Critical Sp( N ) models in 6 − ϵ dimensions and higher spin dS/CFT

Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an Sp( N ) invariant theory of N anti-commuting scalars and one commuting scalar, which has cubic interactions and is renormalizable in 6 dimensions. For any even N we find an IR stable fixed point in 6 − ϵ dimensions at imaginary values of coupling constants. Using calculations up to three loop order, we develop ϵ expansions for several operator dimensions and for the sphere free energy F . The conjectured F -theorem is obeyed in spite of the non-unitarity of the theory. The 1 /N expansion in the Sp( N ) theory is related to that in the corresponding O( N ) symmetric theory by the change of sign of N . Our results point to the existence of interacting non-unitary 5-dimensional CFTs with Sp( N ) symmetry, where operator dimensions are real. We conjecture that these CFTs are dual to the minimal higher spin theory in 6-dimensional de Sitter space with Neumann future boundary conditions on the scalar field. For N = 2 we show that the IR fixed point possesses an enhanced global symmetry given by the super-group OSp(1|2). This suggests the existence of OSp(1|2) symmetric CFTs in dimensions smaller than 6. We show that the 6 − ϵ expansions of the scaling dimensions and sphere free energy in our OSp(1|2) model are the same as in the q → 0 limit of the q -state Potts model

Virasoro conformal blocks in closed form

Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide two new closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary operator dimensions and central charge c . We do so by solving known recursion relations. One representation is a sum over hypergeometric global blocks, whose coefficients we provide at arbitrary level. The other is a sum over semiclassical Virasoro blocks obtained in the limit in which two external operator dimensions scale linearly with large c . In both cases, the 1/ c expansion of the Virasoro blocks is easily extracted. We discuss applications of these expansions to entanglement and thermality in conformal field theories and particle scattering in three-dimensional quantum gravity

Universality in the geometric dependence of Rényi entropy

We derive several new results for Rényi entropy, S n , across generic entangling surfaces. We establish a perturbative expansion of the Rényi entropy, valid in generic quantum field theories, in deformations of a given density matrix. When applied to even-dimensional conformal field theories, these results lead to new constraints on the n -dependence, independent of any perturbative expansion. In 4d CFTs, we show that the n -dependence of the universal part of the ground state Rényi entropy for entangling surfaces with vanishing extrinsic curvature contribution is in fact fully determined by the Rényi entropy across a sphere in flat space. Using holography, we thus provide the first computations of Rényi entropy across non-spherical entangling surfaces in strongly coupled 4d CFTs. Furthermore, we address the possibility that in a wide class of 4d CFTs, the flat space spherical Rényi entropy also fixes the n -dependence of the extrinsic curvature contribution, and hence that of arbitrary entangling surfaces. Our results have intriguing implications for the structure of generic modular Hamiltonians

An axial gauge ansatz for higher spin theories

We present an ansatz which makes the equations of motion more tractable for the simplest of Vasiliev’s four-dimensional higher spin theories. The ansatz is similar to axial gauge in electromagnetism. We present a broad class of solutions in the gauge where the spatial connection vanishes, and we discuss the lift of one of these solutions to a full spacetime solution via a gauge transformation

Strings, vortex rings, and modes of instability

We treat string propagation and interaction in the presence of a background Neveu–Schwarz three-form field strength, suitable for describing vortex rings in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits instabilities which have been recognized for many years, but whose precise boundaries we determine for the first time analytically in the small core limit. Two circular vortices colliding head-on exhibit stronger instabilities which cause splitting into many small vortices at late times. We provide an approximate analytic treatment of these instabilities and show that the most unstable wavelength is parametrically larger than a dynamically generated length scale which in many hydrodynamic systems is close to the cutoff. We also summarize how the string construction we discuss can be derived from the Gross–Pitaevskii Lagrangian, and also how it compares to the action for giant gravitons

Interpolating between a and F

We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F ˜ $$\tilde{F}$$ =sin( πd/ 2) log Z , where Z is the path integral of the Euclidean CFT on the d -dimensional round sphere. F ˜ $$\tilde{F}$$ smoothly interpolates between (−1) d /2 π/ 2 times the a -anomaly coefficient in even d , and (−1) ( d +1)/2 times the sphere free energy F in odd d . We calculate F ˜ $$\tilde{F}$$ in various examples of unitary CFT that can be continued to non-integer dimensions, including free theories, double-trace deformations at large N , and perturbative fixed points in the ϵ expansion. For all these examples F ˜ $$\tilde{F}$$ is positive, and it decreases under RG flow. Using perturbation theory in the coupling, we calculate F ˜ $$\tilde{F}$$ in the Wilson-Fisher fixed point of the O ( N ) vector model in d = 4 − ϵ to order ϵ 4 . We use this result to estimate the value of F in the 3-dimensional Ising model, and find that it is only a few percent below F of the free conformally coupled scalar field. We use similar methods to estimate the F values for the U( N ) Gross-Neveu model in d = 3 and the O ( N ) model in d = 5. Finally, we carry out the dimensional continuation of interacting theories with 4 supercharges, for which we suggest that F ˜ $$\tilde{F}$$ may be calculated exactly using an appropriate version of localization on S d . Our approach provides an interpolation between the a -maximization in d = 4 and the F -maximization in d = 3

Inflationary consistency conditions from a wavefunctional perspective

It is shown that the squeezed limit of inflationary expectation values follows from reparametrization invariance of the wavefunction of the universe. This translates into a constraint on the longitudinal modes of functional derivatives of the wavefunction. Thus, the local non-Gaussianity induced by single field inflation is purely a gauge artifact. We focus on Einstein gravity in de Sitter space and single field inflation, although the formalism only relies on the diffeomorphism invariance of the theory, and thus applies to any theory of gravity

Aspects of the Papadodimas-Raju proposal for the black hole interior

In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1 /N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the “state-dependence” of the proposal with more familiar phenomena, arguing that, unlike in quantum mechanics, the measurement process (including the apparatus) in something like the PR proposal or its earlier manifestations cannot be described by unitary evolution. These issues render the proposal somewhat ambiguous, and it seems new ideas would be needed to make some version of it work. I close with some brief speculation on to what extent quantum mechanics should hold for the experience of an infalling observer

The Capture Solenoid as an Emittance-Reducing Element

Pions are produced at small/zero radius in a thin target, � Their initial emittance is nearly zero! When the pions decay to muons their transverse momentum changes by � 30 Mev/c, � Some increase in transverse emittance, particularly if the pions are well off axis when they decay. But, the major issue is that the RMS emittance = size of phase-space ellipsoid that contains the pions, is large compared to the “true ” emittance. We make a great effort to reduce the RMS emittance by “ionization cooling”. In principle, other methods than ionization cooling can be used to shrink the apparent, RMS emittance to a value closer to the true, small emittance. Such methods can be nondissipative. In particular, magnetic fields alone can be used to decrease the apparent, RMS emittance (although this will not decrease the small, true emittance). The production of pions in a strong magnetic field that later “tapers ” down to � 2 T in the decay and cooling channels can and does serve to reduce the apparent emittance. However, the Collaboration has not made a systematic effort to optimize this process. K. McDonald NFMCC Collaboration Meeting Jan 14, 2010 2The Adiabatic Invariant of a Helical Orbit If a particle is produced with transverse momentum

DECENTRALIZATION Towards a Predictive Theory of

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