Ergin Sezgin

Massless Higher Spins and Holography

Abstract We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R . The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consistent truncation to massless HS fields. A survey of massless HS theories with 32 supersymmetries in D =4,5,7 (where the 7D results are new) is given and the corresponding composite operators are discussed. In the case of AdS 4 , the cubic couplings of a minimal bosonic massless HS gauge theory are described. We examine high energy/small tension limits giving rise to massless HS fields in the type IIB string on AdS 5 × S 5 and M-theory on AdS 4/7 × S 7/4 . We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS 5 × S 5 and AdS 4 × S 7 where the HS symmetry is broken by finite g YM . In AdS 5 × S 5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g YM 2 =0 corresponds to a critical string tension of order 1/ R 2 and a finite string coupling of order 1/ N . In AdS 7 × S 4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the A N −1 (2,0) SCFT, expandable in terms of operators with anomalous dimensions that are asymptotically small for large spin. The minimal energy configurations have semi-classical energy E = s for all s and the geometry of infinitely stretched strings with energy and spin density concentrated at the endpoints.

Holography in 4D (super) higher spin theories and a test via cubic scalar couplings

The correspondences proposed previously between higher spin gauge theories and free singleton fleld theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D = 4 to include the strongly coupled flxed point of the 3d O(N) vector model. Here we propose an N = 1 supersymmetric version of this picture. We also elaborate on the role of parity in constrain- ing the bulk interactions, and in distinguishing two minimal bosonic models obtained as two difierent consistent truncations of the minimal N = 1 model that retain the scalar or the pseudo-scalar fleld. We refer to these models as the type-A and type-B models, respec- tively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the type-A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.

Covariant field equations of the M theory five-brane

Abstract The component form of the equations of motion for the 5-brane in eleven dimensions is derived from the superspace equations. These equations are fully covariant in six dimensions. It is shown that double-dimensional reduction of the bosonic equations gives the equations of motion for a 4-brane in ten dimensions governed by the Born-Infeld action.

D = 11, p = 5

Abstract The equations of motion of the super five-brane in D = 11 dimensions are derived using the formalism of superembeddings. The equations describe highly nonlinear self-interactions of a tensor multiplet in the six dimensional worlsurface, and they have manifest worldsurface local supersymmetry. The geometry of the target space corresponds to D = 11 supergravity.

Stainless super p-branes

The elementary and solitonic supersymmetric p-brane solutions to supergravity theories form families related by dimensional reduction, each headed by a maximal (‘stainless’) member that cannot be isotropically dimensionally oxidized into higher dimensions. We find several new families, headed by stainless solutions in various dimensions D ⩽ 9. In some cases, these occur with dimensions (D, p) that coincide with those of descendants of known families, but since the new solutions are stainless, they are necessarily distinct. The new stainless supersymmetric solutions include a 6-brane and a 5-brane in D = 9, a string in D = 5, and particles in all dimensions 5 ⩽ D ⩽ 9.

Doubletons and 5D higher spin gauge theory

We use Grassmann even spinor oscillators to construct a bosonic higher spin extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and show that the gauging of hs(2,2) gives rise to a spectrum of physical massless fields with spin s = 0,2,4,... that is a UIR of hs(2,2). In addition to a master gauge field which contains the massless s = 2,4,... fields, we construct a scalar master field containing the massless s = 0 field, the generalized Weyl tensors and their derivatives. We give the appropriate linearized constraint on this master scalar field, which together with a linearized curvature constraint produces the correct linearized field equations. A crucial step in the construction of the theory is the identification of a central generator K which is eliminated by means of a coset construction. Its charge vanishes in the spectrum , which is the symmetric product of two spin zero doubletons. We expect our results to pave the way for constructing an interacting theory whose curvature expansion is dual to a CFT based on higher spin currents formed out of free doubletons in the large-N limit. Thus, extending a recent proposal of Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory describes a truncation of the bosonic massless sector of tensionless type-IIB string theory on AdS5 × S5 for large N. This implies AdS/CFT correspondence in a parameter regime where both boundary and bulk theories are perturbative.

Spectrum of D = 6, N = 4b supergravity on AdS3 × S3

Abstract The complete spectrum of D = 6, N = 4 b supergravity with n tensor multiplets compactified on AdS 3 × S 3 is determined. The D = 6 theory obtained from K 3 compactification of Thpe IIB string requires that n = 21, but we let n be arbitrary. The superalgebra that underlies the symmetry of the resulting supergravity theory in AdS 3 coupled to matter is SU (1, 1||2) L × SU (1, 1||2) R . The theory also has an unbroken global SO (4) R × SO ( n ) symmetry inherited from D = 6. The spectrum of states arranges itself into a tower of spin-2 supermultiplets, a tower of spin-1, SO ( n ) singlet supermultiplets, a tower of spin-1 supermultiplets in the vector representation of SO ( n ) and a special spin - 1 2 supermultiplet also in the vector representation of SO ( n ). The SU (2) L × SU (2) R Yang-Mills states reside in the second level of the spin-2 tower and the lowest level of the spin-1, SO ( n ) singlet tower and the associated field theory exhibits interesting properties.

d=8 supergravity

Abstract SU(2) gauged N =2 supergravity in d =8 is constructed by generalized dimensional reduction of d =11 supergravity on SU(2) group manifold. The relation between the field equations of the d =8 and those of d =11 supergravities is established. As a byproduct of this, it is shown that certain compactifications of d =11 supergravity give rise to anti-de Sitter space-time (AdS)⊗S 4 or AdS⊗CP 2 (with or without SU(2) instanton) or AdS⊗S 2 ⊗S 2 compactifications of d =8 supergravity.

Analysis of higher spin field equations in four dimensions

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.

Higher spin N=8 supergravity

The product of two N = 8 supersingletons yields an infinite tower of massless states of higher spin in four dimensional anti de Sitter space. All the states with spin s ≥ 1 correspond to generators of Vasilievs super higher spin algebra shsE(8|4) which contains the D = 4,N = 8 anti de Sitter superalgebra OSp(8|4). Gauging the higher spin algebra and introducing a matter multiplet in a quasi-adjoint representation leads to a consistent and fully nonlinear equations of motion as shown sometime ago by Vasiliev. We show the embedding of the N = 8 AdS supergravity equations of motion in the full system at the linearized level and discuss the implications for the embedding of the interacting theory. We furthermore speculate that the boundary N = 8 singleton field theory yields the dynamics of the N = 8 AdS supergravity in the bulk, including all higher spin massless fields, in an unbroken phase of M-theory.