The appearance of certain undesirable effects due to nonlinear constraints in the hamiltonian analysis are used as a test. Higher spin currents in the orthogonal coset theory. Just as we can build spin foam models starting from a group, we can try to do the same starting with a 2group. Ads description of induced higherspin gauge theory article pdf available in journal of high energy physics 2010 june 20 with 30 reads how we measure reads. Vasiliev lebedev institute, moscow higher structures in m theory durham university, august 17, 2018 1plan general introduction hs symmetries and spacetime unfolded dynamics and l1 nonlinear hs theories from coxeter hs theories to strings and beyond. Higher spin gauge theory on fuzzy s4 n marcus sperling1 and harold c. Gauge theories and the standard model welcome to scipp. Properties of nonlinear higher spin gauge theories of totally symmetric massless higher spin fields in antide sitter space of any dimension are.
Aspects of higher spin gauge theories in three and four. In this paper we calculate the tree level threepoint functions of vasilievs higher spin gauge theory in ads4 and find agreement with the correlators of the. The structure of such a gauge theory has many formal similarities with that of yangmills theory. International workshop on higher spin gauge theories. Higher spin gauge theories in any dimension sciencedirect. Among other things, this fact indicates that higher spin theory should be closely related to string theory because the latter also contains higher spin states. Nonassociative gauge theory and higher spin interactions. The ope between these two n 2 higher spin multiplets is also discussed. Laplacians and lagrangians are a must at some point before translating to the higher math also. An elementary primer for gauge theory and millions of other books are. Find a nonlinear hs theory such that i fronsdal or labastida theory in the free eld limit. Nonabelian gauge symmetries are the symmetries behind theories for massless spin 1 particles, while the reparametrization symmetry is behind einsteins gravity theory for massless spin 2 particles.
Solvay workshop on higher spin gauge theories, topological. Higherspin gauge theories infinitedimensional nonabelian gauge algebras containing the spacetime isometry algebra as maximal finite. Scalar field in any dimension from the higher spin gauge. The higher spin gauge theories in four dimensions have been primarily developed by vasiliev 1.
Johan engquist, olaf hohm, geometry and dynamics of higher spin frame fields arxiv. Ads description of induced higherspin gauge theory arxiv. It is a beautiful new branch of mathematics, with a lot of room left for exploration. Higher spin gauge theories world scientific publishing co. One di erence between string theory and higher spin gauge theory is that the former contains massive higher spin states while the latter only describes massless higher spin states. Pdf an action for higher spin gauge theory in four. Vasiliev lebedev institute, moscow hannover, august 01, 2011 1. Steinacker2 faculty of physics, university of vienna boltzmanngasse 5, a1090 vienna, austria abstract we examine in detail the higher spin elds which arise on the basic fuzzy sphere s4 n in the semiclassical limit. A spin foam model can be seen as a way to quantize a gauge theory or higher gauge theory by discretizing spacetime and rewriting the path integral as a sum 4,33,21. In this paper we calculate the tree level threepoint functi ons of vasilievs higher spin gauge theory in ads 4 and find agreement with the correlators of the free field theory of n massless scalars in three dimensions in the on singlet sector.
However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. Sep 24, 2004 a higher spin field theory on ads4 possesses a conformal theory on the boundary r3 which can be identified with the critical on sigma model of on invariant fields only. Vasiliev lebedev institute, moscow hannover, august 01, 2011. Pdf the masses of gauge fields in higher spin field theory. Vector models and higher spin gauge theory on ads 4 i the conjecture of polyakov and klebanov relates the singlet sector of the three dimensional on vector model to the bosonic higher spin gauge theory on ads 4.
The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. Solutions in bosonic string field theory and ads higher spin algebras dimitri polyakov center for theoretical physics, sichuan university, 29 wangjiang road, chengdu 640064, china. Some general properties of higher spin gauge theories are summarized, with the emphasize on the nonlinear theories in any dimension. The components of the gauge connection are functions on the fuzzy space which transform in higher spin representations of the lorentz group. The prototype model for su 2 u1 electroweak interactions. Symmetries and invariants in higherspin theory higher. Higher spin gauge theory on fuzzy spacetimes from the ikkt matrix model harold steinacker department of physics, university of vienna aei golm, december 2018 h. Nonabelian gauge symmetries are the symmetries behind theories for massless spin1 particles, while the reparametrization symmetry is behind einsteins gravity. Gauge theory, class of quantum field theory, a mathematical theory involving both quantum mechanics and einsteins special theory of relativity that is commonly used to describe subatomic particles and their associated wave fields. This provides substantial evidence that vasiliev theory is dual to the free. For example, on page 26, the author explains why su2 is the group chosen for isotopic spin in ym theory. Indeed, as was shown by bargmann and wigner around the forties 1,2, group theory imposes that such particles should correspond to irreducible represen. We know from adscft that higher spin gauge theory in ads must exist, because there are dual large n free cfts with conserved higher spin currents. In the past strong indications have been given that such theories do not exist.
The n 8 massless higher spin hs gauge theory in d4 is expected to arise as a consistent truncation of mtheory on ads 4. Pdf on curvature expansion of higher spin gauge theory. These cov ariant quantum 4spheres can be viewed as compact v ersions of snyder space 26, 27. Chernsimons formulation is possible in 3 dimensions. It has already been applied to string theory and loop quantum.
The higgs boson is the only particle that has a spin equal to zero which means that it can turn around itself, you can make any angle around it and it still looks the same. Aspects of higher spin gauge theories in three and four dimensions shamik banerjee stanford university december 16, 2012. The idea that higher spin gauge theory appears as the limiting case of string field theory where the string tension vanishes. In supersymmetric theories these particles can be connected also to massless fermionic particles. Higher spin modes november, 2018 abstract we examine several higher spin modes of the poincar. In component form, the gauge theory describes an interacting theory of higher spin fields, which remains nontrivial in the limit where the fuzzy space becomes associative. Steinacker higher spin gauge theory on fuzzy spacetimes from the ikkt matrix model. The other n 2 higher spin multiplet, whoseu1 charge is opposite to the one of the above n 2 higher spin multiplet, is obtained. Pdf ads description of induced higherspin gauge theory. Usually, the spectrum of such theories contains the graviton as a massless spin two field, which explains the second name. Fiantd0800 march 2000 hepthxxxyyzz scalar field in any dimension from the higher spin gauge theory perspective o.
Solutions in bosonic string field theory and ads higher spin algebras. S 7 in an unbroken phase describing the theory at high energies. Solutions in bosonic string field theory and ads higher. Solutions in bosonic string field theory and ads higher spin. Higher spin theory or higher spin gravity is a common name for field theories that contain massless fields of spin greater than two.
Solvay workshop on higher spin gauge theories, topological field theory and deformation quantization brussels, february 17 21, 2020 monday 17 february. Pdf the gaugeinvariant theory of higher spin fields in. Massless fields are gauge fields and the theories should be almost completely fixed by these higher spin symmetries. The group g g in these examples is called the gauge group of the theory. Superspace formulation of 4d higher spin gauge theory.
Vasiliev develops higher spin gravity theories on ads with nontrivial interactions, though only equations of motion are known. General aspects of higher spin gauge theory and unfolded formulation are briefly recalled with some emphasize on the recent results on the breaking of sp8 symmetry by current interactions and on the construction of invariant functionals relevant to the higher spin holography. Tamm department of theoretical physics, lebedev physical institute, leninsky prospect 53, 117924, moscow, russia abstract we formulate the equations of motion of a free scalar eld in the. In this paper we shall only discuss massless hs gauge. Pdf an exact solution of 4d higherspin gauge theory. Generally by a higher spin field theory is meant a quantum field. Higher spin theories in ads and their role for holography. Higher spin gauge theories in fourdimensions, three. Nonabelian gauge symmetry is the symmetry behind theories for massless spin 1 particles, while the reparametrization symmetry is behind einsteins gravity theory for massless spin 2 particles.
It seems totally obvious when it is explained properly. Hs gauge theory should capture e ects of quantum gravity. An action for higher spin gauge theory in four dimensions. Pdf on the uniqueness of minimal coupling in higherspin. Scalar field in any dimension from the higher spin gauge theory perspective o. The gauge field lagrangian gauge invariant lagrangians for spin 0 and spin g helds nonabelian gauge fields conserved charges current conservation gauge theory of u1 annihilation of spinless particles by electromagnetic interaction photons.
Vasiliev lebedev institute, moscow paros, september 2526, 20 1. On the uniqueness of minimal coupling in higher spin gauge theory. Higher spin gauge theory on fuzzy spacetimes from the. Higher spin gauge theories gravity theory with spin 2 gauge field can be extended to theory with spin 2 gauge fields. Crane and sheppeard proposed using the poincar e 2group to. Higher spin gauge theory on fuzzy spacetimes from the ikkt. The action is of the form of a broken topological field theory, and arises by an. With the advent of the adscft duality correspondence even stronger indications have been given that higher spin gauge theories play an. An action principle is presented for vasilievs bosonic higher spin gauge theory in four spacetime dimensions. On curvature expansion of higher spin gauge theory article pdf available in classical and quantum gravity 1816 december 2000 with reads how we measure reads. Vasiliev lebedev institute, moscow paros, september 2526, 20 1plan lecture i iproperties of hs theory iihigher spin algebra lecture ii iiinonlinear hs theory ivspacetime metamorphoses vconclusion 2. The symmetry group g can be expressed in general as a direct product of a. Does nature stop at spin 2 or can there also be massless higher spin theories. Introduction higher spin gauge theories have gained a lot of attention in recent years, in particular because of the proposed higher spin adscft correspondence in.
Metric and framelike higherspin gauge theories in three. The gauge invariant theory of higher spin fields in curved space. Your book will be printed and delivered directly from one of three print stations, allowing you to profit from economic shipping to. The gauge field lagrangian gauge invariant lagrangians for spin0 and sping helds nonabelian gauge fields conserved charges current conservation gauge theory of u1 annihilation of spinless particles by electromagnetic interaction photons. Johan engquist, olaf hohm, geometry and dynamics of higherspin frame fields arxiv. On the uniqueness of minimal coupling in higherspin gauge theory. The 3d theory where currents of all spin are gauged is clearly more complicated than either 3dimensional qed or the induced gravity theory in 1. Higher gauge theory is a generalization of gauge theory that describes parallel transport, not just for point particles, but also for higher dimensional extended objects. Nov 05, 2015 higherspin gauge theory videos serious science.
This provides substantial evidence that vasiliev theory is dual to the fre e field theory, thus verifying a conjecture of klebanov and polyakov. Various n 1,2,4 hs gauge theories can arise in less symmetric compactifications of mtheory. In component form, the gauge theory describes an interacting theory of higher spin. The ability to change the boundary conditions for the spin 1 field makes it plausible 31 that the type a or b vasiliev theory in ads4 with the electric boundary. Higher spin gauge theories solvay workshops and symposia 2004 pdf. In a gauge theory there is a group of transformations of the field. Dijkgraafwitten theory is a gauge theory whose field configurations are g gprincipal bundles for g g a finite group these come with a unique connection, so that in this simple case the connection is no extra datum. Hs gauge theory is a theory of higher symmetries theory of spacetime goal. Pdf superspace formulation of 4d higher spin gauge. Tamm department of theoretical physics, lebedev physical institute.
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