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The classification and construction of symmetry protected topological (SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system. We first demonstrate the essential idea by considering an anomalous topological superconductor with time-reversal symmetry T^2 = 1 in 2D. The physical reason for this is that the fermion parity might be changed locally by certain symmetry action, but it is conserved if we introduce a bulk. Then we discuss the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry G_f = G_b × \mathbb{Z}^f_2. Finally, potential experimental realizations of ASPT states are also addressed.

We present a one-parameter family of large N disordered models, with and without supersymmetry, in three spacetime dimensions. They interpolate from the critical large N vector model dual to a classical higher spin theory toward a theory with a classical string dual. We analyze the spectrum and operator product expansion data of the theories. While the supersymmetric model is always well-behaved the nonsupersymmetric model is unitary only over a small parameter range. We offer some speculations on the origin of strings from the higher spins.

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