Universal properties of the U(1) current at deconfined quantum critical points: comparison with predictions from gauge/gravity duality

The deconfined quantum critical point of a two-dimensional SU(N) antiferromagnet is governed by an Abelian Higgs model in $d=2+1$ spacetime dimensions featuring $N$ complex scalar fields. In this context, we derive for $2\leq d\leq 4$ an exact formula for the central charge of the U(1) current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for $d=2+1$. In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for the charge susceptibility in the large $N$ limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in absence of supersymmetry.Comment: 4.5 pages, 1 figure; v2: accepted in PRD, text restructured to make presentation/discussion clearer, references adde

Hedging Options with Scale-Invariant Models

A price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of contingent claims are model-free. Since options on traded assets are normally priced using some form of scale-invariant process, e.g. a stochastic volatility, jump diffusion or Lévy process, this result has important implications for the hedging literature. However, standard price hedge ratios are not always the optimal hedge ratios to use in a delta or delta-gamma hedge strategy; in fact we recommend the use of minimum variance hedge ratios for scale-invariant models. Our theoretical results are supported by an empirical study that compares the hedging performance of various smile-consistent scale-invariant and non-scale-invariant models. We find no significant difference between the minimum variance hedges in the smile-consistent models but a significant improvement upon the standard, model-free hedge ratiosScale invariance, hedging, minimum variance, hedging, stochastic volatility

Transition amplitude, partition function and the role of physical degrees of freedom in gauge theories

This work explores the quantum dynamics of the interaction between scalar (matter) and vectorial (intermediate) particles and studies their thermodynamic equilibrium in the grand-canonical ensemble. The aim of the article is to clarify the connection between the physical degrees of freedom of a theory in both the quantization process and the description of the thermodynamic equilibrium, in which we see an intimate connection between physical degrees of freedom, Gibbs free energy and the equipartition theorem. We have split the work into two sections. First, we analyze the quantum interaction in the context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics (GSDKP) by using the functional formalism. We build the Hamiltonian structure following the Dirac methodology, apply the Faddeev-Senjanovic procedure to obtain the transition amplitude in the generalized Coulomb gauge and, finally, use the Faddeev-Popov-DeWitt method to write the amplitude in covariant form in the no-mixing gauge. Subsequently, we exclusively use the Matsubara-Fradkin (MF) formalism in order to describe fields in thermodynamical equilibrium. The corresponding equations in thermodynamic equilibrium for the scalar, vectorial and ghost sectors are explicitly constructed from which the extraction of the partition function is straightforward. It is in the construction of the vectorial sector that the emergence and importance of the ghost fields are revealed: they eliminate the extra non-physical degrees of freedom of the vectorial sector thus maintaining the physical degrees of freedom

Use of dialkyldithiocarbamato complexes of bismuth(III) for the preparation of nano- and microsized Bi2S3 particles and the X-ray crystal structures of [Bi{S2CN(CH3)(C6H13)}(3)] and [Bi{S2CN(CH3)(C6H13)}(3)(C12H8N2)]

A range of bismuth(III) dithiocarbamato complexes were prepared and characterized. The X-ray crystal structures of the compounds [Bi{S2CN(CH3)(C6H13)}3] (1) and [Bi{S2CN(CH3)- (C6H13)}3(C12H8N2)] (2) are reported. The preparation of Bi2S3 particulates using a wet chemical method and involving the thermalysis of Bi(III) dialkyldithiocarbamato complexes is described. The influence of several experimental parameters on the optical and morphological properties of the Bi2S3 powders was investigated. Nanosized Bi2S3 colloids were obtained having long-term stability and showing a blue shift on the optical band edge; the presence of particles exhibiting quantum size effects is discussed. Morphological welldefined Bi2S3 particles were obtained in which the fiber-type morphology is prevalent.FCT - POCTI/1999/CTM/ 3545