Abstract:We study the effects of the CP-breaking topological θ-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 θ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive O(θ) 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 constantḡ πN N , finding that it is zero to leading order in the large N c limit.

In this paper, we introduce a novel probabilistic version of retinex. It is based on a probabilistic formalization of the random spray retinex sampling and contributes to the investigation of the spatial properties of the model. Various versions available of the retinex algorithm are characterized by different procedures for exploring the image content (so as to obtain, for each pixel, a reference white value), then used to rescale the pixel lightness. Here we propose an alternative procedure, which computes the reference white value from the percentile values of the pixel population. We formalize two versions of the algorithm: one with global and one with local behavior, characterized by different computational costs.

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $$ \mathcal{N} $$ N = 4 Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large N supergravity predictions and the numerical finite N results already at N∼ 100. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite N, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.

We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible N = 1 multiplets and some cases of interest for N = 2. As an application of the formalism we prove that certain 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 threepoint 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. 23 7. Conclusions25 Appendix A. Details on notation and conventions 26 -1 -Appendix B. Acting on different points 28 Appendix C. Superspace expansion 29 Appendix D. Some identities for the superspace derivatives 30 References 32 In[11]:= chi = Compare[ChiralDp[tOφφb, η2, θ3, x3], variables → Array[C,4]] 20 In the package the derivatives ChiralD represent the derivatives D. When acting on the t use ChiralD instead (D =[esc]scD[esc]). Also note that, when acting on the t, the operators D are sent to D and D to D. See (4.8). 21 In more complicated applications it is better to separate the various orders in θ3 andθ3 and act on each piece only with the operators inside ChiralD (like ∂η∂ θ , ∂η∂xθ etc. . .) that do not give zero when the θ's are suppressed. In the documentation of the package there is a worked out example. 22 See (2.11). 23 This instruction will generate an error but it can be ignored. It can be avoided by replacing the C[i]'s with variables consisting in a single Symbol. It comes up because there is an automatic routine that sets ConstQ to true for the variables in variables, which works only if they are Symbols. This is not an issue because ConstQ[C[i]] is true by default after SUSY3pf is called.