Differential operators for superconformal correlation functions

We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible $\mathcal{N} = 1$ multiplets and some cases of interest for $\mathcal{N} = 2$. As an application of the formalism we prove that certain $\mathcal{N} = 2$ spinning chiral operators (also known as "exotic" chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of three-point functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace.Comment: Fixed typos in Table 2 and Figure

Thermal CFTs in momentum space

We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanishes when the conformal dimension and spin are those of a "double twist" operator $\Delta = 2\Delta_\phi + \ell + 2n$. By analytically continuing to Lorentzian signature we show that the spectral density at high spatial momenta has support on the spectrum condition $|\omega| > |k|$. This leads to a series of sum rules. Finally, we explicitly match the thermal block expansion with the momentum space Green's function at finite temperature in several examples.Comment: Added 1 note and 1 referenc

Neutron electric dipole moment from gauge/string duality

We compute the electric dipole moment of nucleons in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f=2$ degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological $\theta$ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result - a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be $d_n = 1.8 \cdot 10^{-16}\, \theta\;e\cdot \mathrm{cm}$. The electric dipole moment of the proton is exactly the opposite.Comment: Latex, 4 pages; v2: minor corrections, few comments adde

Rebooting quarter-BPS operators in N=4\mathcal{N}=4 Super Yang-Mills

We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of embedding space tensor structures in four dimensions to the problem of computing R-symmetry tensor structures and we use the underlying chiral algebra to obtain the superconformal Ward identities. This allows us to fix the protected part of the four-point correlators, up to few ambiguities. As applications, we use the Lorentzian inversion formula to study the leading order OPE data in the large~$N$ supergravity limit and we make contact with the OPE limit of the five-point function of half-BPS operators.Comment: 65 page

Holographic computation of the Neutron Electric Dipole Moment

The final aim of the thesis is the computation of the Neutron electric dipole moment in the theory of Quantum Chromodynamics. This quantity is easily accessible experimentally and it is P and T violating, so the physical interest consists in the possibility of investigating an eventual P, T violation in QCD. The computation will be performed in the framework of AdS/CFT correspondence, in particular we use the Sakai–Sugimoto model, in which some deformation are added in order to include masses to quarks and a non zero theta parameter. The baryons in this model correspond to instantons in a Yang-Mills - Chern-Simons theory, in analogy with the Skyrme model where they correspond to Skyrmions. Standard quantum mechanic techniques allow us to quantize these solution and to study their properties, such as the electric dipole moment. The work will be organized as follows: first of all we make an introduction to the AdS/CFT cor- respondence, the basic tools of String theory, AdS geometry and D-branes are briefly summarized and then combined to formulate the correspondence, along with a simple example. After this we discuss some important non perturbative aspects of QCD, among them the topological properties, instantons and large N expansion. Then we focus on the Witten's background for QCD, obtained from a supersymmetry breaking compactification in Type II A Supergravity, this is interpreted as a dual of Yang-Mills at low energies. Then the Sakai-Sugimoto model is introduced, which is a setting of D8 branes in the Witten's background, this allows us to describe massless quarks. We then move to the necessary deformations needed to pursue our final computation. Masses to quarks are introduced via a non local term, they are necessary to have a non trivial theta dependence because the U(1)A anomaly has naturally an holographic counterpart. The theta parameter is simply related to a background value of the RR 1 form, which, when the masses are present, can be absorbed in the abelian gauge field. Then follows a review of the instantonic solution of this model, its moduli space and the quantization. This solution is the holographic dual of a baryon, we compute in addition the correction to the baryon mass in presence of a theta parameter. The last part is the actual computation of the electric dipole moment of the neutron, some previous results obtained with different methods are shown. First of all we solve the Yang-Mills - Chern-Simons equations of motion on the D8 branes in presence of the mass perturbation, then we quantize the solution via standard methods and extract the Neutron Electric Dipole moment, to first order in the quark masses and in the theta parameter, in the case of two degenerate flavours. The idea of the computation is inspired to the Skyrme model's counterpart

Spinning correlators in N=2\mathcal{N} = 2 SCFTs: Superspace and AdS amplitudes

We study four-point functions of spinning operators in the flavor current multiplet in four dimensional $\mathcal{N}=2$ SCFTs, using superspace techniques. In particular we explicitly construct the differential operators relating the different components of the super-correlator. As a byproduct of our analysis, we report the computation of the four-point amplitudes of gluons in bosonic Yang-Mills theories on $\mathrm{AdS}_5$ and we give evidence of an AdS double copy relation between the gluon amplitude and its gravitational counterpart.Comment: 54 page

Theta dependence in holographic QCD

We study the effects of the CP-breaking topological $\theta$-term in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f$ degenerate light flavors. We first compute the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, finding agreement with expectations from the QCD chiral effective action. Then, focusing on the $N_f=2$ case, we consider the baryonic sector and determine, to leading order in the small $\theta$ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive ${\cal O}(\theta)$ corrections, this is not the case for observables like the electromagnetic form factor of the nucleons. In particular, it exhibits a dipole term, which turns out to be vector-meson dominated. The resulting neutron electric dipole moment, which is exactly the opposite as that of the proton, is of the same order of magnitude of previous estimates in the literature. Finally, we compute the CP-violating pion-nucleon coupling constant ${\bar g}_{\pi N N}$, finding that it is zero to leading order in the large $N_c$ limit.Comment: Latex, 61 pages, 5 figures; v2: Section 8.5 with a novel analysis of the electric dipole form factor has been added; further comments and references added; typos correcte

AN EXCEPTIONAL REPTILE FIND IN THE NORIAN (LATE TRIASSIC) LAGERSTÄTTEN OF ENDENNA (ZOGNO, BERGAMO, ITALY)

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Fire salamander (Salamandra salamandra) males’ activity during breeding season: effects of microhabitat features and body size

After metamorphosis, fire salamander is considered fully terrestrial, usually inhabiting wooded areas around aquatic habitats. It is often reported that only females go back to water for laying the larvae. The aim of this study is to assess if sites where males are active during the breeding seasons have specific features among microhabitat determinants and distance from the breeding sites. In the autumns of 2013 and 2014, we surveyed 26 transects and 72 plots around six isolated breeding sites in North-Western Italy. During rainy nights, we recorded males position and distance from breeding pools, while during daytime we characterized the environmental features of the plots. Males detection probability was relatively high (mean ± SE: 81.0 ± 4.3%). Several males (15% of the observations) were encountered inside breeding pools where females were laying larvae. Males occurrence was positively related to plots closer to breeding pools and higher leaf litter depth. Larger males were found closer to the breeding pools. This case study shows that the distribution of fire salamander males during the breeding season depends on the breeding sites.