arXiv subjects

Ben Michel

Publications and source records attributed to Ben Michel.

12 recordsLinked to original sources

arXiv2019

Universality in the OPE Coefficients of Holographic 2d CFTs

The thermodynamic stability of large AdS$_3$ black holes implies that Cardy's $Δ\rightarrow\infty$ formula for the density of states remains approximately valid when $Δ\sim c$ in holographic 2d CFTs, constraining their light spectra. Averaged OPE coefficients take a similarly universal asymptotic form, and black hole arguments again imply an extended regime of validity. In this note we study conditions under which the OPE asymptotics extend to $Δ\sim c$ at large central charge. Some of the conditions found are stronger than required by an extended Cardy regime and are violated by permutation orbifolds, such as the D1-D5 system at zero coupling. Our results suggest new bounds on non-vacuum block contributions to correlation functions in holographic CFTs.

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arXiv2019

Typicality and thermality in 2d CFT

We identify typical high energy eigenstates in two-dimensional conformal field theories at finite $c$ and establish that correlation functions of the stress tensor in such states are accurately thermal as defined by the standard canonical ensemble. Typical states of dimension $h$ are shown to be typical level $h/c$ descendants. In the AdS$_3$/CFT$_2$ correspondence, it is such states that should be compared to black holes in the bulk. We also discuss the discrepancy between thermal correlators and those computed in high energy primary states: the latter are reproduced instead by a generalized Gibbs ensemble with extreme values chosen for the chemical potentials conjugate to the KdV charges.

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arXiv2018

Corrections in the relative entropy of black hole microstates

Inspired by the recent work of Bao and Ooguri (BO), we study the distinguishability of the black hole microstates from the thermal state as captured by the average of their relative entropies: the Holevo information. Under the assumption that the vacuum conformal block dominates the entropy calculation, BO find that the average relative entropy vanishes on spatial regions less than half the size of the CFT. However, vacuum block dominance fails for some microstates of the $M=0$ BTZ black hole. We show that this renders the average relative entropy nonzero even on infinitesimal intervals at $O(c^0)$.

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arXiv2017

A rough end for smooth microstate geometries

Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an "evanescent ergosurface" of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorporating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in $AdS_3 \times S^3$ propagating along one of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum $j$, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to $j \sim \sqrt{n_1n_5}$ where the density of microstates is maximal. We argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.

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arXiv2017

Universality of Sparse $d>2$ Conformal Field Theory at Large $N$

We derive necessary and sufficient conditions for large $N$ conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula. These constraints are much tighter than in two dimensions and must be satisfied by any conformal field theory dual to Einstein gravity. We construct and analyze symmetric product orbifold theories on $\mathbb{T}^d$ and show that they only realize the necessary phase structure and extended range of validity if the seed theory is assumed to have a universal vacuum energy.

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arXiv2016

Entanglement Entropy and Boundary Conditions in 1+1 Dimensions

Calculations of the entanglement entropy of a spatial region in continuum quantum field theory require boundary conditions on the fields at the fictitious boundary of the region. These boundary conditions impact the treatment of the zero modes of the fields and their contribution to the entanglement entropy. We explore this issue in the simplest example, the c=1 compact-boson conformal field theory in 1+1 dimensions. We consider three different types of boundary conditions: spatial Neumann, temporal Neumann, and Dirichlet. We argue that the first two are well motivated, and show that they lead to the same result for the Renyi entropies as well as the entanglement entropy, including a constant term that corresponds to the Affleck-Ludwig boundary entropy. The last set of boundary conditions is less well motivated, and leads to a different value of the constant term. The two values are related by a duality transformation on the compact boson. We also verify some of our results with heat-kernel methods.

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arXiv2016

Remarks on Rindler Quantization

We review the quantization of scalar and gauge fields using Rindler coordinates with an emphasis on the physics of the Rindler horizon. In the thermal state at the Unruh temperature, correlators match their Minkowski vacuum values and the renormalized stress tensor vanishes, while at any other temperature the renormalized stress-energy diverges on the horizon. After giving a new derivation of some of these results using canonical quantization in the thermofield double state, we comment on the relevance of fluxes and boundary conditions at the horizon, which have arisen in calculations of entanglement entropy.

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arXiv2016

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 $\frac{δ\text{Area}}{4G_N}$ term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this $\frac{δ\text{Area}}{4G_N}$ term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.

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arXiv2016

Electromagnetic Duality and Entanglement Anomalies

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies.

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arXiv2016

Four-point function in the IOP matrix model

The IOP model is a quantum mechanical system of a large-$N$ matrix oscillator and a fundamental oscillator, coupled through a quartic interaction. It was introduced previously as a toy model of the gauge dual of an AdS black hole, and captures a key property that at infinite $N$ the two-point function decays to zero on long time scales. Motivated by recent work on quantum chaos, we sum all planar Feynman diagrams contributing to the four-point function. We find that the IOP model does not satisfy the more refined criteria of exponential growth of the out-of-time-order four-point function.

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arXiv2015

Remarks on brane and antibrane dynamics

We develop the point of view that brane actions should be understood in the context of effective field theory, and that this is the correct way to treat classical as well as loop divergences. We illustrate this idea in a simple model. We then consider the implications for the dynamics of antibranes in flux backgrounds, focusing on the simplest case of a single antibrane. We argue that there is no tachyonic instability at zero temperature, but there is a nonperturbative process in which an antibrane annihilates with its screening cloud. This is distinct from the NS5-brane instanton decay. Constraints on models of metastable supersymmetry breaking by antibranes may be tightened, but there is no problem of principle with this mechanism.

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arXiv2014

Journey to the Center of the Fuzzball

We study two-charge fuzzball geometries, with attention to the use of the proper duality frame. For zero angular momentum there is an onion-like structure, and the smooth D1-D5 geometries are not valid for typical states. Rather, they are best approximated by geometries with stringy sources, or by a free CFT. For non-zero angular momentum we find a regime where smooth fuzzball solutions are the correct description. Our analysis rests on the comparison of three radii: the typical fuzzball radius, the entropy radius determined by the microscopic theory, and the breakdown radius where the curvature becomes large. We attempt to draw more general lessons.

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