90 research outputs found
Fine Structure of Dark Energy and New Physics
Following our recent work on the cosmological constant problem, in this
letter we make a specific proposal regarding the fine structure (i.e., the
spectrum) of dark energy. The proposal is motivated by a deep analogy between
the blackbody radiation problem, which led to the development of quantum
theory, and the cosmological constant problem, which we have recently argued
calls for a conceptual extension of the quantum theory. We argue that the fine
structure of dark energy is governed by a Wien distribution, indicating its
dual quantum and classical nature. We discuss a few observational consequences
of such a picture of dark energy.Comment: 14 pages, LaTeX, typos fixed, comments, references, and footnotes
added, Sec. 4 revise
On the Shape of Things: From holography to elastica
We explore the question of which shape a manifold is compelled to take when
immersed in another one, provided it must be the extremum of some functional.
We consider a family of functionals which depend quadratically on the extrinsic
curvatures and on projections of the ambient curvatures. These functionals
capture a number of physical setups ranging from holography to the study of
membranes and elastica. We present a detailed derivation of the equations of
motion, known as the shape equations, placing particular emphasis on the issue
of gauge freedom in the choice of normal frame. We apply these equations to the
particular case of holographic entanglement entropy for higher curvature three
dimensional gravity and find new classes of entangling curves. In particular,
we discuss the case of New Massive Gravity where we show that non-geodesic
entangling curves have always a smaller on-shell value of the entropy
functional. Then we apply this formalism to the computation of the entanglement
entropy for dual logarithmic CFTs. Nevertheless, the correct value for the
entanglement entropy is provided by geodesics. Then, we discuss the importance
of these equations in the context of classical elastica and comment on terms
that break gauge invariance.Comment: 54 pages, 8 figures. Significantly improved version, accepted for
publication in Annals of Physics. New section on logarithmic CFTs. Detailed
derivation of the shape equations added in appendix B. Typos corrected,
clarifications adde
On the Physics of the Riemann Zeros
We discuss a formal derivation of an integral expression for the Li
coefficients associated with the Riemann xi-function which, in particular,
indicates that their positivity criterion is obeyed, whereby entailing the
criticality of the non-trivial zeros. We conjecture the validity of this and
related expressions without the need for the Riemann Hypothesis and discuss a
physical interpretation of this result within the Hilbert-Polya approach. In
this context we also outline a relation between string theory and the Riemann
Hypothesis.Comment: 8 pages, LaTeX, Quantum Theory and Symmetries 6 conference
proceeding
Deconstructing the Cosmological Constant
Deconstruction provides a novel way of dealing with the notoriously difficult
ultraviolet problems of four-dimensional gravity. This approach also naturally
leads to a new perspective on the holographic principle, tying it to the
fundamental requirements of unitarity and diffeomorphism invariance, as well as
to a new viewpoint on the cosmological constant problem. The numerical
smallness of the cosmological constant is implied by a unique combination of
holography and supersymmetry, opening a new window into the fundamental physics
of the vacuum.Comment: Fourth Prize, 2003 Gravity Research Foundation Essay Contest; 7
pages, LaTe
Quantum Gravity and Turbulence
We apply recent advances in quantum gravity to the problem of turbulence.
Adopting the AdS/CFT approach we propose a string theory of turbulence that
explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and
Kolmogorov scalings in 2+1 dimensions. In the gravitational context, turbulence
is intimately related to the properties of spacetime, or quantum, foam.Comment: 8 pages, LaTeX; Honorable Mention in the 2010 Gravity Research
Foundation Essay Contes
Restriction enzymes use a 24 dimensional coding space to recognize 6 base long DNA sequences
Restriction enzymes recognize and bind to specific sequences on invading
bacteriophage DNA. Like a key in a lock, these proteins require many contacts
to specify the correct DNA sequence. Using information theory we develop an
equation that defines the number of independent contacts, which is the
dimensionality of the binding. We show that EcoRI, which binds to the sequence
GAATTC, functions in 24 dimensions. Information theory represents messages as
spheres in high dimensional spaces. Better sphere packing leads to better
communications systems. The densest known packing of hyperspheres occurs on the
Leech lattice in 24 dimensions. We suggest that the single protein EcoRI
molecule employs a Leech lattice in its operation. Optimizing density of sphere
packing explains why 6 base restriction enzymes are so common.Comment: Version 1: 31 pages, 3 figures, 1 table; Version 2: 33 pages, 3
figures, 1 table, responses to reviewers, new ref
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