Finding AdS5 × S5 in 2+1 dimensional SCFT physics

We study solutions of type IIB string theory dual to $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory on half of ℝ3,1 coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically AdS5×S5 with boundary geometry ℝ2,1×ℝ+, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré AdS5×S5. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the “missing” half of Poincaré AdS5×S5. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré AdS5×S5 with an angle arbitrarily close to π, with geometrical ETW branes on either side.

Fix the dual geometries of $$T\bar{T}$$ deformed CFT$$_2$$ and highly excited states of CFT$$_2$$

In previous works, we have developed an approach to fix the leading behaviors of the pure AdS$$_3$$ 3 and BTZ black hole from the entanglement entropies of the free CFT$$_2$$ 2 and finite temperature CFT$$_2$$ 2 , respectively. We exclusively use holographic principle only and make no restriction about the bulk geometry, not only the kinematics but also the dynamics. In order to verify the universality and correctness of our method, in this paper, we apply it to the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , which breaks the conformal symmetry. In terms of the physical arguments of the $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 , the derived metric is a deformed BTZ black hole. The requirement that the CFT$$_2$$ 2 lives on a conformally flat boundary leads to $$r_{c}^{2}=\ 6R_{AdS}^{4}/(\pi c\mu )$$ r c 2 = 6 R AdS 4 / ( π c μ ) naturally, in perfect agreement with previous conjectures in literature. The energy spectum and propagation speed calculated with this deformed BTZ metric are the same as these derived from $$T\bar{T}$$ T T ¯ deformed CFT$$_2$$ 2 . We furthermore fix the dual geometry of highly excited states with our approach. The result contains the descriptions for the conical defect and BTZ black hole.

Holo-ween

We argue that given holographic CFT1 in some state with a dual spacetime geometry M, and given some other holographic CFT2, we can find states of CFT2 whose dual geometries closely approximate arbitrarily large causal patches of M, provided that CFT1 and CFT2 can be non-trivially coupled at an interface. Our CFT2 states are “dressed up as” states of CFT1: they are obtained from the original CFT1 state by a regularized quench operator defined using a Euclidean path-integral with an interface between CFT2 and CFT1. Our results are consistent with the idea that the precise microscopic degrees of freedom and Hamiltonian of a holographic CFT are only important in fixing the asymptotic behavior of a dual spacetime, while the interior spacetime of a region spacelike separated from a boundary time slice is determined by more universal properties (such as entanglement structure) of the quantum state at this time slice. Our picture requires that low-energy gravitational theories related to CFTs that can be non-trivially coupled at an interface are part of the same non-perturbative theory of quantum gravity.

EXTERNAL ZONOTOPAL ALGEBRA

Zonotopal algebra studies pairs of dual algebraic structures that are associated with a linear matroid X and are connected to corresponding dual geometries. Both the geometry and the algebra encode in their statistics combinatorial properties of the matroid. We provide in this paper a general, unified, framework for the chapter in zonotopal algebra that is known as external. The approach is critically based on employing simultaneously the two dual algebraic constructs and invokes the underlying matroidal and geometric structures in an essential way.

Fast Far Field Computation of Single and Dual Reflector Antennas

The physical optics (PO) method has been widely used for the analysis of the electromagnetic behavior of single and dual reflector antennas. An extensive work has been done by the authors of this paper in order to increase the speed for obtaining far field patterns from single and dual geometries and also in order to increase the accuracy of the method. This paper reviews these contributions and improves the existing published work with the physical interpretation of the radiation from a single patch and the computer implications when using acceleration techniques such as OpenMP.

FERMIONIC T-DUALITY: A SNAPSHOT REVIEW

Through a self-dual mapping of the geometry AdS5 ×S5, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in [Formula: see text] super-Yang–Mills. Starting with Green–Schwarz sigma-models, we consolidate developments in this area into this small review. In particular, we discuss the translation of fermionic T-duality into the supergravity fields via pure spinor formalism and show that a general class of fermionic transformations can be identified directly in the supergravity. In addition to discussing fermionic T-duality for the geometry AdS4 × ℂ P 3, dual to [Formula: see text] ABJM theory, we review work on other self-dual geometries. Finally, we present a short round-up of studies with a formal interest in fermionic T-duality.