We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the massdeformed theory on N M2-branes: that there should be a set of discrete vacua in one-toone correspondence with partitions on N. For the mass-deformed Lorentzian three-algebra theory, we find only a single classical vacuum, casting doubt on its M2-brane interpretation. For the mass-deformed ABJM theory, we do find a discrete set of solutions, but these are more numerous than predicted. We discuss possible resolutions of this puzzling discrepancy. We argue that the classical vacuum solutions of the mass-deformed ABJM theory display properties of fuzzy three-spheres, as expected from their gravitational dual interpretation.

We present a number of investigations of 5d N = 1 supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed point theory corresponding to SU(N ) gauge theory with Chern-Simons level ±N , enhanced global symmetries in quiver theories, and dualities between quiver theories and non-quiver theories. Instanton contributions play a crucial role throughout.

We consider an infinite class of 5d supersymmetric gauge theories involving products of symplectic and unitary groups that arise from D4-branes at orbifold singularities in Type I' string theory. The theories are argued to be dual to warped AdS 6 × S 4 /Z n backgrounds in massive Type IIA supergravity. In particular, this demonstrates the existence of supersymmetric 5d fixed points of quiver type. We analyze the spectrum of gauge fields and charged states in the supergravity dual, and find a precise agreement with the symmetries and charged operators in the quiver theories. We also comment on other brane objects in the supergravity dual and their interpretation in the field theories.

We present a new supersymmetric AdS(6) solution of type IIB supergravity with SU(2) isometry. Through the AdS/CFT correspondence, this has potentially very interesting implications for 5D fixed point theories. This solution is the result of a non-Abelian T duality on the known supersymmetric AdS(6) solution of massive IIA. The SU(2) R symmetry is untouched, leading to sixteen supercharges and preserved supersymmetry.

We introduce a simple generalization of the basic holographic superconductor model in which the spontaneous breaking of a global U(1) symmetry occurs via the Stückelberg mechanism. This more general setting allows tuning features such as the order of the transition. The physical vacuum of the condensed phase and the order of the transition are determined by a detailed analysis of the free energy of the system. For first order transitions, we identify a metastable phase above the critical temperature. In this case, the conductivity shows additional poles, thus suggesting that the condensate has internal structure.

Based on recent developments, in this letter we find 2 + 1 dimensional gauge theories with scale invariance and N = 8 supersymmetry. The gauge theories are defined by a lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. The theories are parity invariant and do not admit any tunable coupling constant. In the case of SU(N) the moduli space of vacua contains a branch of the form (R 8 ) N /S N . These properties are expected for the field theory living on a stack of M2 branes.

In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS 6 solution constructed in [1]. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS 6 solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.

We construct several examples of (2 + 1) dimensional N = 2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is the gauge theory associated with the cone over Q 111 . For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models. Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.