Time and Tachyon

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born-Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of non-interacting (incoherent), non-rotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late `time' we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler - de Witt equation of quantum gravity.Comment: LaTeX file, 24 page

Background Independent Algebraic Structures in Closed String Field Theory

We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism of this algebra to the BV algebra of string functionals. The construction begins with a graded-commutative free associative algebra \C built from the vector space whose elements are orientable subspaces of moduli spaces of punctured Riemann surfaces. The typical element here is a surface with several connected components. The operation $\Delta$ of sewing two punctures with a full twist is shown to be an odd, second order derivation that squares to zero. It follows that (\C, \Delta) is a Batalin-Vilkovisky algebra. We introduce the odd operator $\delta = \partial + \hbar\Delta$, where $\partial$ is the boundary operator. It is seen that $\delta^2=0$, and that consistent closed string vertices define a cohomology class of $\delta$. This cohomology class is used to construct a Lie algebra on a quotient space of \C. This Lie algebra gives a manifestly background independent description of a subalgebra of the closed string gauge algebra.Comment: phyzzx.tex, MIT-CTP-234

Field Theory of Tachyon Matter

We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: 1) absence of plane-wave solutions around the minimum, and 2) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include non-relativistic matter with arbitrary spatial distribution of energy.Comment: LaTeX file, 9 pages, discussion of classical solutions expanded, other minor change

Fundamental Studies Connected with Electrochemical Energy Storage

Papers are presented which deal with electrochemical research activities. Emphasis is placed on electrochemical energy storage devices. Topics discussed include: adsorption of dendrite inhibitors on zinc; proton discharge process; electron and protron transfer; quantum mechanical formulation of electron transfer rates; and theory of electrochemical kinetics in terms of two models of activation; thermal and electrostatic

Free-field Representations and Geometry of some Gepner models

The geometry of $k^{K}$ Gepner model, where $k+2=2K$ is investigated by free-field representation known as "bc\bet\gm"-system. Using this representation it is shown directly that internal sector of the model is given by Landau-Ginzburg $\mathbb{C}^{K}/\mathbb{Z}_{2K}$-orbifold. Then we consider the deformation of the orbifold by marginal anti-chiral-chiral operator. Analyzing the holomorphic sector of the deformed space of states we show that it has chiral de Rham complex structure of some toric manifold, where toric dates are given by certain fermionic screening currents. It allows to relate the Gepner model deformed by the marginal operator to the $\sigma$-model on CY manifold realized as double cover of $\mathbb{P}^{K-1}$ with ramification along certain submanifold.Comment: LaTex, 14 pages, some acknowledgments adde

Singular tachyon kinks from regular profiles

We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately.Comment: 7 pages, 3 figures. References adde

Remark about Non-BPS D-Brane in Type IIA Theory

In this paper we would like to show simple mechanisms how from the action for non-BPS D-brane we can obtain action describing BPS D(p-1)-brane in Type IIA theory.Comment: 13 pages, completely rewritten pape

Tachyon condensation on brane sphalerons

We consider a sphaleron solution in field theory that provides a toy model for unstable D-branes of string theory. We investigate the tachyon condensation on a Dp-brane. The localized modes, including a tachyon, arise in the spectrum of a sphaleron solution of a \phi^4 field theory on M^{p+1}\times S^1. We use these modes to find a multiscalar tachyon potential living on the sphaleron world-volume. A complete cancelation between brane tension and the minimum of the tachyon potential is found as the size of the circle becomes small.Comment: To appear in JHEP, 13 pages, 2 eps figures, minor changes and references adde

Exactly stable non-BPS spinors in heterotic string theory on tori

Considering SO(32) heterotic string theory compactified on a torus of dimension 4 and less, stability of non-supersymmetric states is studied. A non-supersymmetric state with robust stability is constructed, and its exact stability is proven in a large region of moduli space against all the possible decay mechanisms allowed by charge conservation. Using various T-duality transform matrices, we translate various selection rules about conserved charges into simpler problems resembling partition and parity of integers. For heterotic string on T^4, we give a complete list of BPS atoms with elementary excitations, and we study BPS and non-BPS molecules with various binding energies. Using string-string duality, the results are interpreted in terms of Dirichlet-branes in type IIA string theory compactified on an orbifold limit of a K3 surface.Comment: 47 pages, 14 figures, LaTe