Introduction to Arithmetic Mirror Symmetry

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit example that the number of points of a generic element can be given in terms of p-adic period integrals. We also discuss several approaches to finding zeta functions of mirror manifolds and their factorizations. These notes are based on lectures given at the Fields Institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics

Duality-invariant Quantum Field Theories of Charges and Monopoles

We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST-mechanism. The dynamics for classical point particles is described by an action functional living on a circle, if the Dirac-Schwinger quantization condition for electric and magnetic charges holds. The inconsistent classical field theory depends on an arbitrary, but fixed, external vector field, a generalization of the Dirac-string. Nevertheless, the Quantum Field Theory, obtained from this classical action via a functional integral approach, turns out to be independent of the particular vector field chosen, and thus consistent, if the Dirac-Schwinger quantization condition holds. We provide explicit expressions for the generating functionals of observables, proving that they are Dirac-string independent. Since Lorentz-invariance is manifest at each step, the quantum theory admits also a manifestly diffeomorphism invariant coupling to external gravity. Relations with previous formulations, and with SO(2)--non invariant theories are clarified.Comment: 49 pages, LaTeX, no figure

Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism

Non-BPS D-branes are difficult to describe covariantly in a manifestly supersymmetric formalism. For definiteness we concentrate on type IIB string theory in flat background in light-cone Green-Schwarz formalism. We study both the boundary state and the boundary conformal field theory descriptions of these D-branes with manifest SO(8) covariance and go through various consistency checks. We analyze Sen's original construction of non-BPS D-branes given in terms of an orbifold boundary conformal field theory. We also directly study the relevant world-sheet theory by deriving the open string boundary condition from the covariant boundary state. Both these methods give the same open string spectrum which is consistent with the boundary state, as required by the world-sheet duality. The boundary condition found in the second method is given in terms of bi-local fields that are quadratic in Green-Schwarz fermions. We design a special ``doubling trick'' suitable to handle such boundary conditions and prescribe rules for computing all possible correlation functions without boundary insertions. This prescription has been tested by computing disk one-point functions of several classes of closed string states and comparing the results with the boundary state computation.Comment: 47 pages, 1 figure. Typos corrected, references added and slight modification of certain explanation made. Version accepted for publication in JHE

Non-commutative superspace from string theory

Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS-NS two form B, which gives rise to space-time non-commutativity. In this note we point out that this phenomenon extends to ten-dimensional superspace when employing a covariant quantization of the superstring, generalizing an observation by Ooguri and Vafa in four dimensions. In particular, we will find that RR field strengths give rise to a non-zero $\{\theta,\theta\}$ anti-commutator, just as in four dimensions, whereas the gravitino yields a non-zero value for $[x,\theta]$.Comment: LaTex, 12 page

Vertex Operators for Closed Superstrings

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any generic background in presence of Ramond-Ramond (RR) fields. We extend the procedure to all massive states of open and closed superstrings and we identify two new nilpotent charges which are used to impose the gauge fixing on the physical states. We solve iteratively the equations of the vertex for linear x-dependent RR field strengths. This vertex plays a role in studying non-constant C-deformations of superspace. Finally, we construct an action for the free massless sector of closed strings, and we propose a form for the kinetic term for closed string field theory in the pure spinor formalism.Comment: TeX, harvmac, amssym.tex, 41 pp; references adde

Idling Magnetic White Dwarf in the Synchronizing Polar BY Cam. The Noah-2 Project

Results of a multi-color study of the variability of the magnetic cataclysmic variable BY Cam are presented. The observations were obtained at the Korean 1.8m and Ukrainian 2.6m, 1.2m and 38-cm telescopes in 2003-2005, 56 observational runs cover 189 hours. The variations of the mean brightness in different colors are correlated with a slope dR/dV=1.29(4), where the number in brackets denotes the error estimates in the last digits. For individual runs, this slope is much smaller ranging from 0.98(3) to 1.24(3), with a mean value of 1.11(1). Near the maximum, the slope becomes smaller for some nights, indicating more blue spectral energy distribution, whereas the night-to-night variability has an infrared character. For the simultaneous UBVRI photometry, the slopes increase with wavelength from dU/dR=0.23(1) to dI/dR=1.18(1). Such wavelength dependence is opposite to that observed in non-magnetic cataclysmic variables, in an agreement to the model of cyclotron emission. The principal component analysis shows two (with a third at the limit of detection) components of variablitity with different spectral energy distribution, which possibly correspond to different regions of emission. The scalegram analysis shows a highest peak corresponding to the 200-min spin variability, its quarter and to the 30-min and 8-min QPOs. The amplitudes of all these components are dependent on wavelength and luminosity state. The light curves were fitted by a statistically optimal trigonometrical polynomial (up to 4-th order) to take into account a 4-hump structure. The dependences of these parameters on the phase of the beat period and on mean brightness are discussed. The amplitude of spin variations increases with an increasing wavelength and with decreasing brightnessComment: 30pages, 11figures, accepted in Cent.Eur.J.Phy

Chern-kernels and anomaly cancellation in M-theory

This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of ``unobservability'' of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts.Comment: LaTex, 39 pages, references and comments adde

N=2 Superparticles, RR Fields and Noncommutative Structures of (super)-Spacetime

The recent developments in superstring theory prompted the study of non-commutative structures in superspace. Considering bosonic and fermionic strings in a constant antisymmetric tensor background yields a non-vanishing commutator between the bosonic coordinates of the spacetime. Likewise, the presence of constant Ramond-Ramond (RR) background leads to a non-vanishing anti-commutator for the Grassmann coordinates of the superspace. The non-vanishing commutation relation between bosonic coordinates can also be derived using a particle moving in a magnetic background, we use N=2 pure spinor superparticles and D0-branes to show how the non-commutative structures emerge in superspace. It is argued how a D0-brane in a background of RR fields reproduces the results obtained in string theory.Comment: Based on a lectures given at 43rd International School of Subnuclear Physics, Erice, Sicily, Italy, Aug. 200

Instantons and Matter in N=1/2 Supersymmetric Gauge Theory

We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity parameter C. The profile of the matter superfield is deformed through linear and quadratic corrections in C. Higher order corrections are absent because of the fermionic nature of the back-reaction. The instanton effective action, in addition to the usual 't Hooft term, includes a contribution of order C^2 and is N=1/2 invariant. We argue that the N=1 result for the gluino condensate is not modified by the presence of the new term in the effective action.Comment: 33 pages, harvmac; v2: minor changes, added references; v3: added analysis of the instanton measure in section