The K-process on a tree as a scaling limit of the GREM-like trap model

We introduce trap models on a finite volume $k$-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters of the trap model, we establish its infinite volume limit, given by what we call a $K$-process in an infinite $k$-level tree. From this we deduce that the $K$-process also is the scaling limit of the GREM-like trap model on extreme time scales under a fine tuning assumption on the volumes.Comment: Published in at http://dx.doi.org/10.1214/13-AAP937 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes

We present a class of 3D Black Holes based on flat connections which are polynomials in the BTZ $hs(\lambda) \times hs(\lambda)$-valued connection. We solve analytically the fluctuation equations of matter in their background and find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary two-point functions. We also relate our results and those arising in other backgrounds discussed recently in the literature on the subject.Comment: v3: typo corrected in first line of Eq (4.2), improved presentatio

Partition Function of N=2N=2 Gauge Theories on a Squashed S4S^4 with SU(2)×U(1)SU(2)\times U(1) Isometry

We study $N=2$ supersymmetric gauge theories on a large family of squashed 4-spheres preserving $SU(2)\times U(1)\subset SO(4)$ isometry and determine the conditions under which this background is supersymmetric. We then compute the partition function of the theories by using localization technique. The results indicate that for $N=2$ SUSY, including both vector-multiplets and hypermultiplets, the partition function is independent of the arbitrary squashing functions as well as of the other supergravity background fields.Comment: version to appear in Nuclear Physics

On Classification of QCD defects via holography

We discuss classification of defects of various codimensions within a holographic model of pure Yang-Mills theories or gauge theories with fundamental matter. We focus on their role below and above the phase transition point as well as their weights in the partition function. The general result is that objects which are stable and heavy in one phase are becoming very light (tensionless) in the other phase. We argue that the $\theta$ dependence of the partition function drastically changes at the phase transition point, and therefore it correlates with stability properties of configurations. Some possible applications for study the QCD vacuum properties above and below phase transition are also discussed.Comment: 21 pages, 2 figure

No Amendment? No Problem: Judges, “Informal Amendment,” and the Evolution of Constitutional Meaning in the Federal Democracies of Australia, Canada, India, and the United States

This article considers the way in which judges play a significant role in developing the meaning of a constitution through the exercise of interpretive choices that have the effect of “informally amending” the text. We demonstrate this by examining four written federal democratic constitutions: those of the United States, the first written federal democratic constitution; India, the federal constitution of the largest democracy on earth; and the constitutions of Canada and Australia, both federal and democratic, but emerging from the English unwritten tradition. We divide our consideration of these constitutions into two ideal types, identified by Bruce Ackerman: the “revolutionary” constitutions of the United States and India, and the “adaptive establishmentarian” constitutions of Canada and Australia. In this way, we show that judicial informal amendment changes constitutional meaning in both revolutionary and adaptive settings. We conclude that whatever the origins of a federal democratic constitution, be it revolutionary or adaptive establishmentarian, and whatever the background of the judges and the text with which they work, in the absence of formal amendment, judges use an image of the constitution to give and to change the meaning of a written text over time. This allows a constitution to adapt to changing social, economic, and political conditions where formal amendment, for whatever reason, proves difficult. But, in some cases, it might also leave a federal democracy with a constitution which the Framers did not intend. Whatever the outcome, though, the judges play a central role in the evolution of constitutional meaning over time, for good or for ill

No Amendment? No Problem: Judges, Informal Amendment, and the Evolution of Constitutional Meaning in the Federal Democracies of Australia, Canada, India, and the United States

This article considers the way in which judges play a significant role in developing the meaning of a constitution through the exercise of interpretive choices that have the effect of “informally amending” the text. We demonstrate this by examining four written federal democratic constitutions: those of the United States, the first written federal democratic constitution; India, the federal constitution of the largest democracy on earth; and the constitutions of Canada and Australia, both federal and democratic, but emerging from the English unwritten tradition. We divide our consideration of these constitutions into two ideal types, identified by Bruce Ackerman: the “revolutionary” constitutions of the United States and India, and the “adaptive establishmentarian” constitutions of Canada and Australia. In this way, we show that judicial informal amendment changes constitutional meaning in both revolutionary and adaptive settings. We conclude that whatever the origins of a federal democratic constitution, be it revolutionary or adaptive establishmentarian, and whatever the background of the judges and the text with which they work, in the absence of formal amendment, judges use an image of the constitution to give and to change the meaning of a written text over time. This allows a constitution to adapt to changing social, economic, and political conditions where formal amendment, for whatever reason, proves difficult. But, in some cases, it might also leave a federal democracy with a constitution which the Framers did not intend. Whatever the outcome, though, the judges play a central role in the evolution of constitutional meaning over time, for good or for ill

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte