The Hanging Drape: a Vertex Analogy

We present a novel, rigidly folding vertex inspired by the shape of the simplest hanging drape. Fold lines in the vertex correspond to pleats and ridges in the drape, and are symmetrically arranged to enable synchronised at folding of facet pairs. We calculate the folded rotation angles exactly using a spherical image specialised for inextensible vertex folding. We show that the vertex shape is bounded by a pair of conical surfaces whose apex semi-angles directly correspond with fold-line rotations, which expresses a geometrical equivalence between the external shape and internal folding motion of the vertex. We discuss how the vertex viz. drape perform as a novel type of conical defect based on its spherical image topography; and we highlight the meaning of bistable behaviour for the vertex, in analytical- and practical terms.

The Regge limit of AdS3 holographic correlators with heavy states: towards the black hole regime

We examine the Regge limit of holographic 4-point correlation functions in AdS3× S3 involving two heavy and two light operators. In this kinematic regime such correlators can be reconstructed from the bulk phase shift accumulated by the light probe as it traverses the geometry dual to the heavy operator. We work perturbatively — but to arbitrary orders — in the ratio of the heavy operator’s conformal dimension to the dual CFT2’s central charge, thus going beyond the low order results of [1] and [2]. In doing so, we derive all-order relations between the bulk phase shift and the Regge limit OPE data of a class of heavy-light multi-trace operators exchanged in the cross-channel. Furthermore, we analyse two examples for which the relevant 4-point correlators are known explicitly to all orders: firstly the case of heavy operators dual to AdS3 conical defect geometries and secondly the case of non-trivial smooth geometries representing microstates of the two-charge D1-D5 black hole.

Surgical treatment of cleft foot in an adult patient

Cleft foot is a rare congenital malformation characterized by a central conical defect extending from the periphery of the foot towards the tarsus, affecting one or more central rays. Surgical intervention should be attempted at a very early age to prevent further pathological adaptations. The authors present the case of an adult woman admitted with painful callosities on the feet and difficulty selecting shoes. She was diagnosed with cleft foot and submitted to surgical treatment. The postoperative period was uneventful and the patient was very satisfied with the results of the surgery. This is only the second reported case of surgical management of cleft foot in an adult patient, and the first to describe the use of internal fixation. Level of Evidence V; Therapeutic Studies; Expert Opinion.

Partition functions of the tensionless string

We consider string theory on AdS3× S3× 𝕋4 in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal AdS3, the BTZ black hole, conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on thermal AdS3 and the conical defect with a torus boundary is shown to agree, thus giving evidence for the equivalence of the tensionless string on these different background geometries. We also find that thermal AdS3 and the BTZ black hole are dual descriptions and the vacuum of the BTZ black hole is mapped to a single long string winding many times asymptotically around thermal AdS3. Thus the system yields a concrete example of the string-black hole transition. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. We argue that the same mechanism can lead to a resolution of the factorization problem when geometries with disconnected boundaries are considered, since the connected and disconnected geometries give the same contribution and we do not have to include them separately.

AdS3 from M-branes at conical singularities

M-theory is known to possess supersymmetric solutions where the geometry is AdS3 × S3 × S3 warped over a Riemann surface Σ2. The simplest examples in this class can be engineered by placing M2 and M5 branes as defects inside of a stack of background M5 branes. In this paper we show that a generalization of this construction yields more general solutions in the aforementioned class. The background branes are now M5’s carrying M2 brane charge, while the defect branes are now placed at the origin of a flat hyperplane with a conical defect. The equations of motion imply a relation between the deficit angle produced by the conical defect and the M2 charge carried by the background branes.

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.

The Regge limit of AdS3 holographic correlators

We study the Regge limit of 4-point AdS3× S3 correlators in the tree-level supergravity approximation and provide various explicit checks of the relation between the eikonal phase derived in the bulk picture and the anomalous dimensions of certain double-trace operators. We consider both correlators involving all light operators and HHLL correlators with two light and two heavy multi-particle states. These heavy operators have a conformal dimension proportional to the central charge and are pure states of the theory, dual to asymptotically AdS3× S3 regular geometries. Deviation from AdS3× S3 is parametrised by a scale μ and is related to the conformal dimension of the dual heavy operator. In the HHLL case, we work at leading order in μ and derive the CFT data relevant to the bootstrap relations in the Regge limit. Specifically, we show that the minimal solution to these equations relevant for the conical defect geometries is different to the solution implied by the microstate geometries dual to pure states.