34 research outputs found
Emergent Spacetime and Holographic CFTs
We discuss universal properties of conformal field theories with holographic
duals. A central feature of these theories is the existence of a low-lying
sector of operators whose correlators factorize. We demonstrate that
factorization can only hold in the large central charge limit. Using conformal
invariance and factorization we argue that these operators are naturally
represented as fields in AdS as this makes the underlying linearity of the
system manifest. In this class of CFTs the solution of the conformal bootstrap
conditions can be naturally organized in structures which coincide with Witten
diagrams in the bulk. The large value of the central charge suggests that the
theory must include a large number of new operators not captured by the
factorized sector. Consequently we may think of the AdS hologram as an
effective representation of a small sector of the CFT, which is embedded inside
a much larger Hilbert space corresponding to the black hole microstates.Comment: 89 pages, 8 figures, typos correcte
Open G2 Strings
We consider an open string version of the topological twist previously
proposed for sigma-models with G2 target spaces. We determine the cohomology of
open strings states and relate these to geometric deformations of calibrated
submanifolds and to flat or anti-self-dual connections on such submanifolds. On
associative three-cycles we show that the worldvolume theory is a gauge-fixed
Chern-Simons theory coupled to normal deformations of the cycle. For
coassociative four-cycles we find a functional that extremizes on
anti-self-dual gauge fields. A brane wrapping the whole G2 induces a
seven-dimensional associative Chern-Simons theory on the manifold. This theory
has already been proposed by Donaldson and Thomas as the higher-dimensional
generalization of real Chern-Simons theory. When the G2 manifold has the
structure of a Calabi-Yau times a circle, these theories reduce to a
combination of the open A-model on special Lagrangians and the open
B+\bar{B}-model on holomorphic submanifolds. We also comment on possible
applications of our results.Comment: 55 pages, no figure
Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
We use the conformal bootstrap to perform a precision study of the operator
spectrum of the critical 3d Ising model. We conjecture that the 3d Ising
spectrum minimizes the central charge c in the space of unitary solutions to
crossing symmetry. Because extremal solutions to crossing symmetry are uniquely
determined, we are able to precisely reconstruct the first several Z2-even
operator dimensions and their OPE coefficients. We observe that a sharp
transition in the operator spectrum occurs at the 3d Ising dimension
Delta_sigma=0.518154(15), and find strong numerical evidence that operators
decouple from the spectrum as one approaches the 3d Ising point. We compare
this behavior to the analogous situation in 2d, where the disappearance of
operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a
special issue of J.Stat.Phys. in memory of Kenneth Wilso
Black Hole Bound States in AdS(3) x S**2
We systematically construct the geometries dual to the 1+1 dimensional (0, 4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S1 Ă CY3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS3 Ă S2. In addition, we find many geometries that develop multiple, mutually decoupled AdS3 Ă S2 throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S2, a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the "Entropy Enigma" in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.Physic
Solving the 3d Ising Model with the Conformal Bootstrap II. c -Minimization and Precise Critical Exponents
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z 2 -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Î Ï = 0.518154 ( 15 ) , and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations
Solving the 3D Ising Model with the Conformal Bootstrap
We study the constraints of crossing symmetry and unitarity in general 3D
Conformal Field Theories. In doing so we derive new results for conformal
blocks appearing in four-point functions of scalars and present an efficient
method for their computation in arbitrary space-time dimension. Comparing the
resulting bounds on operator dimensions and OPE coefficients in 3D to known
results, we find that the 3D Ising model lies at a corner point on the boundary
of the allowed parameter space. We also derive general upper bounds on the
dimensions of higher spin operators, relevant in the context of theories with
weakly broken higher spin symmetries.Comment: 32 pages, 11 figures; v2: refs added, small changes in Section 5.3,
Fig. 7 replaced; v3: ref added, fits redone in Section 5.
Question Decomposition Improves the Faithfulness of Model-Generated Reasoning
As large language models (LLMs) perform more difficult tasks, it becomes
harder to verify the correctness and safety of their behavior. One approach to
help with this issue is to prompt LLMs to externalize their reasoning, e.g., by
having them generate step-by-step reasoning as they answer a question
(Chain-of-Thought; CoT). The reasoning may enable us to check the process that
models use to perform tasks. However, this approach relies on the stated
reasoning faithfully reflecting the model's actual reasoning, which is not
always the case. To improve over the faithfulness of CoT reasoning, we have
models generate reasoning by decomposing questions into subquestions.
Decomposition-based methods achieve strong performance on question-answering
tasks, sometimes approaching that of CoT while improving the faithfulness of
the model's stated reasoning on several recently-proposed metrics. By forcing
the model to answer simpler subquestions in separate contexts, we greatly
increase the faithfulness of model-generated reasoning over CoT, while still
achieving some of the performance gains of CoT. Our results show it is possible
to improve the faithfulness of model-generated reasoning; continued
improvements may lead to reasoning that enables us to verify the correctness
and safety of LLM behavior.Comment: For few-shot examples and prompts, see
https://github.com/anthropics/DecompositionFaithfulnessPape
Kerr/CFT, dipole theories and nonrelativistic CFTs
We study solutions of type IIB supergravity which are SL(2,R) x SU(2) x
U(1)^2 invariant deformations of AdS_3 x S^3 x K3 and take the form of products
of self-dual spacelike warped AdS_3 and a deformed three-sphere. One of these
backgrounds has been recently argued to be relevant for a derivation of
Kerr/CFT from string theory, whereas the remaining ones are holographic duals
of two-dimensional dipole theories and their S-duals. We show that each of
these backgrounds is holographically dual to a deformation of the DLCQ of the
D1-D5 CFT by a specific supersymmetric (1,2) operator, which we write down
explicitly in terms of twist operators at the free orbifold point. The
deforming operator is argued to be exactly marginal with respect to the
zero-dimensional nonrelativistic conformal (or Schroedinger) group - which is
simply SL(2,R)_L x U(1)_R. Moreover, in the supergravity limit of large N and
strong coupling, no other single-trace operators are turned on. We thus propose
that the field theory duals to the backgrounds of interest are nonrelativistic
CFTs defined by adding the single Schroedinger-invariant (1,2) operator
mentioned above to the original CFT action. Our analysis indicates that the
rotating extremal black holes we study are best thought of as finite
right-moving temperature (non-supersymmetric) states in the above-defined
supersymmetric nonrelativistic CFT and hints towards a more general connection
between Kerr/CFT and two-dimensional non-relativistic CFTs.Comment: 48+8 pages, 4 figures; minor corrections and references adde