Comments on D-Instantons in c<1 Strings

We suggest that the boundary cosmological constant \zeta in c<1 unitary string theory be regarded as the one-dimensional complex coordinate of the target space on which the boundaries of world-sheets can live. From this viewpoint we explicitly construct analogues of D-instantons which satisfy Polchinski's ``combinatorics of boundaries.'' We further show that our operator formalism developed in the preceding articles is powerful in evaluating D-instanton effects, and also demonstrate for simple cases that these effects exactly coincide with the stringy nonperturbative effects found in the exact solutions of string equations.Comment: 12 pages with 1 figure, LaTex, Version to appear in PL

Electron Cloud Observations and Predictions at KEKB, PEP-II and SuperB Factories

Electron cloud observations at B factories, i.e. KEKB and PEP-II, are reviewed. Predictions of electron cloud effects at Super B factories, i.e. SuperB and Super KEKB, are also reviewed.Comment: 4 pages, contribution to the Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects: ECLOUD'12; 5-9 Jun 2012, La Biodola, Isola d'Elba, Ital

Effective non-vanishing of global sections of multiple adjoint bundles for polarized 3-folds

Let $X$ be a smooth complex projective variety of dimension three and let $L$ be an ample line bundle on $X$. In this paper, we provide a lower bound of the dimension of the global sections of $m(K_{X}+L)$ under the assumption that $\kappa(K_{X}+L)$ is non-negative. In particular, we get the following: (1) if $\kappa(K_{X}+L)$ is greater than or equal to zero and less than or equal to two, then $h^{0}(K_{X}+L)$ is positive. (2) If $\kappa(K_{X}+L)$ is equal to three, then $h^{0}(2(K_{X}+L))$ is greater than or equal to three. Moreover we get a classification of $(X,L)$ such that $\kappa(K_{X}+L)$ is equal to three and $h^{0}(2(K_{X}+L))$ is equal to three or four.Comment: 25 page

Holographic Renormalization Group Structure in Higher-Derivative Gravity

Classical higher-derivative gravity is investigated in the context of the holographic renormalization group (RG). We parametrize the Euclidean time such that one step of time evolution in (d+1)-dimensional bulk gravity can be directly interpreted as that of block spin transformation of the d-dimensional boundary field theory. This parametrization simplifies the analysis of the holographic RG structure in gravity systems, and conformal fixed points are always described by AdS geometry. We find that higher-derivative gravity generically induces extra degrees of freedom which acquire huge mass around stable fixed points and thus are coupled to highly irrelevant operators at the boundary. In the particular case of pure R^2-gravity, we show that some region of the coefficients of curvature-squared terms allows us to have two fixed points (one is multicritical) which are connected by a kink solution. We further extend our analysis to Minkowski time to investigate a model of expanding universe described by the action with curvature-squared terms and positive cosmological constant, and show that, in any dimensionality but four, one can have a classical solution which describes time evolution from a de Sitter geometry to another de Sitter geometry, along which the Hubble parameter changes drastically.Comment: 26 pages, 6 figures, typos correcte

Gradient flow and the renormalization group

We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for scalar field theory that determines the evolution of the action, and argue that the equation can be regarded as a RG equation if one makes a field-variable transformation at every step such that the kinetic term is kept to take the canonical form. We consider a local potential approximation (LPA) to our equation, and show that the result has a natural interpretation with Feynman diagrams. We make an $\varepsilon$ expansion of the LPA and show that it reproduces the eigenvalues of the linearized RG transformation around both the Gaussian and the Wilson-Fisher fixed points to the order of $\varepsilon$.Comment: 11 pages, 1 figure; v2, v3: typos corrected, some discussions improve