Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent $z=\frac{2}{3}$. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.Comment: 27 pages, revtex; added discussions, added formulas, added referenc

On Scale Versus Conformal Symmetry in Turbulence

We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally covariant, with the only possible exception being the direct enstrophy cascade in two space dimensions. We argue that the same conclusions hold for compressible non-relativistic turbulence as well as for relativistic turbulence. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators. We consider the issue of non-locality of the stress-energy tensor of inertial range turbulence field theory.Comment: 4 pages, revtex, ref. added. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operator

The United States after unipolarity: American democracy promotion and the ‘Arab Spring’

In the aftermath of the 11 September 2001 terrorist attacks the United States increasingly sought to promote democracy in the Middle East and North Africa (MENA). However, although this strategy came to be largely associated with the invasion of Iraq, and the belief that a benign domino effect would spread throughout the region, there was far more nuance to the policy President Obama inherited. President George W. Bush’s democracy promotion legacy is one of institutional construction within the US foreign policy bureaucracy, creating the Middle East Partnership Initiative (MEPI), the Middle East Free Trade Area (MEFTA), and the Broader Middle East and North Africa initiative (BMENA). Furthermore, it was President Bush who codified his democracy promotion strategy in National Security Presidential Directive 58, entitled Institutionalising the Freedom Agenda, and who signed the ADVANCE Democracy Act of 2007 into law.1 By the time that President Bush left office hundreds of millions of dollars had been spent on promoting democracy in the MENA, and the US had declared with the force of law that it would prioritise, along with other foreign policy goals, the promotion of democracy and human rights around the world

Jeans Instability in Superfluids

We analyze the effect of a gravitational field on the sound modes of superfluids. We derive an instability condition that generalizes the well known Jeans instability of the sound mode in normal fluids. We discuss potential experimental implications.Comment: 9 pages, Late

A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation

The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.Comment: 23 pages, 1 appendi

Supergravity and D-branes Wrapping Supersymmetric 3-Cycles

We construct dual supergravity descriptions of D3-branes wrapping associative 3-cycles $L$. We analyse the conditions for having five-dimensional background solutions of the form $AdS_2 \times L$ and show that they require $L$ to be of constant negative curvature type. This provides $AdS_2$ background solutions when $L$ is the hyperbolic space $H^3$ or its quotients by subgroups of its isometry group. We construct a regular numerical solution interpolating between $AdS_5$ in the UV and $AdS_2 \times H^3$ in the IR. The IR fixed point exists at the ``intersection'' of the Coulomb and Higgs branches. We analyse the singular supergravity solutions which correspond to moving into the Higgs and the Coulomb branches. For negative constant curvature spaces the singularity is of a ``good'' type in the Higgs branch and of a ``bad'' type in the Coulomb branch. For positive constant curvature spaces such as $S^3$ the singularity is of a ``bad'' type in both the Higgs and the Coulomb branches. We discuss the meaning of these results.Comment: 30 pages, 9 figures, Latex; interpretation of the supergravity solutions corrected, other results and ref. adde

Consistent Bargaining

This short paper demonstrates that the equilibrium payoffs of an alternating-offers bargaining game over a unit of surplus converge to equal division provided that the parties are allowed to bargain over all the surpluses generated by the "right" to be the first to make offers. The result obtained in the present paper may provide some "justification" for other division procedures such as the divide-and-choose or the moving-knife mechanisms.Bargaining theory, Alternating offers, First-mover advantage, Equal division.

Small Instantons and Weak Scale String Theory

We consider heterotic string compactifications to four dimensions when instantons shrink to zero size. If the standard model gauge group originates from the new gauge symmetry associated with the small instantons singularity, then the weakly or strongly coupled heterotic string scales can be taken to be arbitrarily low. The SO(32) and E_8\times E_8 gauge groups can then be very weakly coupled even at the string scale and behave as non-abelian global symmetries. We comment on a possible role of small instantons in supersymmetry breaking.Comment: 9 pages, Late