64 research outputs found
The Kerr/CFT Correspondence
Quantum gravity in the region very near the horizon of an extreme Kerr black
hole (whose angular momentum and mass are related by J=GM^2) is considered. It
is shown that consistent boundary conditions exist, for which the asymptotic
symmetry generators form one copy of the Virasoro algebra with central charge
c_L=12J / \hbar. This implies that the near-horizon quantum states can be
identified with those of (a chiral half of) a two-dimensional conformal field
theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state
reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi
and conjugate energy given by the zero mode generator, L_0, of the Virasoro
algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy
S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic
Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any
consistent unitary quantum theory of gravity with a Kerr solution. We
accordingly conjecture that extreme Kerr black holes are holographically dual
to a chiral two-dimensional conformal field theory with central charge c_L=12J
/ \hbar, and in particular that the near-extreme black hole GRS 1915+105 is
approximately dual to a CFT with c_L \sim 2 \times 10^{79}.Comment: 21 pages, no figure
States, symmetries and correlators of and symmetric orbifolds
We derive various properties of symmetric product orbifolds of and
- deformed CFTs from a field-theoretical perspective. First, we
generalise the known formula for the torus partition function of a symmetric
orbifold theory in terms of the one of the seed to non-conformal
two-dimensional QFTs; specialising this to seed and -
deformed CFTs reproduces previous results in the literature. Second, we show
that the single-trace and deformations preserve the
Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold
CFT, including their fractional counterparts, as well as the KdV charges.
Finally, we discuss correlation functions in these theories. By extending a
previously-proposed basis of operators for - deformed CFTs to the
single-trace case, we explicitly compute the correlation functions of both
untwisted and twisted-sector operators and compare them to an appropriate set
of holographic correlators. Our derivations are based mainly on Hilbert space
techniques and completely avoid the use of conformal invariance, which is not
present in these models.Comment: 50 pp, 5 figure
Classical and quantum symmetries of -deformed CFTs
It has previously been proven that - deformed CFTs possess Virasoro
Virasoro symmetry at the full quantum level, whose generators are
obtained by simply transporting the original CFT generators along the
flow. In this article, we explicitly solve the corresponding flow equation in
the classical limit, obtaining an infinite set of conserved charges whose
action on phase space is well-defined even when the theory is on a compact
space. The field-dependent coordinates that are characteristic of the
deformation are shown to emerge unambiguously from the flow. Translating the
symmetry transformations from the canonical to the covariant formalism, we find
that they are different from those that have been previously proposed in the
Lagrangian context, but that they agree precisely with those obtained from
holography. We also comment on different possible bases for the symmetry
generators and on how our explicit classical results could be extended
perturbatively to the quantum level.Comment: 26 page
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