Some Computations in Background Independent Open-String Field Theory

Recently, background independent open-string field theory has been formally defined in the space of all two-dimensional world-sheet theories. In this paper, to make the construction more concrete, I compute the action for an off-shell tachyon field of a certain simple type. From the computation it emerges that, although the string field action does not coincide with the world-sheet (matter) partition function in general, these functions do coincide on shell. This can be demonstrated in general, as long as matter and ghosts are decoupled.Comment: 14 p

Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.Comment: 17 pages, no figure

Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.Comment: 16 page

Hyökkäysvaununtorjunta tulella. Teknilliset perusedellytykset.

Artikkelin alkuosassa on lyhyesti ja pääpiirteisesti käsitelty hyökkäysvaunujen käyttöä ja torjunta-aseistuksen yleisperiaatteita. Päähuomio artikkelissa on kohdistettu yhtenäisen ja perustellun kokonaiskuvan luomiseen niistä tekijöistä, joiden perusteella on teoreettisesti arvioiden valittavissa edullisin torjunta-ase. Artikkelissa tarkastellaan tuolloin tiedossa olleita asetyyppejä luettelona. Lisäksi artikkelissa on tarkasteltu melkoisen yksityiskohtaisesti Ruotsin armeijan kokeiluja ja niitä tuloksia, joihin siellä on päädytty. "Olemme katsoneet tämän tarpeelliseksi ennen kaikkea siitä syytä, että täten samalla voimme antaa muutamia kokemukseen perustuvia tietoja, jotka valaisevat erään, käsityksemme mukaan edullisinta hyvin lähellä olevan asetyypin käyttöä ja taisteluarvoa. Artikkelin toisessa luvussa tarkastellaan hyökkäysvaunua ja sen käyttöä. Taulukkomuodossa esitetään ensimmäisen maailmansodan hyökkäysvaunut ja Venäjän kirjoitushetken hyökkäysvaunut.Kolmannessa luvussa esitellään yksityiskohtaisia taulukoina eri aikakausien panssarintorjuntaan soveltuvaa aseistusta. Seuraavissa luvuissa tarkastellaan osin taulukkojen ja matemaattisen mallinnuksen avulla panssarintorjunta-aseistuksen ominaisuuksia ja meille soveltuvalle aseelle esitettäviä vaatimuksia. Kuudennessa luvussa käsitellään Ruotsin panssarintorjunta-aseistusta. Johtopäätöksissä kirjoittajat päätyvät muun muassa siihen, että panssarintorjunnalla tulee olemaan yliote taistelussa hyökkäysvaunuja vastaan

Fluctuation force exerted by a planar self-avoiding polymer

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.Comment: 7 pages, 22 figure

The Volume of a Local Nodal Domain

Let M either be a closed real analytic Riemannian manifold or a closed smooth Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball provided that this component enters the ball deeply enough.Comment: 21 pages; introduction improved putting the problem in a larger context

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure

The Universal Phase Space of AdS3 Gravity

We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are realized as submanifolds. The universal phase space is parametrized by two copies of the Universal Teichm\"uller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we obtain a relation between the generators of quasiconformal deformations in each T(1) sector and the chiral Brown-Henneaux vector fields. We also relate the charges arising in the holographic description (such as the mass and angular momentum of an AdS3 spacetime) to the periods of the quadratic differentials arising via the Bers embedding of T(1)xT(1). Our construction also yields a symplectic map from T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting.Comment: 41 pages, 2 figures, revised version accepted for publication in Commun.Math.Phy