208 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
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Modular matrix models
Inspired by a formal resemblance of certain q-expansions of modular forms and the master field formalism of matrix models in terms of Cuntz operators, we construct a Hermitian one-matrix model, which we dub the ``modular matrix model.'' Together with an N=1 gauge theory and a special Calabi-Yau geometry, we find a modular matrix model that naturally encodes the Klein elliptic j-invariant, and hence, by Moonshine, the irreducible representations of the Fischer-Griess Monster group
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
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
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Eigenvalue Density, Li’s Positivity, and the Critical Strip
We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution; this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicate 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 also offer a physical interpretation of the result and discuss the Hilbert-Polya approach
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