F-theory,T-duality on K3 surfaces,and N = 2 supersymmetric gauge theories in four dimensions

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane RR charge and a 0-brane RR charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N = 2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N = 1 duality scenario.     

Sterile neutrinos in lepton number and lepton flavor violating decays

We study the contribution of massive dominantly sterile neutrinos, N, to the lepton number and lepton flavor violating semileptonic decays of τ and B, D, K-mesons. We focus on special domains of sterile neutrino masses mN where it is close to its mass-shell. This leads to an enormous resonant enhancement of the decay rates of these processes. This allows us to derive stringent limits on the sterile neutrino mass mN and its mixing UαN with active flavors. We apply a joint analysis of the existing experimental bounds on the decay rates of the studied processes. In contrast to other approaches in the literature our limits are free from ad hoc assumptions on the relative size of the sterile neutrino mixing parameters. We analyze the impact of this sort of assumptions on the extraction of the limits on mN and UαN, and discuss the effect of finite detector size. Special attention was paid to the limits on meson decays with e^±e^± in final state, derived from non-observation of 0νββ-decay. We point out that observation of these decays may, in particular, shed light on the Majorana phases of the neutrino mixing matrix.     

Comments on mesonic correlators in the worldline formalism

We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-Nc two-dimensional QCD (the ?t Hooft model) and relate it to a single harmonic oscillator. We also discuss the dependence of the Peskin S-parameter on the number of massless flavors and their representation and compare our expression to the corresponding expression obtained at weak coupling. Finally, we use the worldline formalism to discuss how the Veneziano limit of QCD is realized in holography in the limit of small Nf/Nc.     

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.     

Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

Non-backtracking Random Walk

We consider non-backtracking random walk (NBW) in the nearest-neighbor setting on the ? ^d -lattice and on tori. We evaluate the eigensystem of the m×m-dimensional transition matrix of NBW where m denote the degree of the graph. We use its eigensystem to show a functional central limit theorem for NBW on ? ^d and to obtain estimates on the convergence towards the stationary distribution for NBW on the torus.     

The Constituent Chiral Quark Model revisited

We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of SUL(3)×SUR(3) external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the large-Nc limit. We show, however, that the number of the required counterterms depends crucially on the value of gA and it is minimized for gA=1. We then find that with a rather small value for the constituent quark mass, which we fix phenomenologically to MQ=(190±40) MeV, the model reproduces rather well the values of several well-known low-energy constants. We also comment on the limitations of the model as well as on a few exceptional applications, to more complicated low-energy observables, where one can expect the model to make reasonably good predictions.     

Testing the rotational symmetry of theSU(3) potential

We test the static quark-antiquark potential inSU(3) lattice gauge theory, at β=5.8 on a 16⁴ lattice. We find an anisotropy on the level of 3% for small distances,r?3a. We discuss the implications of this effect on the determination of the string tension.     

On the number of solutions for the two-point boundary value problem on Riemannian manifolds

We study the solutions joining two fixed points of a time-independent dynamical system on a Riemannian manifold (M,g) from an enumerative point of view. We prove a finiteness result for solutions joining two points p,q∈M that are non-conjugate in a suitable sense, under the assumption that (M,g) admits a non-trivial convex function. We discuss in some detail the notion of conjugacy induced by a general dynamical system on a Riemannian manifold. Using techniques of infinite dimensional Morse theory on Hilbert manifolds we also prove that, under generic circumstances, the number of solutions joining two fixed points is odd. We present some examples where our theory applies.     

Some Exact Results on Bond Percolation

We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice ?? by ? bonds connecting the same adjacent vertices, thereby yielding the lattice ?? _? . This relation is used to calculate the bond percolation threshold on ?? _? . We show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality d??2 but changes it on a one-dimensional lattice and quasi-one-dimensional infinite-length strips. We also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the N???? limits of several families of N-vertex graphs. Finally, we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as N????.     

Asymptotics of the S-matrix for perturbed Hill operators

We consider the Schrödinger operator with a periodic potential p plus a compactly supported potential q on the real line. We assume that both p and q have m ? 0 derivatives. For generic p, the essential spectrum of the operator has an infinite sequence of open gaps. We determine the asymptotics of the S-matrix at high energy.     

Bounds on supersymmetric flavour violating parameters from B→Xsγ

We investigate the constraints on the flavour violating parameters from the decay B→X_sγ, taking into account the interplay of the various sources of flavour violation in the unconstrained MSSM. We present a systematic leading logarithmic QCD analysis of these model-independent constraints, including contributions from gluinos, neutralinos, charginos, charged Higgs bosons and interferences between them. We show that two simple combinations of elements of the down squark mass matrix are stringently bounded over large parts of the parameter space where only weak assumptions on the hierarchical structure of the squark mass matrices are made. We also briefly analyse up to which values SUSY contributions, compatible with B→X_sγ, can enhance the Wilson coefficient C₈(m_W), which plays an important role in the phenomenology of charmless hadronic B decays.     

Charmonia production in hadron colliders and the extraction of colour-octet matrix elements

We present the results of our analysis on charmonia (J/ψ andψ′) hadroproduction taking into account higher-order QCD effects induced by initial-state radiation in a Monte Carlo framework, with the colour-octet mechanism implemented in the event generation. We find that those colour-octet matrix elements extracted so far from Fermilab Tevatron data for both J/ψ and ψ′ production have to be lowered significantly. We finally make predictions for charmonia production at the LHC, presenting a simple code for a fast simulation with PYTHIA based on the colour-octet model.     

Symmetry breaking in a supersymmetric model of strong and electroweak interactions

We describe a supersymmetric model of strong and electroweak interactions based on the gauge groupSU(3)×SU(2)×U(1)×?(1). We concentrate on the pattern of the spontaneous symmetry breaking by the tree level scalar potential. It is possible to break the?(1) factor at superlarge energies relative to the simultaneous breaking scale ofSU(2)×U(1) and supersymmetry. The model has?(1) anomalies. Attempts to make an anomaly-free model based on the groupE ₆ are described. We also comment on possible modifications of the?(1) anomaly problem due to gravitational effects.     

A Note on Strongly Closed Subspaces in an Inner Product Space

We study some weak states on the orthocomplemented lattice F(S) of all strongly closed subspaces in an inner product space. We show that F(S) always possesses two-valued weak states, and we derive a characterization of (topological) completeness of S in terms of two-valued weak states. We also prove an extension theorem for weak states.     

A q-deformed Lorentz algebra

We derive a q-deformed version of the Lorentz algebra by deforming the algebraSL(2,C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified withSL _q(2,C) generateSU _q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limitq→1 the generators are those of the classical Lorentz algebra plus an additionalU(1). Thus we have a deformation ofSL(2,C)×U(1).     

Solutions of Euler-Lagrange equations for self-interacting field of linear frames on product manifold of group space

We investigate a model of self-interacting field of linear frames on the product manifold M × G, where G is a semisimple Lie group acting freely and transitively on a manifold M. We find two families of solutions of the Euler-Lagrange equations for the field of frames.     

Low-energy analysis of M- and F-theories on Calabi-Yau threefolds

We elucidate the interplay between gauge and supersymmetry anomalies in six-dimensional N = 1 supergravity with generalized couplings between tensor and vector multiplets. We derive the structure of the five-dimensional supergravity resulting from the S₁ reduction of these models and give the constraints on Chem-Simons couplings that follow from duality to M-theory compactified on a Calabi-Yau threefold. The duality is supported only on a restricted class of Calabi-Yau threefolds and requires a special type of intersection form. We derive five-dimensional central-charge formulas and briefly discuss the associated phase transitions. Finally, we exhibit connections with F-theory compactifications on Calabi-Yau manifolds that admit elliptic fibrations. This analysis suggests that F-theory unifies type-IIb three-branes and M-theory five-branes.