Photodissociation of alkyl iodides in solution: Substituent effects on the early-time dynamics

Resonance Raman spectra, including absolute scattering cross sections, have been measured for ethyl, isopropyl, and tert-butyl iodides in cyclohexane solution at seven to ten wavelengths between 303 and 200 nm. Spectra of fully deuterated ethyl iodide have also been obtained at five wavelengths. Spectra excited in the 300-250 nm region, on resonance with the directly dissociative A state, are dominated by long overtone progressions in the nominal C-I stretching mode near 500 cm-1. In all three molecules the fundamental of the C-I stretch is unexpectedly weak relative to the overtones when excited near the peak of the A band. This is shown to arise from interference between the A-state resonant part of the fundamental Raman amplitude and preresonant contributions from higher electronic states. In addition to the C-I stretching activity, A-state excitation generates significant intensity in fundamentals, overtones, and combination bands of modes nominally assigned as bending and CC stretching vibrations, suggesting a multidimensional character to the reaction coordinate. The absorption spectra and A-state resonant Raman intensities are modeled successfully through wave-packet propagation on a multidimensional locally harmonic potential with a preresonant contribution to the fundamental intensities included. The short-time photodissociation dynamics are then examined by using the normal-mode coefficients to convert the wave-packet motion from dimensionless normal coordinates into internal coordinates. It is found that while the dominant motion during the first 10 fs involves stretching of the C-I bond, other stretching and bending motions are also involved, although the precision of these conclusions for isopropyl and tert-butyl iodides is limited by the indeterminacy in the signs of the normal-mode displacements obtained from the intensity analysis. Comparison of the results for normal and perdeuterated ethyl iodide is used to resolve most of the sign indeterminacies for this molecule. The present results are compared and contrasted to conclusions of previous studies of energy partitioning in the vapor-phase photodissociation. © 1991 American Institute of Physics.published_or_final_versio

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large r go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the Nth order Lovelock {\Lambda}-vacuum solu- tions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.Comment: 19 page

Higher Derivative Corrections to R-charged Black Holes: Boundary Counterterms and the Mass-Charge Relation

We carry out the holographic renormalization of Einstein-Maxwell theory with curvature-squared corrections. In particular, we demonstrate how to construct the generalized Gibbons-Hawking surface term needed to ensure a perturbatively well-defined variational principle. This treatment ensures the absence of ghost degrees of freedom at the linearized perturbative order in the higher-derivative corrections. We use the holographically renormalized action to study the thermodynamics of R-charged black holes with higher derivatives and to investigate their mass to charge ratio in the extremal limit. In five dimensions, there seems to be a connection between the sign of the higher derivative couplings required to satisfy the weak gravity conjecture and that violating the shear viscosity to entropy bound. This is in turn related to possible constraints on the central charges of the dual CFT, in particular to the sign of c-a.Comment: 30 pages. v2: references added, some equations simplifie

From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))

The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for exploring the properties of strongly interacting superconformal Chern-Simons theories in 2+1 dimensions. In this paper, we use this matrix model to study necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge groups in the limit of large N. In its simplest application, the matrix model computes the free energy of the gauge theory on S^3. The conjectured F-theorem states that this quantity should decrease under renormalization group flow. We show that for a simple class of such flows, the F-theorem holds for our necklace theories. We also provide a relationship between matrix model eigenvalue distributions and numbers of chiral operators that we conjecture holds more generally. Through the AdS/CFT correspondence, there is therefore a natural dual geometric interpretation of the matrix model saddle point in terms of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d submanifolds. As a final bonus, our analysis gives us the partition function of the T(U(N)) theory on S^3.Comment: 3 figures, 41 pages; v2 minor improvements, refs adde

Corner contributions to holographic entanglement entropy

The entanglement entropy of three-dimensional conformal field theories contains a universal contribution coming from corners in the entangling surface. We study these contributions in a holographic framework and, in particular, we consider the effects of higher curvature interactions in the bulk gravity theory. We find that for all of our holographic models, the corner contribution is only modified by an overall factor but the functional dependence on the opening angle is not modified by the new gravitational interactions. We also compare the dependence of the corner term on the new gravitational couplings to that for a number of other physical quantities, and we show that the ratio of the corner contribution over the central charge appearing in the two-point function of the stress tensor is a universal function for all of the holographic theories studied here. Comparing this holographic result to the analogous functions for free CFT's, we find fairly good agreement across the full range of the opening angle. However, there is a precise match in the limit where the entangling surface becomes smooth, i.e., the angle approaches $\pi$, and we conjecture the corresponding ratio is a universal constant for all three-dimensional conformal field theories. In this paper, we expand on the holographic calculations in our previous letter arXiv:1505.04804, where this conjecture was first introduced.Comment: 62 pages, 6 figures, 1 table; v2: minor modifications to match published version, typos fixe

On renormalization group flows and the a-theorem in 6d

We study the extension of the approach to the a-theorem of Komargodski and Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton effective action is obtained up to 6th order in derivatives. The anomaly flow a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this action. It then appears at order p^6 in the low energy limit of n-point scattering amplitudes of the dilaton for n > 3. The detailed structure with the correct anomaly coefficient is confirmed by direct calculation in two examples: (i) the case of explicitly broken conformal symmetry is illustrated by the free massive scalar field, and (ii) the case of spontaneously broken conformal symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the latter example, the dilaton is a dynamical field so 4-derivative terms in the action also affect n-point amplitudes at order p^6. The calculation in the (2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4. Given the confirmation in two distinct models, we attempt to use dispersion relations to prove that the anomaly flow is positive in general. Unfortunately the 4-point matrix element of the Euler anomaly is proportional to stu and vanishes for forward scattering. Thus the optical theorem cannot be applied to show positivity. Instead the anomaly flow is given by a dispersion sum rule in which the integrand does not have definite sign. It may be possible to base a proof of the a-theorem on the analyticity and unitarity properties of the 6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure

Light States in Chern-Simons Theory Coupled to Fundamental Matter

Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T^2, we find light states at small `t Hooft coupling \lambda=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \sqrt {\lambda}/N and in the critical scalar theory and the free fermion theory they are of order \lambda/N. The entropy of these states grows like N Log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.Comment: 58 pages, LaTeX, no figures, Minor error corrected, references added, The main results of the paper have not change

The Constraints of Conformal Symmetry on RG Flows

If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new proof of Zamolodchikov's theorem. We then review how this simple observation also leads to a derivation of the a-theorem. We exemplify the general procedure in some interacting theories in four space-time dimensions. We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled by ordinary and conformal perturbation theories, respectively. We compute explicitly the dependence of the path integral on the coupling constants and extract the change in the a-anomaly (this agrees with more conventional computations of the same quantity). We also discuss some general properties of the sum rule found in arXiv:1107.3987 and study it in several examples.Comment: 25 pages, 5 figure

Z-extremization and F-theorem in Chern-Simons matter theories

The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition function localized on a three sphere. Here we verify this statement at weak coupling. We give a detailed analysis for two classes of models. The first one is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter fields, while the second is a flavored version of the ABJ theory, where the CS levels are large but they do not necessarily sum up to zero. We study in both cases superpotential deformations and compute the R charges at different fixed points. When these fixed points are connected by an RG flow we explicitly verify that the free energy decreases at the endpoints of the flow between the fixed points, corroborating the conjecture of an F-theorem in three dimensions.Comment: 28 pages, 3 figures, JHEP.cls, minor corrections, references adde