Yoshiaki Tanii

Conformally invariant supersymmetric field theories on Sp × S1 and super p-branes

Abstract We construct supersymmetric field theories on Sp × S1 for p = 1,…,5. These spaces are the boundaries of the anti-de Sitter space in (p + 2)-dimensions. Thesetheories are invariant under the super extension of the anti-de Sitter group in (p + 2)-dimensions, whose bosonic subalgebra is SO (p + 1,2) ⊛ SO (N) , for N = 1,2,4,8. The anti-de Sitter group SO(p + 1,2) acts as the conformal group on Sp × S1. We conjecture that these theories describe the super p-branes propagating in AdSp + 2 × SN−1. The internal space is always one of the parallelizable spheres, namely S1, S3 or S7.

Singletons, higher spin massless states and the supermembrane

Abstract We analyse the spectrum of the eleven-dimensional supermembrane quantized in AdS 4 × S 7 background. The classical membranes lives at the boundary of AdS 4 which is S 2 × S 1 , and has OSp(8,4) symmetry. We find that the spectrum contains, in addition to the N =8 supersymmetric (massive) singletons (which may possibly be the ultimate preons), also massless states of all higher integer and half-integer spin. These states fill the irreducible representations of OSp(8,4) with highest spin s max =2,4,6,… The S max = 2 multiplet corresponds to the states of the de Wit-Nicolais N = 8 gauged supergravity in four dimensions.

Hamiltonian formulation of the supermembrane

The hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence-free 2-vectors are unfixed.

N = 8 supersingleton quantum field theory

Abstract We quantize the N = 8 supersymmetric singleton field theory which is formulated on the boundary of the four-dimensional anti-de Sitter spacetime (AdS 4 ). The theory has rigid OSp(8,4) symmetry which acts as a superconformal group on the boundary of AdS 4 . We show that the generators of this symmetry satisfy the full quantum OSp(8,4) algebra. The spectrum of the theory contains massless states of all higher integer and half-integer spin which fill the irreducible representations of OSp(8,4) with highest spin s max = 2,4,6,…. Remarkably, these are in one-to-one correspondence with the generators of Vasilievs infinite-dimensional extended higher spin superalgebra shs(8,4), suggesting that we may have stumbled onto a field-theoretic realization of this algebra. We also discuss the possibility of a connection between the N = 8 supersingleton theory with the eleven-dimensional supermembrane in an AdS 4 × S 7 background.

SUPER WEYL ANOMALIES IN THE AdS/CFT CORRESPONDENCE

Anomalies of N=(4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge and super Weyl transformations are anomalous, while general coordinate, local Lorentz, vector gauge and local supertransformations are not. The coefficients of the anomalies show that the superconformal field theories have the central charge expected in the AdS/CFT correspondence.

LOCAL SYMMETRIES IN THE AdS7/CFT6 CORRESPONDENCE

It is shown that local symmetry transformations of the maximal AdS supergravity in seven-dimensional anti de Sitter space induce those of the N=(2,0) conformal supergravity on the six-dimensional boundary at infinity. Boundary values of the AdS supergravity fields form a supermultiplet of the conformal supergravity.

DUALITY SYMMETRIES IN NONLINEAR GAUGE THEORIES

Duality symmetries are discussed for nonlinear gauge theories of (n-1)th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant nonlinear theories. We also discuss how to enlarge the duality symmetries to noncompact groups by coupling scalar fields described by nonlinear sigma models.

SUPERGRAVITY IN 2+∊ DIMENSIONS

Supergravity theory in

Vertex functions in the path integral formalism of open string theories

2+epsilon

One-loop amplitudes and divergences in unoriented string theories

dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In quantizing the supergravity, a gauge fixing condition is devised which explicitly isolates conformal and superconformal modes. The renormalization of the gravitationally dressed operators is studied and their anomalous dimensions are computed. Problems to use the dimensional reduction are also examined.