p-adic CFT is a holographic tensor network

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The p-adic AdS/CFT is a holographic duality based on the p-adic number field Q p . For a p-adic CFT living on Q p and with complex-valued fields, the bulk theory is defined on the Bruhat-Tits tree, which can be viewed as the bulk dual of Q p . We propose that bulk theory can be formulated as a lattice gauge theory of PGL(2, Q p ) on the Bruhat-Tits tree, and show that the Wilson line networks in this lattice gauge theory can reproduce all the correlation functions of the boundary p-adic CFT.A A few identities for shadow operator 28 A.1 Orthogonality between operator and its shadow operator 28 A.2 Three point function involving the shadow operator 29 IntroductionThe p-adic AdS/CFT proposed in [1,2] is a holographic duality between conformal field theories based on the p-adic number field Q p and bulk theories living on the Bruhat-Tits tree [3] -a (p+1)-valent tree that can be viewed as the bulk dual of Q p [4]. It shares many important features of ordinary AdS/CFT based on the real field R. The field Q p results from completing the rational field Q using the p-adic norm rather than the Euclidean norm.In fact, it is the only field other than R that can be obtained by completing Q while subject to the four axioms of Euclidean norm [5]. The generalization of AdS/CFT from R to Q p suggests that the holography is more universal than in spacetime based on R. There has been many recent developments in the last two years, see. [6][7][8][9][10][11][12][13][14][15]. Tensor network originally started as an ansatz for solving N -body wavefunctions (see e.g. review [16] and references therein) and recently has been used to realize discrete versions of holographic duality [17,18], where the tensor network lives on a discretized bulk spacetime (hence the bulk isometry is broken to a discrete subgroup of the conformal group). Many important features of the AdS/CFT dictionary, most notably Ryu-Takayanagi formula and the structure of the entanglement wedge, are naturally captured by a suitable tensor network (at least qualitatively) [19]. This suggests that tensor network might help uncover the mechanism of AdS/CFT correspondence.In [20], we proposed that one can use a tree-type tensor network living on the Bruhat-Tits tree to provide a concrete realization of p-adic AdS/CFT. In this realization, the dictionary between the boundary and bulk sides of the p-adic AdS/CFT is derived from the tensor network instead of being treated as a conjecture. In particular, we have derived the bulk reconstruction formula and shown how to recover boundary correlation functions from the tensor network. 1 In a more recent work [26], we reproduced explicitly the complete set of correlation functions of any p-adic CFT with given spectra and structure constants.In the p-adic AdS/CFT discussed so far, boundary correlation functions are reproduced by bulk Witten diagrams. In AdS 3 /CFT 2 based on R, the bulk Einstein gravity can be reformulated as an SL(2, C) Chern-Simons theory [27,28] and accordingly the boundary correlation functions can also be reprod...

Section: Pgl(2 Q P ) Representations For Primariessupporting

confidence: 54%

Section: Jhep05(2019)118mentioning

confidence: 99%

Section: Review: Pure Ads 3 Configurationmentioning

confidence: 99%

Section: Individual Tensors and Bulk Wl Junction With Nearest Neighborsmentioning

confidence: 99%

Section: Individual Tensors and Bulk Wl Junction With Nearest Neighborsmentioning

confidence: 99%

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Wilson line networks in p-adic AdS/CFT

Hung

Melby-Thompson

2019

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Thread/State correspondence: from bit threads to qubit threads

Lin

Jin

2023

Starting from an interesting coincidence between the bit threads and SS (surface/state) correspondence, both of which are closely related to the holographic RT formula, we introduce a property of bit threads that has not been explicitly proposed before, which can be referred to as thread/state correspondence (see [50] for a brief pre-release version). Using this thread/state correspondence, we can construct the explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the SS correspondence, and nicely characterize their entanglement structure. Based on this understanding, we use the locking bit thread configurations to construct a holographic qubit threads model as a new toy model of the holographic principle, and show that it is closely related to the holographic tensor networks, the kinematic space, and the connectivity of spacetime.

A multipoint conformal block chain in d dimensions

Parikh

2020

Conformal blocks play a central role in CFTs as the basic, theory-independent building blocks. However, only limited results are available concerning multipoint blocks associated with the global conformal group. In this paper, we systematically work out the d-dimensional n-point global conformal blocks (for arbitrary d and n) for external and exchanged scalar operators in the so-called comb channel. We use kinematic aspects of holography and previously worked out higher-point AdS propagator identities to first obtain the geodesic diagram representation for the (n + 2)-point block. Subsequently, upon taking a particular double-OPE limit, we obtain an explicit power series expansion for the n-point block expressed in terms of powers of conformal cross-ratios. Interestingly, the expansion coefficient is written entirely in terms of Pochhammer symbols and (n − 4) factors of the generalized hypergeometric function 3 F 2 , for which we provide a holographic explanation. This generalizes the results previously obtained in the literature for n = 4, 5. We verify the results explicitly in embedding space using conformal Casimir equations.