Classical and Quantum D-branes in 2D String Theory

These lectures provide an introduction to the subject of tachyon condensation in the open bosonic string. The problem of tachyon condensation is first described in the context of the low-energy Yang-Mills description of a system of multiple D-branes, and then using the language of string field theory. An introduction is given to Witten's cubic open bosonic string field theory. The Sen conjectures on tachyon condensation in open bosonic string field theory are introduced, and ...

We study the dynamics of parallel brane-brane and brane-antibrane scattering in string theory in flat spacetime, focusing on the pair production of open strings that stretch between the branes. We are particularly interested in the case of scattering at small impact parameter $b < l_s$, where there is a tachyon in the spectrum when a brane and an antibrane approach within a string length. Our conclusion is that despite the tachyon, branes and antibranes can pass through each ...

We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation removes the degeneracy of the non-perturbed curve and allows to identify its singularities with ZZ branes. Also, using the constructed curve, we find non-perturbative corrections to the free energy and elucidate their CFT o...

The mechanism of recombination of intersecting D-branes is investigated within the framework of effective tachyon field theory. We regard the branes as the kink-type tachyon condensed states and use the effective two-tachyon Lagrangian to study the off-diagonal fluctuations therein. It is seen that there is a tachyonic mode in the off-diagonal fluctuations, which signs the instability of the intersecting D-branes. We diagonalize the two-by-two tachyonic matrix field and see t...

We further investigate the dimensional duality (D-duality) proposed in arXiv:0705.0550 by mainly focusing on the properties of D-branes in this background. We derive the world-sheet correspondence of static D-branes, and discuss the fate of non-static D-branes from the world-sheet viewpoint. The quantum string production with or without D-branes is also studied from the time-like Liouville theory. We find that the closed string production from the background is much larger th...

D-branes, topological defects in string theory on which string endpoints can live, may give new insight into the understanding of the cosmological evolution of the Universe at early epochs. We analyze the dynamics of D-branes in curved backgrounds and discuss the parameter space of M-theory as a function of the coupling constant and of the curvature of the Universe. We show that D-branes may be efficiently produced by gravitational effects. Furthermore, in curved spacetimes t...

We present an analytic solution for tachyon condensation on a non-BPS D-brane in Berkovits' open superstring field theory. The solution is presented as a product of $2\times 2$ matrices in two distinct $GL_2$ subgroups of the open string star algebra. All string fields needed for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen's conjecture. We also comment on how D-brane...

We study a matrix version of the purely cubic open string field theory as describing the expansion around the closed string vacuum. Any D-branes in the given closed string background can appear as classical solutions by using the identity projectors. Expansion around this solution gives the correct kinetic term for the open strings on the created D-branes while there are some subtleties in the unwanted degree of freedom.

String theory in two-dimensional spacetime illuminates two main threads of recent development in string theory: (1) Open/closed string duality, and (2) Tachyon condensation. In two dimensions, many aspects of these phenomena can be explored in a setting where exact calculations can be performed. These lectures review the basic aspects of this system.

It is shown that classical decay of unstable D-branes in bosonic and superstring theories produces pressureless gas with non-zero energy density. The energy density is stored in the open string fields, even though around the minimum of the tachyon potential there are no open string degrees of freedom. We also give a description of this phenomenon in an effective field theory.