Built on

L.-Y. Hung, W. Li, and C. M. Melby-Thompson, “ p p -adic CFT is a holographic tensor network,” arXiv:1902.01411 [hep-th]
Original
1902
Earlier work this paper cites.
W. B. Saunders, 1969
Gelfand, I. M., Graev, M. I., Pyatetskii-Shapiro, I. I., Hirsch, K. A. (Translator), Representation Theory and Automorphic Functions · 1969
Earlier work this paper cites.
F. Bruhat and J. Tits, “Groupes réductifs sur un corps local,” Inst. Hautes Études Sci. Publ. Math
1972
Earlier work this paper cites.
P. G. O. Freund and M. Olson, “NONARCHIMEDEAN STRINGS,” Phys. Lett
1987
Earlier work this paper cites.
P. G. O. Freund and E. Witten, “ADELIC STRING AMPLITUDES,” Phys. Lett
1987
Earlier work this paper cites.
E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys
1988
Earlier work this paper cites.
L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, “Nonarchimedean String Dynamics,” Nucl. Phys
1988
Earlier work this paper cites.
A. V. Zabrodin, “Nonarchimedean Strings and Bruhat-tits Trees,” Commun. Math. Phys
1989
Earlier work this paper cites.
E. Melzer, “Nonarchimedean Conformal Field Theories,” Int. J. Mod. Phys
1989
Earlier work this paper cites.
Springer, 1994
Koblitz, N, p p -adic Numbers, p p -adic Analysis and Zeta-Functions · 1994
Earlier work this paper cites.
Springer, 1997
Gouvêa, F. Q., p p -adic Numbers: An Introduction · 1997
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys
1998
Earlier work this paper cites.

Similar

M. Banados, “Three-dimensional quantum geometry and black holes,” AIP Conf. Proc
1999
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Local bulk operators in AdS/CFT: A Boundary view of horizons and locality,” Phys. Rev
2006
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev
2006
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Local bulk operators in AdS/CFT: A Holographic description of the black hole interior,” Phys. Rev
2007
Cited alongside, same era.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev
Original
2012
Cited alongside, same era.

Then

A. Bhatta, P. Raman, and N. V. Suryanarayana, “Holographic Conformal Partial Waves as Gravitational Open Wilson Networks,” JHEP
Original
2016
Later among the works it cites.
M. Besken, A. Hegde, E. Hijano, and P. Kraus, “Holographic conformal blocks from interacting Wilson lines,” JHEP
Original
2016
Later among the works it cites.
S. S. Gubser, J. Knaute, S. Parikh, A. Samberg, and P. Witaszczyk, “ p p -adic AdS/CFT,” Commun. Math. Phys
Original
2017
Later among the works it cites.
S. S. Gubser, M. Heydeman, C. Jepsen, M. Marcolli, S. Parikh, I. Saberi, B. Stoica, and B. Trundy, “Edge length dynamics on graphs with applications to p p -adic AdS/CFT,” JHEP
Original
2017
Later among the works it cites.
S. S. Gubser and S. Parikh, “Geodesic bulk diagrams on the Bruhat-Tits tree,” Phys. Rev

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2018

Wilson line networks in $p$-adic AdS/CFT

Hung, Ling-Yan, Li, Wei, Melby-Thompson, Charles M.

Understand

The $p$-adic AdS/CFT is a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$.

For a $p$-adic CFT living on $\mathbb{Q}_p$ and with complex-valued fields, the bulk theory is defined on the Bruhat-Tits tree, which can be viewed as the bulk dual of $\mathbb{Q}_p$.
We propose that bulk theory can be formulated as a lattice gauge theory of PGL$(2,\mathbb{Q}_p)$ 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.

Built on

L.-Y. Hung, W. Li, and C. M. Melby-Thompson, “ p p -adic CFT is a holographic tensor network,” arXiv:1902.01411 [hep-th]
Original
1902
Earlier work this paper cites.
W. B. Saunders, 1969
Gelfand, I. M., Graev, M. I., Pyatetskii-Shapiro, I. I., Hirsch, K. A. (Translator), Representation Theory and Automorphic Functions · 1969
Earlier work this paper cites.
F. Bruhat and J. Tits, “Groupes réductifs sur un corps local,” Inst. Hautes Études Sci. Publ. Math
1972
Earlier work this paper cites.
P. G. O. Freund and M. Olson, “NONARCHIMEDEAN STRINGS,” Phys. Lett
1987
Earlier work this paper cites.
P. G. O. Freund and E. Witten, “ADELIC STRING AMPLITUDES,” Phys. Lett
1987
Earlier work this paper cites.
E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,” Nucl. Phys
1988
Earlier work this paper cites.
L. Brekke, P. G. O. Freund, M. Olson, and E. Witten, “Nonarchimedean String Dynamics,” Nucl. Phys
1988
Earlier work this paper cites.
A. V. Zabrodin, “Nonarchimedean Strings and Bruhat-tits Trees,” Commun. Math. Phys
1989
Earlier work this paper cites.
E. Melzer, “Nonarchimedean Conformal Field Theories,” Int. J. Mod. Phys
1989
Earlier work this paper cites.
Springer, 1994
Koblitz, N, p p -adic Numbers, p p -adic Analysis and Zeta-Functions · 1994
Earlier work this paper cites.
Springer, 1997
Gouvêa, F. Q., p p -adic Numbers: An Introduction · 1997
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett
1998
Earlier work this paper cites.
E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys
1998
Earlier work this paper cites.

Similar

M. Banados, “Three-dimensional quantum geometry and black holes,” AIP Conf. Proc
1999
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Local bulk operators in AdS/CFT: A Boundary view of horizons and locality,” Phys. Rev
2006
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Holographic representation of local bulk operators,” Phys. Rev
2006
Cited alongside, same era.
A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, “Local bulk operators in AdS/CFT: A Holographic description of the black hole interior,” Phys. Rev
2007
Cited alongside, same era.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev
Original
2012
Cited alongside, same era.