Function Of Operating Point Research Articles

Holographic surface defects in D=5 , N=4 gauged supergravity

Solutions describing holographic surface defects in $D=5,N=4$ gauged supergravity theories are constructed. It is shown that a surface defect solution in pure Romans' gauged supergravity is singular. Adding a single vector multiplet allows for the construction of a non-singular solution. The on-shell action and one point functions of operators in the presence of the defect are computed using holographic renormalization.

Spinning conformal blocks

For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

Area-scaling of quantum fluctuations

We show that fluctuations of bulk operators that are restricted to some region of space scale as the surface area of the region, independently of its geometry, provided that the operators satisfy certain conditions on their long and short range behavior. Specifically, we consider two point functions of operators that are integrals over local operator densities whose two point functions falls off rapidly at large distances, and does not diverge too strongly at short distances. We show that the two point function of such bulk operators is proportional to the area of the common boundary of the two spatial regions. Consequences of this, relevant to the holographic principle and to area-scaling of Unruh radiation are briefly discussed.

Massive bosons and the dS/CFT correspondence

We compute the boundary two point functions of operators corresponding to massive spin 1 and spin 2 de Sitter fields by an extension of the ``S-matrix'' approach developed for bulk scalars. In each case the two point functions are of the form required for conformal invariance of the dual boundary field theory. We emphasize that in the context of dS/CFT one should consider unitary representations of the Euclidean conformal group, without reference to analytic continuation of the boundary theory to the Lorentzian signature.