479 research outputs found
Virasoro Conformal Blocks and Thermality from Classical Background Fields
We show that in 2d CFTs at large central charge, the coupling of the stress
tensor to heavy operators can be re-absorbed by placing the CFT in a
non-trivial background metric. This leads to a more precise computation of the
Virasoro conformal blocks between heavy and light operators, which are shown to
be equivalent to global conformal blocks evaluated in the new background. We
also generalize to the case where the operators carry U(1) charges. The refined
Virasoro blocks can be used as the seed for a new Virasoro block recursion
relation expanded in the heavy-light limit. We comment on the implications of
our results for the universality of black hole thermality in , or
equivalently, the eigenstate thermalization hypothesis for at large
central charge.Comment: 27+7 pages, 3 figures; typos corrected, citations adde
Universality of Long-Distance AdS Physics from the CFT Bootstrap
We begin by explicating a recent proof of the cluster decomposition principle
in AdS_{d+1} from the CFT_d bootstrap in d > 2. The CFT argument also computes
the leading interactions between distant objects in AdS, and we confirm the
universal agreement between the CFT bootstrap and AdS gravity in the
semi-classical limit. We proceed to study the generalization to 2d CFTs, which
requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit.
We compute these blocks in a semiclassical, large central charge approximation,
and use them to prove a suitably modified theorem. In particular, from the 2d
bootstrap we prove the existence of large spin operators with fixed 'anomalous
dimensions' indicative of the presence of deficit angles in AdS_3. As we
approach the threshold for the BTZ black hole, interpreted as a CFT scaling
dimension, the twist spectrum of large spin operators becomes dense. Due to the
exchange of the Virasoro identity block, primary states above the BTZ threshold
mimic a thermal background for light operators. We derive the BTZ quasi-normal
modes, and we use the bootstrap equation to prove that the twist spectrum is
dense. Corrections to thermality could be obtained from a more refined
computation of the Virasoro conformal blocks.Comment: 34+31 pages, references added, typo in higher-dimensional energy
shift corrected, discussion of coefficient density bounds expande
Nonperturbative Matching Between Equal-Time and Lightcone Quantization
We investigate the nonperturbative relation between lightcone (LC) and
standard equal-time (ET) quantization in the context of theory
in . We discuss the perturbative matching between bare parameters and the
failure of its naive nonperturbative extension. We argue that they are
nevertheless the same theory nonperturbatively, and that furthermore the
nonperturbative map between bare parameters can be extracted from ET
perturbation theory via Borel resummation of the mass gap. We test this map by
using it to compare physical quantities computed using numerical Hamiltonian
truncation methods in ET and LC.Comment: 22+8 pages, 10 figure
A Conformal Truncation Framework for Infinite-Volume Dynamics
We present a new framework for studying conformal field theories deformed by
one or more relevant operators. The original CFT is described in infinite
volume using a basis of states with definite momentum, , and conformal
Casimir, . The relevant deformation is then considered using
lightcone quantization, with the resulting Hamiltonian expressed in terms of
this CFT basis. Truncating to states with , one can numerically find the resulting spectrum, as well
as other dynamical quantities, such as spectral densities of operators. This
method requires the introduction of an appropriate regulator, which can be
chosen to preserve the conformal structure of the basis. We check this
framework in three dimensions for various perturbative deformations of a free
scalar CFT, and for the case of a free CFT deformed by a mass term and a
non-perturbative quartic interaction at large-. In all cases, the truncation
scheme correctly reproduces known analytic results. We also discuss a general
procedure for generating a basis of Casimir eigenstates for a free CFT in any
number of dimensions.Comment: 48+37 pages, 17 figures; v2: references added, small clarification
New Light Species and the CMB
We consider the effects of new light species on the Cosmic Microwave
Background. In the massless limit, these effects can be parameterized in terms
of a single number, the relativistic degrees of freedom. We perform a thorough
survey of natural, minimal models containing new light species and numerically
calculate the precise contribution of each of these models to this number in
the framework of effective field theory. After reviewing the relevant details
of early universe thermodynamics, we provide a map between the parameters of
any particular theory and the predicted effective number of degrees of freedom.
We then use this map to interpret the recent results from the Cosmic Microwave
Background survey done by the Planck satellite. Using this data, we present new
constraints on the parameter space of several models containing new light
species. Future measurements of the Cosmic Microwave Background can be used
with this map to further constrain the parameter space of all such models.Comment: 38 pages plus appendices and references; 10 figures and 1 table;
references added, discussion of anapole moments added; supernovae cooling
bounds added, discussion of models condense
Hawking from Catalan
The Virasoro algebra determines all `graviton' matrix elements in
AdS/CFT. We study the explicit exchange of any number of Virasoro
gravitons between heavy and light CFT operators at large central charge.
These graviton exchanges can be written in terms of new on-shell tree diagrams,
organized in a perturbative expansion in , the heavy operator dimension
divided by the central charge. The Virasoro vacuum conformal block, which is
the sum of all the tree diagrams, obeys a differential recursion relation
generalizing that of the Catalan numbers. We use this recursion relation to sum
the on-shell diagrams to all orders, computing the Virasoro vacuum block.
Extrapolating to large determines the Hawking temperature of a BTZ
black hole in dual AdS theories.Comment: 19+8 pages, 5 figure
Eikonalization of Conformal Blocks
Classical field configurations such as the Coulomb potential and
Schwarzschild solution are built from the t-channel exchange of many light
degrees of freedom. We study the CFT analog of this phenomenon, which we term
the `eikonalization' of conformal blocks. We show that when an operator
appears in the OPE , then the large spin
Fock space states also appear in this OPE with a
computable coefficient. The sum over the exchange of these Fock space states in
an correlator
build the classical ` field' in the dual AdS description. In some limits the
sum of all Fock space exchanges can be represented as the exponential of a
single exchange in the 4-pt correlator of . Our results should
be useful for systematizing perturbation theory in general CFTs and
simplifying the computation of large spin OPE coefficients. As examples we
obtain the leading dependence of Fock space conformal block
coefficients, and we directly compute the OPE coefficients of the simplest
`triple-trace' operators.Comment: 32+17 pages, 6 figures; references added, discussion of eikonal limit
clarifie
RG Flow from Theory to the 2D Ising Model
We study 1+1 dimensional theory using the recently proposed method
of conformal truncation. Starting in the UV CFT of free field theory, we
construct a complete basis of states with definite conformal Casimir,
. We use these states to express the Hamiltonian of the full
interacting theory in lightcone quantization. After truncating to states with
, we numerically diagonalize the
Hamiltonian at strong coupling and study the resulting IR dynamics. We compute
non-perturbative spectral densities of several local operators, which are
equivalent to real-time, infinite-volume correlation functions. These spectral
densities, which include the Zamolodchikov -function along the full RG flow,
are calculable at any value of the coupling. Near criticality, our numerical
results reproduce correlation functions in the 2D Ising model.Comment: 31+12 page
Flux Correlators and Semiclassics
We consider correlators for the flux of energy and charge in the background
of operators with large global charge in conformal field theory (CFT).
It has recently been shown that the corresponding Euclidean correlators
generically admit a semiclassical description in terms of the effective field
theory (EFT) for a conformal superfluid. We adapt the semiclassical description
to Lorentzian observables and compute the leading large charge behavior of the
flux correlators in general symmetric CFTs. We discuss the regime of
validity of the large charge EFT for these Lorentzian observables and the
subtleties in extending the EFT approach to subleading corrections. We also
consider the Wilson-Fisher fixed point in dimensions, which
offers a specific weakly coupled realization of the general setup, where the
subleading corrections can be systematically computed without relying on an
EFT.Comment: 33 pages, 8 figure
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