Barton Zwiebach

Generalized metric formulation of double field theory

The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

Tachyon condensation in string field theory

It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found to cancel about 70% of the D-brane tension. Keeping relevant scalars up to four mass levels above the tachyon, the energy density at the shifted stationary point cancels 99% of the D-brane tension.

Background independent action for double field theory

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.

Tachyon potentials, star products and universality

We develop an efficient recursive method to evaluate the tachyon potential using the relevant universal subalgebra of the open string star algebra. This method, using off-shell versions of Virasoro Ward identities, avoids explicit computation of conformal transformations of operators and does not require a choice of background. We illustrate the procedure with a pedagogic computation of the level six tachyon potential in an arbitrary gauge, and the evaluation of a few simple star products. We give a background independent construction of the so-called identity of the star algebra, and show how it fits into family of string fields generating a commutative subalgebra.

Superstring theory on AdS2 × S2 as a coset supermanifold

Instituto de Fisica Teorica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, Sao Paulo

Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons

Both in string field theory and in p-adic string theory the equations of motion involve infinite number of time derivatives. We argue that the initial value problem is qualitatively different from that obtained in the limit of many time derivatives in that the space of initial conditions becomes strongly constrained. We calculate the energy-momentum tensor and study in detail time dependent solutions representing tachyons rolling on the p-adic string theory potentials. For even potentials we find surprising small oscillations at the tachyon vacuum. These are not conventional physical states but rather anharmonic oscillations with a nontrivial frequency-amplitude relation. When the potentials are not even, small oscillatory solutions around the bottom must grow in amplitude without a bound. Open string field theory resembles this latter case, the tachyon rolls to the bottom and ever growing oscillations ensue. We discuss the significance of these results for the issues of emerging closed strings and tachyon matter.

Tachyon condensation in superstring field theory

Abstract It has been conjectured that at the stationary point of the tachyon potential for the D-brane–anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess–Zumino–Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension.

The spacetime of double field theory: Review, remarks, and outlook

We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized coordinate transformations fails to associate. Moreover, in dimensional reduction, the O(d,d) T-duality transformations of fields can be obtained as generalized diffeomorphisms. Restricted to a half-dimensional subspace, DFT includes ‘generalized geometry’, but is more general in that local patches of the doubled space may be glued together with generalized coordinate transformations. Indeed, we show that for certain T-fold backgrounds with nongeometric fluxes, there are generalized coordinate transformations that induce, as gauge symmetries of DFT, the requisite O(d,d;Z) monodromy transformations. Finally we review recent results on the α ′ extension of DFT which, reduced to the half-dimensional subspace, yields intriguing modifications of the basic structures of generalized geometry.

D-BRANES, TACHYONS, AND STRING FIELD THEORY

In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Wittens cubic bosonic open string field theory. We use both the low-energy Yang-Mills description and the language of string field theory to explain the problem of tachyon condensation on unstable D-branes. We give a self-contained introduction to open string field theory using both conformal field theory and overlap integrals. Our main subjects are the Sen conjectures on tachyon condensation in open string field theory and the evidence that supports these conjectures. We conclude with a discussion of vacuum string field theory and projectors of the star-algebra of open string fields. We comment on the possible role of string field theory in the construction of a nonperturbative formulation of string theory that captures all possible string backgrounds.

Closed string field theory from polyhedra

A fully nonpolynomial framework for closed string field theory is studied. All interactions are geometrical, the pattern of string overlaps gives polyhedra with equal perimeter faces and three edges at each vertex. All interactions are cubic in the sense that at most three strings can coincide at a point. The three point vertex used is that of Witten which is seen to be quite natural in the framework of quadratic differentials and to induce a very symmetric decomposition of moduli space.