Vacuum String Field Theory Research Articles

New approach to vacuum string field theory

We discuss the possibility of applying a purely ghost kinetic operator in open string field theory from the perspective of a modern analytic method based on the KBc subalgebra. A purely ghost kinetic operator is obtained as a result of gauge fixing string field theory around the identity-based tachyon vacuum solution. We show that the obtained kinetic operator is not equivalent to the midpoint insertion of a conformal ghost, to which an extensive literature is devoted. We also show that the equation of motion does not admit nontrivial solutions.

Bubbling AdS and vacuum string field theory

We show that a family of 1/2-BPS states of N = 4 SYM is in correspondence with a family of classical solutions of VSFT with a B-field playing the role of the inverse Planck constant. We show this correspondence by relating the Wigner distributions of the N fermion systems representing such states, to low energy space profiles of systems of VSFT D-branes. In this context the Pauli exclusion principle appears as a consequence of the VSFT projector equation. The family of 1/2-BPS states maps through coarse-graining to droplet LLM supergravity solutions. We discuss the possible meaning of the corresponding coarse graining in the VSFT side.

Boundary and Midpoint Behaviors of Lump Solutions in Vacuum String Field Theory

Boundary and Midpoint Behaviors of Lump Solutions in Vacuum String Field Theory

Exact results on equations of motion in vacuum string field theory

We prove some algebraic relations on the translationally invariant solutions and the lump solutions in vacuum string field theory. We show that up to the subtlety at the midpoint the definition of the half-string projectors of the known sliver solution can be generalized to other solutions. We also find that we can embed the translationally invariant solution into the matrix equation of motion with the zero-mode.

Chan-Paton factors and higgsing from vacuum string field theory

We give a description of open strings stretched between N parallel D-branes in VSFT. We show how higgsing is generated as the branes are displaced: the shift in the mass formula for on-shell states stretched between different branes is due to a twist anomaly, a contribution localized at the midpoint.

Boundary and midpoint behaviors of lump solutions in vacuum string field theory

We discuss various issues concerning the behaviors near the boundary ($\ensuremath{\sigma}=0,\ensuremath{\pi}$) and the midpoint ($\ensuremath{\sigma}=\ensuremath{\pi}/2$) of the open string coordinate $X(\ensuremath{\sigma})$ and its conjugate momentum $P(\ensuremath{\sigma})=\ensuremath{-}i\ensuremath{\delta}/\ensuremath{\delta}X(\ensuremath{\sigma})$ acting on the matter projectors of vacuum string field theory. Our original interest is in the dynamical change of the boundary conditions of the open string coordinate from the Neumann one in the translationally invariant backgrounds to the Dirichlet one in the D-brane backgrounds. We find that the Dirichlet boundary condition is realized on a lump solution only partially and only when its parameter takes a special value. On the other hand, the string midpoint has a mysterious property: it obeys the Neumann (Dirichlet) condition in the translationally invariant (lump) background.

Vacuum string field theory without matter-ghost factorization

We show that vacuum string field theory with the singular kinetic operator conjectured by Gaiotto, Rastelli, Sen and Zwiebach can be obtained by field redefinition from a regular theory constructed by Takahashi and Tanimoto. We solve the equation of motion both by level truncation and by a series expansion using the regulated butterfly state, and we find evidence that the energy density of a D25-brane is well defined and finite. Although the equation of motion naively factorizes into the matter and ghost sectors in the singular limit, subleading terms in the kinetic operator are relevant and the factorization does not strictly hold. Nevertheless, solutions corresponding to different D-branes can be constructed by changing the boundary condition in the boundary conformal field theory formulation of string field theory, and ratios of D-brane tensions are shown to be reproduced correctly.

Fundamental strings in SFT

In this Letter we show that vacuum string field theory contains exact solutions that we propose to interpret as macroscopic fundamental strings. They are formed by a condensate of infinitely many completely space-localized solutions (D0-branes).

Exact time-localized solutions in vacuum string field theory

We address the problem of finding star algebra projectors that exhibit localized time profiles. We use the double Wick rotation method, starting from a Euclidean (unconventional) lump solution, which is characterized by the Neumann matrix being the conventional one for the continuous spectrum, while the inverse of the conventional one for the discrete spectrum. This is still a solution of the projector equation and we show that, after inverse Wick-rotation, its time profile has the desired localized time dependence. We study it in detail in the low energy regime (field theory limit) and in the extreme high energy regime (tensionless limit) and show its similarities with the rolling tachyon solution.

Perturbative spectrum of the dressed sliver

We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311198, in the operator formulation of Vacuum String Field Theory. We derive the tachyon wave function and then analyze the higher level fluctuations. We show that the dressing is responsible for implementing the transversality condition on the massless vector. In order to consistently deal with the singular $k=0$ mode we introduce a string midpoint regulator and we show that it is possible to accommodate all the open string states among the solutions to the linearized equations of motion. We finally show how the dressing can give rise to the correct ratio between the energy density of the dressed sliver and the brane tension computed via the three-tachyons-coupling.

Rolling tachyon solution in vacuum string field theory

We construct a time-dependent solution in vacuum string field theory and investigate whether the solution can be regarded as a rolling tachyon solution. First, compactifying one space direction on a circle of radius $R$, we construct a space-dependent solution given as an infinite number of $*$ products of a string field with center-of-mass momentum dependence of the form ${e}^{\ensuremath{-}b{p}^{2}/4}$. Our time-dependent solution is obtained by an inverse-Wick rotation of the compactified space direction. We focus on one particular component field of the solution, which takes the form of the partition function of a Coulomb system on a circle with temperature ${R}^{2}$. Analyzing this component field both analytically and numerically using Monte Carlo simulation, we find that the parameter $b$ in the solution must be set equal to zero for the solution to approach a finite value in the large time limit ${x}^{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. We also explore the possibility that the self-dual radius $R=\sqrt{{\ensuremath{\alpha}}^{\ensuremath{'}}}$ is a phase transition point of our Coulomb system.

Solving Witten’s string field theory using the butterfly state

We solve the equation of motion of Witten's cubic open string field theory in a series expansion using the regulated butterfly state. The expansion parameter is given by the regularization parameter of the butterfly state, which can be taken to be arbitrarily small. Unlike the case of level truncation, the equation of motion can be solved for an arbitrary component of the Fock space up to a positive power of the expansion parameter. The energy density of the solution is well-defined and remains finite even in the singular butterfly limit, and it gives approximately 68% of the D25-brane tension for the solution at the leading order. Moreover, it simultaneously solves the equation of motion of vacuum string field theory, providing support for the conjecture at this order. We further improve our ansatz by taking into account next-to-leading terms, and find two numerical solutions which give approximately 88% and 109%, respectively, of the D25-brane tension for the energy density. These values are interestingly close to those by level truncation at level 2 without gauge fixing studied by Rastelli and Zwiebach and by Ellwood and Taylor.

Gauge Structure of Vacuum String Field Theory

We study the gauge structure of vacuum string field theory expanded around the D-brane solution, namely, the gauge transformation and the transversality condition of the massless vector fluctuation mode. We find that the gauge transformation on massless vector field is induced as an anomaly; an infinity multiplied by an infinitesimal factor. The infinity comes from the singularity at the edge of the eigenvalue distribution of the Neumann matrix, while the infinitesimal factor from the violation of the equation of motion of the fluctuation modes due to the regularization for the infinity. However, the transversality condition cannot be obtained even if we take into account the anomaly contribution.

Some exact computations on the twisted butterfly state in string field theory

The twisted butterfly state solves the equation of motion of vacuum string field theory in the singular limit. The finiteness of the energy density of the solution is an important issue, but possible conformal anomaly resulting from the twisting has prevented us from addressing this problem. We present a description of the twisted regulated butterfly state in terms of a conformal field theory with a vanishing central charge which consists of the ordinary bc ghosts and a matter system with c=26. Various quantities relevant to vacuum string field theory are computed exactly using this description. We find that the energy density of the solution can be finite in the limit, but the finiteness depends on the subleading structure of vacuum string field theory. We further argue, contrary to our previous expectation, that contributions from subleading terms in the kinetic term to the energy density can be of the same order as the contribution from the leading term which consists of the midpoint ghost insertion.

Dressed Sliver solutions in Vacuum String Field Theory

We consider a new class of solutions (dressed slivers) in Vacuum String Field Theory, which represent D25-branes. For each dressed sliver we introduce a deformation parameter and define a family of states which are characterized by new abelian star-subalgebras. We show that this deformation parameter can be used as a regulator: it allows us to define for each such solution a finite norm and energy density. Finally we show how to generalize these results to parallel coincident and to lower dimensional branes.

On different actions for the vacuum of bosonic string field theory

We study a family of kinetic operators in string field theory describing the theory around the closed string vacuum. Those operators are based on the analytical classical solutions of Takahashi and Tanimoto and are analogous to the pure ghost action usually referred to as "vacuum string field theory," but are much more general, and less singular than the pure ghost operator. The closed string vacuum is related to the D-brane vacuum by large, singular, gauge transformations or field redefinition, and all those different representations are related to each other by small gauge transformations. We try to clarify the nature of this singular gauge transformation. We also show that by choosing the Siegel gauge one recovers the propagator proposed in hep-th/0207266 that generates closed string surfaces.

String field theory vertices for fermions of integral weight

We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity, the reflector and the interaction vertex are treated in detail paying attention to the zero mode conditions and the U(1) charge anomaly. The Neumann coefficients for the interaction vertex are shown to be intimately connected with the coefficients for bosons allowing a simple proof that the reparametrization anomaly of the fermionic first order system cancels the contribution of two real bosons. This agrees with their contribution c=-2 to the central charge. The overlap equations for the interaction vertex are shown to hold. Our results have applications in N=2 string field theory, Berkovits' hybrid formalism for superstring field theory, the \eta\xi-system and the twisted bc-system used in bosonic vacuum string field theory.

GMS solitons from vacuum string field theory

AbstractWe construct a set of tachyonic lumps in Vacuum String Field Theory that, in the presence of a background B field, give in the low energy limit exactly the complete sequence of noncommutative GMS solitons.

Butterfly tachyons in vacuum string field theory

We use geometrical conformal field theory methods to investigate tachyon fluctuations about the butterfly projector state in Vacuum String Field Theory. We find that the on-shell condition for the tachyon field is equivalent to the requirement that the quadratic term in the string-field action vanish on shell. This further motivates the interpretation of the butterfly state as a D-brane. We begin a calculation of the tension of the butterfly, and conjecture that this will match the case of the sliver and further strengthen this interpretation.

Vacuum String Field Theory ancestors of the GMS solitons

We define a sequence of VSFT D-branes whose low energy limit leads exactly to a corresponding sequence of GMS solitons. The D-branes are defined by acting on a fixed VSFT lump with operators defined by means of Laguerre polynomials whose argument is quadratic in the string creation operators. The states obtained in this way form an algebra under the SFT star product, which is isomorphic to a corresponding algebra of GMS solitons under the Moyal product. In order to obtain a regularized field theory limit we embed the theory in a constant background B field.