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We construct the type-IIB AdS4 K supergravity solutions which are dual to the three-dimensional N=4 superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple (ρ,...,L) subject to constraints, where ρ and ... are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five-branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a C4/(ZkZǩ) orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple (ρ,...,L), together with the enhanced non-abelian flavour symmetries of the superconformal field theories, are precisely reproduced by the supergravity solutions. As a bonus, we uncover a novel type of "orbifold equivalence" between different quantum field theories and provide quantitative evidence for this equivalence. [ABSTRACT FROM AUTHOR]

We lift the bosonic AdS4 × CP3 solution of type IIA supergravity preserving 24 supersymmetries to a D = 10 superspace which has 32 Grassmann-odd directions. The type IIA superspace is obtained from D = 11 via dimensional reduction of the coset superspace OSp(8|4)/SO(7) × SO(1,3) by realizing the latter as a Hopf fibration over the former. This construction generalizes to superspace the Hopf fibration of S7 as a U(1) bundle over CP3, and is suitable for writing the explicit form of Green-Schwarz-type actions encoding the dynamics of the type IIA string and branes in the AdS4 × CP3 superbackground. We show that the OSp(6|4)/U(3) × SO(1,3) supercoset string action describes only a subsector of the complete Green-Schwarz superstring. Thus, even though the superstring equations of motion in the OSp(6|4)/U(3) × SO(1,3) subsector are classically integrable, the fact that the full AdS4 × CP3 superspace is not a supercoset requires the use of more general methods to determine whether the superstring in the complete AdS4 × CP3 superbackground is classically integrable. [ABSTRACT FROM AUTHOR]

We find a new sector of string theory in AdS5 × S5 describing non-relativistic superstrings in that geometry. The worldsheet theory of non-relativistic strings in AdS5 × S5 is derived and shown to reduce to a supersymmetric free field theory in AdS2. Non-relativistic string theory provides a new calculable setting in which to study holography. [ABSTRACT FROM AUTHOR]