broken currents, for any value of the spin, follows from crossing symmetry. After discussing a generic model of a single scalar field, we focus on vector models with $O(N)$ global symmetry. We rediscover the spectrum of several models, including the $O(N)$ Wilson-Fisher mod…
It was shown that the spin chain model coming from AdS/CFT correspondence satisfies the Yangian symmetry if we assume evaluation representation, though so far there is no explicit proof that the evaluation representation satisfies the Serre relation, which is one of the defining equations of the Yangian algebra imposing constraints on the whole algebraic structure. We prove completely that the evaluation representation adopted in the model satisfies the Serre relation by introducing a three-dimensional gamma matrix. After studying the Serre relation, we proceed to the whole Yangian algebraic s…
We extend our earlier work on the minimal unitary representation of $SO(d,2)$ and its deformations for $d=4,5$ and $6$ to arbitrary dimensions $d$. We show that there is a one-to-one correspondence between the minrep of $SO(d,2)$ and its deformations and massless conformal fields in Minkowskian spacetimes in $d$ dimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep, and its enveloping algebra yields…
