SciPost Phys. 9, 019 (2020) ·
published 13 August 2020

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It has long been expected that the 3d Ising model can be thought of as a
string theory, where one interprets the domain walls that separate up spins
from down spins as twodimensional string worldsheets. The usual Ising
Hamiltonian measures the area of these domain walls. This theory has string
coupling of unit magnitude. We add new local terms to the Ising Hamiltonian
that further weight each spin configuration by a factor depending on the genus
of the corresponding domain wall, resulting in a new 3d Ising model that has a
tunable bare string coupling $g_s$. We use a combination of analytical and
numerical methods to analyze the phase structure of this model as $g_s$ is
varied. We study statistical properties of the topology of worldsheets and
discuss the prospects of using this new deformation at weak string coupling to
find a worldsheet description of the 3d Ising transition.
SciPost Phys. 8, 075 (2020) ·
published 13 May 2020

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We study quantum corrections to holographic entanglement entropy in
AdS$_3$/CFT$_2$; these are given by the bulk entanglement entropy across the
RyuTakayanagi surface for all fields in the effective gravitational theory. We
consider bulk $U(1)$ gauge fields and gravitons, whose dynamics in AdS$_3$ are
governed by ChernSimons terms and are therefore topological. In this case the
relevant Hilbert space is that of the edge excitations. A novelty of the
holographic construction is that such modes live not only on the bulk
entanglement cut but also on the AdS boundary. We describe the interplay of
these excitations and provide an explicit map to the appropriate extended
Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum
state and find that the effect of the bulk entanglement entropy is to
renormalize the relation between the effective holographic central charge and
Newton's constant. We also consider excited states obtained by acting with the
$U(1)$ current on the vacuum, and compute the difference in bulk entanglement
entropy between these states and the vacuum. We compute this UVfinite
difference both in the bulk and in the CFT finding a perfect agreement.
SciPost Phys. 6, 006 (2019) ·
published 14 January 2019

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We discuss generalized global symmetries and their breaking. We extend
Goldstone's theorem to higher form symmetries by showing that a perimeter law
for an extended $p$dimensional defect operator charged under a continuous
$p$form generalized global symmetry necessarily results in a gapless mode in
the spectrum. We also show that a $p$form symmetry in a conformal theory in
$2(p+1)$ dimensions has a free realization. In four dimensions this means any
1form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics,
i.e. the current can be photonized. The photonized theory has infinitely many
conserved 0form charges that are constructed by integrating the symmetry
currents against suitable 1forms. We study these charges by developing a
twistorbased formalism that is a 4d analogue of the usual holomorphic complex
analysis familiar in $CFT_2$. The charges are shown to obey an algebra with
central extension, which is an analogue of the 2d Abelian KacMoody algebra for
higher form symmetries.
SciPost Phys. 5, 024 (2018) ·
published 20 September 2018

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We compute the bulk entanglement entropy across the RyuTakayanagi surface
for a oneparticle state in a scalar field theory in AdS$_3$. We work directly
within the bulk Hilbert space and include the spatial spread of the scalar
wavefunction. We give closed form expressions in the limit of small interval
sizes and compare the result to a CFT computation of entanglement entropy in an
excited primary state at large $c$. Including the contribution from the
backreacted minimal area, we find agreement between the CFT result and the FLM
and JLMS formulas for quantum corrections to holographic entanglement entropy.
This provides a nontrivial check in a state where the answer is not dictated
by symmetry. Along the way, we provide closedform expressions for the scalar
field Bogoliubov coefficients that relate the global and Rindler slicings of
AdS$_3$.
SciPost Phys. 4, 005 (2018) ·
published 29 January 2018

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We study the holographic duals of fourdimensional field theories with 1form
global symmetries, both discrete and continuous. Such higherform global
symmetries are associated with antisymmetric tensor gauge fields in the bulk.
Various different realizations are possible: we demonstrate that a Maxwell
action for the bulk antisymmetric gauge field results in a nonconformal field
theory with a marginally running doubletrace coupling. We explore its
hydrodynamic behavior at finite temperature and make contact with recent
symmetrybased formulations of magnetohydrodynamics. We also argue that
discrete global symmetries on the boundary are dual to discrete gauge theories
in the bulk. Such gauge theories have a bulk ChernSimons description: we
clarify the conventional 0form case and work out the 1form case. Depending on
boundary conditions, such discrete symmetries may be embedded in continuous
higherform symmetries that are spontaneously broken. We study the resulting
boundary Goldstone mode, which in the 1form case may be thought of as a
boundary photon. Our results clarify how the global form of the field theory
gauge group is encoded in holography. Finally, we study the interplay of
Maxwell and ChernSimons terms put together. We work out the operator content
and demonstrate the existence of new backreacted anisotropic scaling solutions
that carry higherform charge.
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