Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding

Certain topological invariants of the moduli space of gravitational instantons are defined and studied. Several amplitudes of two and four dimensional topological gravity are computed. A notion of puncture in four dimensions, that is particularly meaningful in the class of Weyl instantons, is introduced. The topological embedding, a theoretical framework for constructing physical amplitudes that are well-defined order by order in perturbation theory around instantons, is explicitly applied to the computation of the correlation functions of Dirac fermions in a punctured gravitational background, as well as to the most general QED and QCD amplitude. Various alternatives are worked out, discussed and compared. The quantum background affects the propagation by generating a certain effective ``quantum'' metric. The topological embedding could represent a new chapter of quantum field theory.Comment: LaTeX, 18 pages, no figur

Near-IR Transmission Spectrum of HAT-P-32b using HST/WFC3

We report here the analysis of the near-infrared transit spectrum of the hot Jupiter HAT-P-32b, which was recorded with the Wide Field Camera 3 (WFC3) on board the Hubble Space Telescope. HAT-P-32b is one of the most inflated exoplanets discovered, making it an excellent candidate for transit spectroscopic measurements. To obtain the transit spectrum, we have adopted different analysis methods, both parametric and non-parametric (Independent Component Analysis, ICA), and compared the results. The final spectra are all consistent within 0.5σ. The uncertainties obtained with ICA are larger than those obtained with the parametric method by a factor of ∼1.6–1.8. This difference is the tradeoff for higher objectivity due to the lack of any assumption about the instrument systematics compared to the parametric approach. The ICA error bars are therefore worst-case estimates. To interpret the spectrum of HAT-P-32b we used -REx, our fully Bayesian spectral retrieval code. As for other hot Jupiters, the results are consistent with the presence of water vapor (log H O 3.45 2 1.65 1.83 = - - + ), clouds (top pressure between 5.16 and 1.73 bar). Spectroscopic data over a broader wavelength range are needed to de-correlate the mixing ratio of water vapor from clouds and identify other possible molecular species in the atmosphere of HAT-P-32b

Covariant Pauli-Villars Regularization of Quantum Gravity at the One Loop Order

We study a regularization of the Pauli-Villars kind of the one loop gravitational divergences in any dimension. The Pauli-Villars fields are massive particles coupled to gravity in a covariant and nonminimal way, namely one real tensor and one complex vector. The gauge is fixed by means of the unusual gauge-fixing that gives the same effective action as in the context of the background field method. Indeed, with the background field method it is simple to see that the regularization effectively works. On the other hand, we show that in the usual formalism (non background) the regularization cannot work with each gauge-fixing.In particular, it does not work with the usual one. Moreover, we show that, under a suitable choice of the Pauli-Villars coefficients, the terms divergent in the Pauli-Villars masses can be corrected by the Pauli-Villars fields themselves. In dimension four, there is no need to add counterterms quadratic in the curvature tensor to the Einstein action (which would be equivalent to the introduction of new coupling constants). The technique also works when matter is coupled to gravity. We discuss the possible consequences of this approach, in particular the renormalization of Newton's coupling constant and the appearance of two parameters in the effective action, that seem to have physical implications.Comment: 26 pages, LaTeX, SISSA/ISAS 73/93/E

More on the Subtraction Algorithm

We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on redefinitions $\delta\lambda$ of the parameters $\lambda$ of the classical Lagrangian and canonical transformations, by generalizing a well- known conjecture on the form of the divergent terms. We also show that it is possible to reach a complete control on the effects of the subtraction algorithm on the space ${\cal M}_{gf}$ of the gauge-fixing parameters. A principal fiber bundle ${\cal E}\rightarrow {\cal M}_{gf}$ with a connection $\omega_1$ is defined, such that the canonical transformations are gauge transformations for $\omega_1$. This provides an intuitive geometrical description of the fact the on shell physical amplitudes cannot depend on ${\cal M}_{gf}$. A geometrical description of the effect of the subtraction algorithm on the space ${\cal M}_{ph}$ of the physical parameters $\lambda$ is also proposed. At the end, the full subtraction algorithm can be described as a series of diffeomorphisms on ${\cal M}_{ph}$, orthogonal to ${\cal M}_{gf}$ (under which the action transforms as a scalar), and gauge transformations on ${\cal E}$. In this geometrical context, a suitable concept of predictivity is formulated. We give some examples of (unphysical) toy models that satisfy this requirement, though being neither power counting renormalizable, nor finite.Comment: LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/E

A population study of gaseous exoplanets

We present here the analysis of 30 gaseous extrasolar planets, with temperatures between 600 and 2400 K and radii between 0.35 and 1.9 $R_\mathrm{Jup}$. The quality of the HST/WFC3 spatially scanned data combined with our specialized analysis tools allow us to study the largest and most self-consistent sample of exoplanetary transmission spectra to date and examine the collective behavior of warm and hot gaseous planets rather than isolated case-studies. We define a new metric, the Atmospheric Detectability Index (ADI) to evaluate the statistical significance of an atmospheric detection and find statistically significant atmospheres around 16 planets out of the 30 analysed. For most of the Jupiters in our sample, we find the detectability of their atmospheres to be dependent on the planetary radius but not on the planetary mass. This indicates that planetary gravity plays a secondary role in the state of gaseous planetary atmospheres. We detect the presence of water vapour in all of the statistically detectable atmospheres, and we cannot rule out its presence in the atmospheres of the others. In addition, TiO and/or VO signatures are detected with 4$\sigma$ confidence in WASP-76 b, and they are most likely present in WASP-121 b. We find no correlation between expected signal-to-noise and atmospheric detectability for most targets. This has important implications for future large-scale surveys.Comment: 14 pages, 12 figures, 3 tables, published in A

Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.Comment: 19 pages. Introductory paragraph, misprint corrected and updated references. CQG in pres

On field theory quantization around instantons

With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical minima (instantons, for example), the physical implications are discussed in a ``theoretical'' framework, the ideas are collected in a simple logical scheme and the topological version of the Ginzburg-Landau theory of superconductivity is solved in the intermediate situation between type I and type II superconductors.Comment: 27 pages, 5 figures, LaTe

Deformed dimensional regularization for odd (and even) dimensional theories

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves to be efficient in practical computations. This technique is particularly convenient in three dimensions for Chern-Simons gauge fields, two-component fermions and four-fermion models in the large N limit, eventually coupled with quantum gravity. Differently from even dimensions, in odd dimensions it is not always possible to have propagators with fully Lorentz invariant denominators. The main features of the deformed technique are illustrated in a set of sample calculations. The regularization is universal, local, manifestly gauge-invariant and Lorentz invariant in the physical sector of spacetime. In flat space power-like divergences are set to zero by default. Infinitely many evanescent operators are automatically dropped.Comment: 27 pages, 3 figures; v2: expanded presentation of some arguments, IJMP

Topological field theory and physics

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin $SU(2)$ instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind of matter (hyperinstantons). The physical relevance of topological field theory and its invariants is discovered. By embedding topological Yang-Mills theory into pure Yang-Mills theory, it is shown that the topological version TQFT of a quantum field theory QFT allows us to formulate consistently the perturbative expansion of QFT in the topologically nontrivial sectors. In particular, TQFT classifies the set of good measures over the instanton moduli space and solves the inconsistency problems of the previous approaches. The qualitatively new physical implications are pointed out. Link numbers in QCD are related to a non abelian analogoue of the Aharonov-Bohm effect.Comment: 23 pages, 1 figure. Revision: additional explanation

Inequalities for trace anomalies, length of the RG flow, distance between the fixed points and irreversibility

I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: i) the scheme-invariant area Delta(a') of the graph of the effective beta function between the fixed points defines the length of the RG flow; ii) the minimum of Delta(a') in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points; iii) in even dimensions, the distance between the fixed points is equal to Delta(a)=a_UV-a_IR. In even dimensions, these statements imply the inequalities 0 =< Delta(a)=< Delta(a') and therefore the irreversibility of the RG flow. Another consequence is the inequality a =< c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain "oriented-triangle inequalities", imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is irreversible also in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d=3 theories where the RG flow is integrable at each order of the large N expansion.Comment: 24 pages, 3 figures; expanded intro, improved presentation, references added - CQ