Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the AdS$_3$/CFT$_2$ correspondence

@article{Heydeman2016TensorN,
  title={Tensor networks, \$p\$-adic fields, and algebraic curves: arithmetic and the AdS\$_3\$/CFT\$_2\$ correspondence},
  author={Matthew Heydeman and M. Marcolli and Ingmar Saberi and B. Stoica},
  journal={arXiv: High Energy Physics - Theory},
  year={2016}
}
  • Matthew Heydeman, M. Marcolli, +1 author B. Stoica
  • Published 2016
  • Physics, Mathematics
  • arXiv: High Energy Physics - Theory
  • One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. This opens the door to interesting generalizations, obtained by taking another choice of field: for instance, the $p$-adics. We generalize the AdS/CFT… CONTINUE READING
    45 Citations
    Geodesic bulk diagrams on the Bruhat-Tits tree
    • 36
    • Highly Influenced
    • PDF
    Building Archimedean Space
    • 9
    • PDF
    Spin in $p$-adic AdS/CFT.
    • 23
    • Highly Influenced
    • PDF
    General relativity from $p$-adic strings
    • 8
    • PDF
    Exploring the tensor networks/AdS correspondence
    • 30
    • PDF
    Probing holography in $p$-adic CFT
    • 1
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 67 REFERENCES
    Holography and Riemann surfaces
    • 155
    • PDF
    Holography principle and arithmetic of algebraic curves
    • 68
    • PDF
    Anti-de Sitter space and holography
    • 9,951
    • Highly Influential
    • PDF
    NONARCHIMEDEAN CONFORMAL FIELD THEORIES
    • 28
    • Highly Influential
    Modular Index Invariants of Mumford Curves
    • 9
    • PDF
    Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence
    • 61
    • PDF
    p-adic numbers in physics
    • 247
    • Highly Influential
    Noncommutative Geometry
    • 1,664
    • PDF
    Universal terms for the entanglement entropy in 2+1 dimensions
    • 114
    • PDF