Lagrangian space consistency relation for large scale structure

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.Comment: 19 pages, no figure

Effective string theory for vortex lines in fluids and superfluids

We discuss the effective string theory of vortex lines in ordinary fluids and low-temperature superfluids, by describing the bulk fluid flow in terms of a two-form field to which vortex lines can couple. We derive the most general low-energy effective Lagrangian that is compatible with (spontaneously broken) Poincare invariance and worldsheet reparameterization invariance. This generalizes the effective action developed by Lund and Regge and by Endlich and Nicolis. By applying standard field-theoretical techniques, we show that certain low-energy coupling constants -- most notably the string tension -- exhibit RG running already at the classical level. We discuss applications of our techniques to the study of Kelvin waves, vortex rings, and the coupling to bulk sound modes.Comment: 62 pages, 6 figure

Perturbations of vortex ring pairs

We study pairs of co-axial vortex rings starting from the action for a classical bosonic string in a three-form background. We complete earlier work on the phase diagram of classical orbits by explicitly considering the case where the circulations of the two vortex rings are equal and opposite. We then go on to study perturbations, focusing on cases where the relevant four-dimensional transfer matrix splits into two-dimensional blocks. When the circulations of the rings have the same sign, instabilities are mostly limited to wavelengths smaller than a dynamically generated length scale at which single-ring instabilities occur. When the circulations have the opposite sign, larger wavelength instabilities can occur.Comment: 62 pages, 21 figure

Moduli Stabilization and the Holographic RG for AdS and dS

We relate moduli stabilization ($V'=0$) in the bulk of $AdS_D$ or $dS_D$ to basic properties of the Wilsonian effective action in the holographic dual theory on $dS_{D-1}$: the single-trace terms in the action have vanishing beta functions, and higher-trace couplings are determined purely from lower-trace ones. In the de Sitter case, this encodes the maximal symmetry of the bulk spacetime in a quantity which is accessible within an observer patch. Along the way, we clarify the role of counterterms, constraints, and operator redundancy in the Wilsonian holographic RG prescription, reproducing the expected behavior of the trace of the stress-energy tensor in the dual for both $AdS_D$ and $dS_D$. We further show that metastability of the gravity-side potential energy corresponds to a nonperturbatively small imaginary contribution to the Wilsonian action of pure de Sitter, a result consistent with the need for additional degrees of freedom in the holographic description of its ultimate decay.Comment: 28 pages; v2: minor modifications, published version in JHE

Exploring eternal stability with the simple harmonic universe

We construct nonsingular cyclic cosmologies that respect the null energy condition, have a large hierarchy between the minimum and maximum size of the universe, and are stable under linearized fluctuations. The models are supported by a combination of positive curvature, a negative cosmological constant, cosmic strings and matter that at the homogeneous level behaves as a perfect fluid with equation of state -1 < w < -1/3. We investigate analytically the stability of the perturbation equations and discuss the role of parametric resonances and nonlinear corrections. Finally, we argue that Casimir energy contributions associated to the compact spatial slices can become important at short scales and lift nonperturbative decays towards vanishing size. This class of models (particularly in the static limit) can then provide a useful framework for studying the question of the ultimate (meta)stability of an eternal universe.Comment: 22 pages, 2 figure