32,153 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
Suppression of Dephasing of Optically Trapped Atoms
Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent
superposition of their hyperfine ground states, decohere as they interact with
their environment. We demonstrate than the loss in coherence in an "echo"
experiment, which is caused by mechanisms such as Rayleigh scattering, can be
suppressed by the use of a new pulse sequence. We also show that the coherence
time is then limited by mixing to other vibrational levels in the trap and by
the finite lifetime of the internal quantum states of the atoms
Spin swap vs. double occupancy in quantum gates
We propose an approach to realize quantum gates with electron spins localized
in a semiconductor that uses double occupancy to advantage. With a fast
(non-adiabatic) time control of the tunnelling, the probability of double
occupancy is first increased and then brought back exactly to zero. The quantum
phase built in this process can be exploited to realize fast quantum
operations. We illustrate the idea focusing on the half-swap operation, which
is the key two-qubit operation needed to build a CNOT gate.Comment: 5 pages, 2 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
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