The boundary theory of a spinor field theory on the Bruhat-Tits tree

Qu, Feng; Gao, Yi-hong

doi:10.1016/j.physletb.2020.135331

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…As in the usual AdS/CFT dictionary where computing correlation functions of a small number of operator insertions can be done by considering quantum field theories in the pure AdS background without worrying about back-reaction to the geometry, the p-adic AdS/CFT works in the same way. Witten diagrams on the BT tree have been studied extensively [3,[5][6][7][8][9][10], and the results satisfy all the expected features of the p-adic CFT [11].…”

mentioning

confidence: 74%

Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree

Chen,

Liu,

Hung

2021

Preprint

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In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel "exponential function" on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL(2, Q p ) Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the padic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the "pure" Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree. * Chen and Liu are co-first authors of the manuscript.

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mentioning

confidence: 74%

Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree

Chen,

Liu,

Hung

2021

Preprint

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“…The action (1) requires sgn τ (−1) = −1, otherwise it will vanish identically due to the anti-commutativity of ψ. The authors of [28,27] considered a complex ψ, that would imply having ψ * instead of one of the fields ψ in (1). This eliminates the need for including sgn τ at all, but whether or not sgn τ (−1) = −1 determines if (1) is symmetric or antisymmetric under the exchange ψ ↔ ψ * .…”

Section: A P-adic Fermionic Actionmentioning

confidence: 99%

“…[27]. Motivated in part by these works, in [28] was studied the fermionic field theory on the Bruhat-Tits tree and its effective action on the boundary.…”

Section: Introductionmentioning

confidence: 99%

Towards Non-archimedean Superstrings

García‐Compeán¹,

Lopez²

2022

Preprint

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An action for a prospect of a p-adic open superstring on a target Minkowski space is proposed. The action is constructed for 'worldsheet' fields taking values in the p-adic field Q p , but it is assumed to be obtained from a discrete action on the Bruhat-Tits tree. This action is proven to have an analog of worldsheet supersymmetry and the superspace action is also constructed in terms of superfields. The action does not have conformal symmetry, however it is implemented in the definition of the amplitudes. The tree-level amplitudes for this theory are obtained for N vertex operators corresponding to tachyon superfields and a Koba-Nielsen formula is obtained. Finally, four-point amplitudes are computed explicitly and they are compared to previous work on p-adic superstring amplitudes.

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“…As in the usual AdS/CFT dictionary where computing correlation functions of a small number of operator insertions can be done by considering quantum field theories in the pure AdS background without worrying about back-reaction to the geometry, the p-adic AdS/CFT works in the same way. Witten diagrams on the BT tree have been studied extensively [3,5,[5][6][7][8][9][10], and the results satisfy all the expected features of the p-adic CFT [11]. A natural question would be to JHEP09(2021)097 ask whether one can include dynamics of the background so that the bulk theory becomes an analogue of gravitational theory on AdS.…”

Section: Introductionmentioning

confidence: 99%

Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree

Chen

Liu

Hung

2021

J. High Energ. Phys.

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In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel “exponential function” on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL(2, Qp) Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the p-adic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the “pure” Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree.

show abstract

The boundary theory of a spinor field theory on the Bruhat-Tits tree

Cited by 8 publications

References 21 publications

Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree

Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree

Towards Non-archimedean Superstrings

Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree

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