Holographic predictions for cosmological 3-point functions

We present the holographic predictions for cosmological 3-point correlators, involving both scalar and tensor modes, for a universe which started in a non-geometric holographic phase. Holographic formulae relate the cosmological 3-point functions to stress tensor correlation functions of a holographically dual three-dimensional non-gravitational QFT. We compute these correlators at 1-loop order for a theory containing massless scalars, fermions and gauge fields, and present an extensive analysis of the constraints due to Ward identities showing that they uniquely determine the correlators up to a few constants. We define shapes for all cosmological bispectra and compare the holographic shapes to the slow-roll ones, finding that some are distinguishable while others, perhaps surprisingly, are not.Comment: 51pp; 4 fig

Exact ground states for the four-electron problem in a Hubbard ladder

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.Comment: 10 pages, 7 figure

Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes

We show how the Hopf algebra structure of multiple polylogarithms can be used to simplify complicated expressions for multi-loop amplitudes in perturbative quantum field theory and we argue that, unlike the recently popularized symbol-based approach, the coproduct incorporates information about the zeta values. We illustrate our approach by rewriting the two-loop helicity amplitudes for a Higgs boson plus three gluons in a simplified and compact form involving only classical polylogarithms.Comment: 46 page

Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.Comment: 20 pages, many figures. Two references added. Published versio

Graviton Vertices and the Mapping of Anomalous Correlators to Momentum Space for a General Conformal Field Theory

We investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$ with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex $TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the $TOO$ or $TVV$ vertex functions respectively, and three independent tensor structures for the $TTT$ vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general $d$ dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$, since vector fields are conformal only in $d=4$. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach [...]Comment: 57 pages, 7 figures. Refs adde

Heavy fermions and two loop electroweak corrections to b→s+γb\rightarrow s+\gamma

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+\gamma$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of $B\rightarrow X_{_s}\gamma$ can reach 5% as the energy scale of new physics $\Lambda_{_{\rm NP}}=200$ GeV.Comment: 30 pages,4 figure

Supersymmetric Higgs Yukawa Couplings to Bottom Quarks at next-to-next-to-leading Order

The effective bottom Yukawa couplings are analyzed for the minimal supersymmetric extension of the Standard Model at two-loop accuracy within SUSY-QCD. They include the resummation of the dominant corrections for large values of tg(beta). In particular the two-loop SUSY-QCD corrections to the leading SUSY-QCD and top-induced SUSY-electroweak contributions are addressed. The residual theoretical uncertainties range at the per-cent level.Comment: 25 pages, 9 figures, added comments and references, typos corrected, results unchanged, published versio

Leptogenesis from loop effects in curved spacetime

We describe a new mechanism -- radiatively-induced gravitational leptogenesis -- for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how the size of the radiative corrections relevant for leptogenesis becomes enhanced by increasing the mass hierarchy of the sterile neutrinos, and show that for realistic phenomenological parameters this mechanism can generate the observed baryon-to-photon ratio of the Universe

NLO QCD bottom corrections to Higgs boson production in the MSSM

We present a calculation of the two-loop bottom-sbottom-gluino contributions to Higgs boson production via gluon fusion in the MSSM. The calculation is based on an asymptotic expansion in the masses of the supersymmetric particles, which are assumed to be much heavier than the bottom quark and the Higgs bosons. We obtain explicit analytic results that allow for a straightforward identification of the dominant contributions in the NLO bottom corrections. We emphasize the interplay between the calculations of the masses and the production cross sections of the Higgs bosons, discussing sensible choices of renormalization scheme for the parameters in the bottom/sbottom sector.Comment: 25 pages, 4 figures. v2: references and two figures added, version published in JHE