5,039 research outputs found
Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic
quantum error-correcting code to provide a toy model for bulk gauge fields or
linearized gravitons. The key new elements are the introduction of degrees of
freedom on the links (edges) of the associated tensor network and their
connection to further copies of the HaPPY code by an appropriate isometry. The
result is a model in which boundary regions allow the reconstruction of bulk
algebras with central elements living on the interior edges of the (greedy)
entanglement wedge, and where these central elements can also be reconstructed
from complementary boundary regions. In addition, the entropy of boundary
regions receives both Ryu-Takayanagi-like contributions and further corrections
that model the term of Faulkner, Lewkowycz,
and Maldacena. Comparison with Yang-Mills theory then suggests that this
term can be reinterpreted as a part of the
bulk entropy of gravitons under an appropriate extension of the physical bulk
Hilbert space.Comment: 20 pages, 11 figure
Theta series, wall-crossing and quantum dilogarithm identities
Motivated by mathematical structures which arise in string vacua and gauge
theories with N=2 supersymmetry, we study the properties of certain generalized
theta series which appear as Fourier coefficients of functions on a twisted
torus. In Calabi-Yau string vacua, such theta series encode instanton
corrections from Neveu-Schwarz five-branes. The theta series are determined
by vector-valued wave-functions, and in this work we obtain the transformation
of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms.
This effectively provides a quantum version of these transformations, where the
quantization parameter is inversely proportional to the five-brane charge .
Consistency with wall-crossing implies a new five-term relation for Faddeev's
quantum dilogarithm at , which we prove. By allowing the torus to
be non-commutative, we obtain a more general five-term relation valid for
arbitrary and , which may be relevant for the physics of five-branes at
finite chemical potential for angular momentum.Comment: 26 pages; v2: added discussion on relation to complex Chern-Simons,
misprints correcte
Boundary Conditions in Rational Conformal Field Theories
We develop further the theory of Rational Conformal Field Theories (RCFTs) on
a cylinder with specified boundary conditions emphasizing the role of a triplet
of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that
solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is
equivalent to finding integer valued matrix representations of the Verlinde
algebra. These matrices allow us to naturally associate a graph to each
RCFT such that the conformal boundary conditions are labelled by the nodes of
. This approach is carried to completion for theories leading to
complete sets of conformal boundary conditions, their associated cylinder
partition functions and the -- classification. We also review the
current status for WZW theories. Finally, a systematic generalization
of the formalism of Cardy-Lewellen is developed to allow for multiplicities
arising from more general representations of the Verlinde algebra. We obtain
information on the bulk-boundary coefficients and reproduce the relevant
algebraic structures from the sewing constraints.Comment: 71 pages. Minor changes with respect to 2nd version. Recently
published in Nucl.Phys.B but mistakenly as 1st version. Will be republished
in Nucl.Phys.B as this (3rd) versio
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