A
bstract
We study the spectral statistics of primary operators in the recently formulated ensemble average of Narain’s family of free boson conformal field theories, which provides an explicit ...(though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of “U(1) gravity” in AdS
3
. We give an exact formula for the two-point correlation function of the density of primary states. We compute the spectral form factor and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.
A
bstract
A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge
c
and a sparse low energy spectrum. This constrains the OPE coefficients ...and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large
c
. The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.
A
bstract
Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to “double-twist” composites with ...vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT
2
analytic bootstrap, and extract several implications for AdS
3
quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a “Virasoro Mean Field Theory” (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge
c
and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT
2
with
c >
1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin
ℓ
. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in
ℓ
for fixed
c
. We analyze our results in various large
c
limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic
c
; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS
3
.
Pure gravity and conical defects Benjamin, Nathan; Collier, Scott; Maloney, Alexander
The journal of high energy physics,
09/2020, Letnik:
2020, Številka:
9
Journal Article
Recenzirano
Odprti dostop
A
bstract
We revisit the spectrum of pure quantum gravity in AdS
3
. The computation of the torus partition function will — if computed using a gravitational path integral that includes only smooth ...saddle points — lead to a density of states which is not physically sensible, as it has a negative degeneracy of states for some energies and spins. We consider a minimal cure for this non-unitarity of the pure gravity partition function, which involves the inclusion of additional states below the black hole threshold. We propose a geometric interpretation for these extra states: they are conical defects with deficit angle 2
π
(1
−
1
/N
), where
N
is a positive integer. That only integer values of
N
should be included can be seen from a modular bootstrap argument, and leads us to propose a modest extension of the set of saddle-point configurations that contribute to the gravitational path integral: one should sum over orbifolds in addition to smooth manifolds. These orbifold states are below the black hole threshold and are regarded as massive particles in AdS, but they are not perturbative states: they are too heavy to form multi-particle bound states. We compute the one-loop determinant for gravitons in these orbifold backgrounds, which confirms that the orbifold states are Virasoro primaries. We compute the gravitational partition function including the sum over these orbifolds and find a finite, modular invariant result; this finiteness involves a delicate cancellation between the infinite tower of orbifold states and an infinite number of instantons associated with PSL(2
,
ℤ) images.
Modular bootstrap revisited Collier, Scott; Lin, Ying-Hsuan; Yin, Xi
The journal of high energy physics,
09/2018, Letnik:
2018, Številka:
9
Journal Article
Recenzirano
Odprti dostop
A
bstract
We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge
c >
1 using modular bootstrap. Upper bounds on the gap in the dimension of primary ...operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with
c <
8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for
c <
25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.
A sedentary lifestyle and lack of physical activity are well-established risk factors for chronic disease and adverse health outcomes. Thus, there is enormous interest in measuring physical activity ...in biomedical research. Many consumer physical activity monitors, including Basis Health Tracker, BodyMedia Fit, DirectLife, Fitbit Flex, Fitbit One, Fitbit Zip, Garmin Vivofit, Jawbone UP, MisFit Shine, Nike FuelBand, Polar Loop, Withings Pulse O
, and others have accuracies similar to that of research-grade physical activity monitors for measuring steps. This review focuses on the unprecedented opportunities that consumer physical activity monitors offer for human physiology and pathophysiology research because of their ability to measure activity continuously under real-life conditions and because they are already widely used by consumers. We examine current and potential uses of consumer physical activity monitors as a measuring or monitoring device, or as an intervention in strategies to change behavior and predict health outcomes. The accuracy, reliability, reproducibility, and validity of consumer physical activity monitors are reviewed, as are limitations and challenges associated with using these devices in research. Other topics covered include how smartphone apps and platforms, such as the Apple ResearchKit, can be used in conjunction with consumer physical activity monitors for research. Lastly, the future of consumer physical activity monitors and related technology is considered: pattern recognition, integration of sleep monitors, and other biosensors in combination with new forms of information processing.
Universal dynamics of heavy operators in CFT2 Collier, Scott; Maloney, Alexander; Maxfield, Henry ...
The journal of high energy physics,
07/2020, Letnik:
2020, Številka:
7
Journal Article
Recenzirano
Odprti dostop
A
bstract
We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with
c >
1. This formula is valid when one ...or more of the operators has large dimension or — in the presence of a twist gap — has large spin. Our formula is universal in the sense that it depends only on the central charge and not on any other details of the theory. This result unifies all previous asymptotic formulas for CFT2 structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving crossing kernels for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the conformal blocks. The higher genus modular kernels are obtained by sewing together the elementary kernels for four-point crossing and modular transforms of torus one-point functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics of heavy operators in any CFT. The large central charge limit provides a link with 3D gravity, where the averaging over heavy states corresponds to a coarse-graining over black hole microstates in holographic theories. Our formula also provides an improved understanding of the Eigenstate Thermalization Hypothesis (ETH) in CFT
2
, and suggests that ETH can be generalized to other kinematic regimes in two dimensional CFTs.
Genus two modular bootstrap Cho, Minjae; Collier, Scott; Yin, Xi
The journal of high energy physics,
04/2019, Letnik:
2019, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
We study the Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a ℤ
3
-invariant Riemann surface that is a three-fold ...cover of the Riemann sphere branched at four points, and explore constraints from genus two modular invariance and unitarity. In particular, we find “critical surfaces” that constrain the structure constants of a CFT beyond what is accessible via the crossing equation on the sphere.
Bootstrapping boundaries and branes Collier, Scott; Mazáč, Dalimil; Wang, Yifan
The journal of high energy physics,
02/2023, Letnik:
2023, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum ...chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in rational CFTs, where the local operator data is completely determined. We initiate a systematic bootstrap study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large central charge. These potentially have implications for end-of-the-world branes in pure gravity on AdS
3
.
Harmonic analysis of 2d CFT partition functions Benjamin, Nathan; Collier, Scott; Fitzpatrick, A. Liam ...
The journal of high energy physics,
09/2021, Letnik:
2021, Številka:
9
Journal Article
Recenzirano
Odprti dostop
A
bstract
We apply the theory of harmonic analysis on the fundamental domain of SL(2
,
ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of
c
...free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2
,
ℤ), and of target space moduli space
O
(
c, c
; ℤ)\
O
(
c, c
; ℝ)/
O
(
c
)
×
O
(
c
). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS
3
gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
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