Leonardo Rastelli

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.

Boundary CFT Construction of D-branes in Vacuum String Field Theory

In previous papers we built (multiple) D-branes in flat space-time as classical solutions of the string field theory based on the tachyon vacuum. In this paper we construct classical solutions describing all D-branes in any fixed space-time background defined by a two dimensional CFT of central charge 26. A key role is played by the geometrical definition of the sliver state in general boundary CFTs. The correct values for ratios of D-brane tensions arise because the norm of the sliver solution is naturally related to the disk partition function of the appropriate boundary CFT. We also explore the possibility of reproducing the known spectrum of physical states on a D-brane as deformations of the sliver.

Half-strings, projectors and multiple D-branes

A sliver state is a classical solution of the string field theory of the tachyon vacuum that represents a background with a single D25-brane. We show that the sliver wavefunctional factors into functionals of the left and right halves of the string, and hence can be naturally regarded as a rank-one projector in a space of half-string functionals. By developing an algebraic oscillator approach we are able to construct higher rank projectors that describe configurations of multiple D-branes of various dimensionalities and located at arbitrary positions. The results bear remarkable similarities with non-commutative solitons.

Closed strings as imaginary D-branes

Abstract Sen has recently drawn attention to an exact time-dependent boundary conformal field theory with the space–time interpretation of brane creation and annihilation. An interesting limit of this BCFT is formally equivalent to an array of D-branes located in imaginary time. This raises the question: what is the meaning of D-branes in imaginary time? The answer we propose is that D-branes in imaginary time define purely closed string backgrounds. In particular we prove that the disk scattering amplitude of m closed strings off an arbitrary configuration of imaginary branes is equivalent to a sphere amplitude with m +1 closed string insertions. The extra puncture is a specific closed string state, generically normalizable, that depends on the details of the brane configuration. We study in some detail the special case of the array of imaginary D-branes related to Sens BCFT and comment on its space–time interpretation. We point out that a certain limit of our set-up allows to study classical black hole creation and suggests a relation between Choptuiks critical behavior and a phase-transition a la Gregory–Laflamme. We speculate that open string field theory on imaginary D-branes is dual to string theory on the corresponding closed string background.

A paradigm of open/closed duality Liouville D-branes and the Kontsevich model

We argue that topological matrix models (matrix models of the Kontsevich type) are examples of exact open/closed duality. The duality works at finite N and for generic t Hooft couplings. We consider in detail the paradigm of the Kontsevich matrix integral for two-dimensional topological gravity. We demonstrate that the Kontsevich model arises by topological localization of cubic open string field theory on N stable branes. Our analysis is based on standard worldsheet methods in the context of non-critical bosonic string theory. The stable branes have Neumann (FZZT) boundary conditions in the Liouville direction. Several generalizations are possible.

Star algebra spectroscopy

The spectrum of the infinite dimensional Neumann matrices M11, M12 and M21 in the oscillator construction of the three-string vertex determines key properties of the star product and of wedge and sliver states. We study the spectrum of eigenvalues and eigenvectors of these matrices using the derivation K1 = L1 + L−1 of the star algebra, which defines a simple infinite matrix commuting with the Neumann matrices. By an exact calculation of the spectrum of K1, and by consideration of an operator generating wedge states, we are able to find analytic expressions for the eigenvalues and eigenvectors of the Neumann matrices and for the spectral density. The spectrum of M11 is continuous in the range [−1/3,0) with degenerate twist even and twist odd eigenvectors for every eigenvalue except for -1/3.

Experimental string field theory

We develop efficient algorithms for level-truncation computations in open bosonic string field theory. We determine the classical action in the universal subspace to level (18,54) and apply this knowledge to numerical evaluations of the tachyon condensate string field. We obtain two main sets of results. First, we directly compute the solutions up to level L = 18 by extremizing the level-truncated action. Second, we obtain predictions for the solutions for 18

Star algebra projectors

>L>18 from an extrapolation to higher levels of the functional form of the tachyon effective action. We find that the energy of the stable vacuum overshoots -1 (in units of the brane tension) at L = 14, reaches a minimum Emin = −1.00063 at L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L→∞. Our data are entirely consistent with the recent perturbative analysis of Taylor and strongly support the idea that level-truncation is a convergent approximation scheme. We also check systematically that our numerical solution, which obeys the Siegel gauge condition, actually satisfies the full gauge-invariant equations of motion. Finally we investigate the presence of analytic patterns in the coefficients of the tachyon string field, which we are able to reliably estimate in the L→∞ limit.

A Note on a Proposal for the Tachyon State in Vacuum String Field Theory

Surface states are open string field configurations which arise from Riemann surfaces with a boundary and form a subalgebra of the star algebra. We find that a general class of star algebra projectors arise from surface states where the open string midpoint reaches the boundary of the surface. The projector property of the state and the split nature of its wave-functional arise because of a non-trivial feature of conformal maps of nearly degenerate surfaces. Moreover, all such projectors are invariant under constant and opposite translations of their half-strings. We show that the half-string states associated to these projectors are themselves surface states. In addition to the sliver, we identify other interesting projectors. These include a butterfly state, which is the tensor product of half-string vacua, and a nothing state, where the Riemann surface collapses.

Is Θ+(1540) a kaon–skyrmion resonance?

We discuss the proposal of Hata and Kawano for the tachyon fluctuation around a solution of vacuum string field theory representing a D25-brane. We give a conformal field theory construction of their state --- a local insertion of a tachyon vertex operator on the sliver surface state, and explain why the on-shell momentum condition emerges correctly. We also show that a naive computation of the D25-brane tension using data for the three point coupling of this state gives an answer that is (π2/3)(16/27 ln 2)3 2.0558 times the expected answer. We demonstrate that this problem arises because the HK state does not satisfy the equations of motion in a strong sense required for the computation of D-brane tension from the on-shell 3-tachyon coupling.