Rolling Tachyon Boundary State, Conserved Charges and Two Dimensional String Theory

The boundary state associated with the rolling tachyon solution on an unstable D-brane contains a part that decays exponentially in the asymptotic past and the asymptotic future, but it also contains other parts which either remain constant or grow exponentially in the past or future. We argue that the time dependence of the latter parts is completely determined by the requirement of BRST invariance of the boundary state, and hence they contain information about certain conserved charges in the system. We also examine this in the context of the unstable D0-brane in two dimensional string theory where these conserved charges produce closed string background associated with the discrete states, and show that these charges are in one to one correspondence with the symmetry generators in the matrix model description of this theory.Comment: LaTeX file, 37 pages; v3: references added; v4: minor change

QED and String Theory

We analyze the D9-D9bar system in type IIB string theory using Dp-brane probes. It is shown that the world-volume theory of the probe Dp-brane contains two-dimensional and four-dimensional QED in the cases with p=1 and p=3, respectively, and some applications of the realization of these well-studied quantum field theories are discussed. In particular, the two-dimensional QED (the Schwinger model) is known to be a solvable theory and we can apply the powerful field theoretical techniques, such as bosonization, to study the D-brane dynamics. The tachyon field created by the D9-D9bar strings appears as the fermion mass term in the Schwinger model and the tachyon condensation is analyzed by using the bosonized description. In the T-dualized picture, we obtain the potential between a D0-brane and a D8-D8bar pair using the Schwinger model and we observe that it consists of the energy carried by fundamental strings created by the Hanany-Witten effect and the vacuum energy due to a cylinder diagram. The D0-brane is treated quantum mechanically as a particle trapped in the potential, which turns out to be a system of a harmonic oscillator. As another application, we obtain a matrix theory description of QED using Taylor's T-duality prescription, which is actually applicable to a wide variety of field theories including the realistic QCD. We show that the lattice gauge theory is naturally obtained by regularizing the matrix size to be finite.Comment: 33 pages, Latex, 4 figures, a reference adde

On The Problem of Particle Production in c=1 Matrix Model

We reconsider and analyze in detail the problem of particle production in the time dependent background of $c=1$ matrix model where the Fermi sea drains away at late time. In addition to the moving mirror method, which has already been discussed in hep-th/0403169 and hep-th/0403275, we describe yet another method of computing the Bogolubov coefficients which gives the same result. We emphasize that these Bogolubov coefficients are approximately correct for small value of the deformation parameter. We also study the time evolution of the collective field theory stress-tensor with a special point-splitting regularization. Our computations go beyond the approximation of the previous treatments and are valid at large coordinate distances from the boundary at a finite time and up-to a finite coordinate distance from the boundary at late time. In this region of validity our regularization produces a certain singular term that is precisely canceled by the collective field theory counter term in the present background. The energy and momentum densities fall off exponentially at large distance from the boundary to the values corresponding to the static background. This clearly shows that the radiated energy reaches the asymptotic region signaling the space-time decay.Comment: 37 pages, 5 figures. Section 6 is modified to clarify main accomplishments of the paper including a discussion comparing stress-tensor analysis with those preexisted in literature. Other modifications include minor changes in the text and addition of one reference. Version accepted for publication in JHE

Strings from Tachyons

We propose a new interpretation of the c=1 matrix model as the world-line theory of N unstable D-particles, in which the hermitian matrix is provided by the non- abelian open string tachyon. For D-particles in 1+1-d string theory, we find a direct quantitative match between the closed string emission due to a rolling tachyon and that due to a rolling eigenvalue in the matrix model. We explain the origin of the double-scaling limit, and interpret it as an extreme representative of a large equivalence class of dual theories. Finally, we define a concrete decoupling limit of unstable D-particles in IIB string theory that reduces to the c=1 matrix model, suggesting that 1+1-d string theory represents the near-horizon limit of an ultra-dense gas of IIB D-particles.Comment: 30 pages, 4 figures; v2: added references, improved discussion of Liouville boundary states, v3: small correction

Decoupling of Degenerate Positive-norm States in Witten's String Field Theory

We show that the degenerate positive-norm physical propagating fields of the open bosonic string can be gauged to the higher rank fields at the same mass level. As a result, their scattering amplitudes can be determined from those of the higher spin fields. This phenomenon arises from the existence of two types of zero-norm states with the same Young representations as those of the degenerate positive-norm states in the old covariant first quantized (OCFQ) spectrum. This is demonstrated by using the lowest order gauge transformation of Witten's string field theory (WSFT) up to the fourth massive level (spin-five), and is found to be consistent with conformal field theory calculation based on the first quantized generalized sigma-model approach. In particular, on-shell conditions of zero-norm states in OCFQ stringy gauge transformation are found to correspond, in a one-to-one manner, to the background ghost fields in off-shell gauge transformation of WSFT. The implication of decoupling of scalar modes on Sen's conjectures was also briefly discussed.Comment: 18 pages, use Latex with revtex

Thermal Partition Functions for S-branes

We calculate the thermal partition functions of open strings on the S-brane backgrounds (the bouncing or rolling tachyon backgrounds) both in the bosonic and superstring cases. According to hep-th/0302146, we consider the discretized temperatures compatible with the pure imaginary periodicity of tachyon profiles. The ``effective Hagedorn divergence'' is shown to appear no matter how low temperature is chosen (including zero-temperature). This feature is likely to be consistent with the large rate of open string pair production discussed in hep-th/0209090 and also emission of closed string massive modes hep-th/0303139. We also discuss the possibility to remove the divergence by considering the space-like linear dilaton backgrounds as in hep-th/0306132.Comment: 33 pages, no figure; v2 typos corrected, a reference adde

D-brane anti-D-brane effective action and brane interaction in open string channel

We construct the effective action of a $D_p$-brane-anti-$D_p$-brane system by making use of the non-abelian extension of tachyonic DBI action. We succeed the construction by restricting the Chan-Paton factors of two non-BPS $D_p$-branes in the action to the Chan-Paton factors of a $D_p\bar{D}_p$ system. For the special case that both branes are coincident, the action reduces to the one proposed by A. Sen. \\The effective $D_p\bar{D}_p$ potential indicates that when branes separation is larger than the string length scale, there are two minima in the tachyon direction. As branes move toward each other under the gravitational force, the tachyon tunneling from false to true vacuum may make a bubble formation followed by a classical evolution of the bubble. On the other hand, when branes separation is smaller than the string length scale, the potential shows one maximum and one minimum. In this case, a homogeneous tachyon rolling in real time makes an attractive potential for the branes distance. This classical force is speculated to be the effective force between the two branes.Comment: Latex, 14 pages, 1 figure, the version appears in JHE

Notes on D-branes in 2D Type 0 String Theory

In this paper we construct complete macroscopic operators in two dimensional type 0 string theory. They represent D-branes localized in the time direction. We give another equivalent description of them as deformed Fermi surfaces. We also discuss a continuous array of such D-branes and show that it can be described by a matrix model with a deformed potential. For appropriate values of parameters, we find that it has an additional new sector hidden inside its strongly coupled region.Comment: harvmac, 18 pages, 2 figures, references adde

Two-dimensional superstrings and the supersymmetric matrix model

We present evidence that the supersymmetric matrix model of Marinari and Parisi represents the world-line theory of N unstable D-particles in type II superstring theory in two dimensions. This identification suggests that the matrix model gives a holographic description of superstrings in a two-dimensional black hole geometry.Comment: 22 pages, 2 figures; v2: corrected eqn 4.6; v3: corrected appendices and discussion of vacua, added ref