We find a codimension one lump solution of closed bosonic string field theory. We consider vertices up to quartic order and include in the string field the tachyon, the ghost dilaton, and a metric fluctuation. While the tachyon profile clearly is that of a lump, we observe that the ghost dilaton is roughly constant in the direction transverse to the lump, equal to the value it takes in the nonperturbative tachyon vacuum. We explain, with a simple model, why this should be expected.
We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $ϕ^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence issues.
We study some properties of the tachyonic lumps in the level truncation scheme of bosonic cubic string field theory. We find that several gauges work well and that the size of the lump as well as its tension is approximately independent of these gauge choices at level (2,4). We also examine the fluctuation spectrum around the lump solution, and find that a tachyon with m^2=-0.96 and some massive scalars appear on the lump world-volume. This result strongly supports the conjecture that a codimension 1 lump solution is identified with a D-brane of one lower dimension within the framework of boso…
We construct tachyon lump solutions of bosonic D2-branes on SU(2) group manifolds by level truncation approximation in cubic string field theory, which are regarded as D0-branes. The energies for these solutions show good agreement with the expected values.
In hep-th/0008227, the unstable lump solution of ϕ^3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the \ell=3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an \ell\to \infty scalar field theory model whose lump solution mimics remarkably the string theory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite levels, there is no continuous spectrum, and nothing survives after tachyon cond…
It has been conjectured that the tachyonic lump solution of the open bosonic string field theory describing a D-brane represents a D-brane of one lower dimension. We place the lump on a circle of finite radius and develop a variant of the level expansion scheme that allows systematic account of all higher derivative terms in the string field theory action, and gives a calculational scheme that can be carried to arbitrary accuracy. Using this approach we obtain lump masses that agree with expected D-brane masses to an accuracy of about 1%. We find convincing evidence that in string field theory…
We construct a kink solution on a non-BPS D-brane using Berkovits' formulation of superstring field theory in the level truncation scheme. The tension of the kink reproduces 95% of the expected BPS D-brane tension. We also find a lump-like solution which is interpreted as a kink--antikink pair, and investigate some of its properties. These results may be considered as successful tests of Berkovits' superstring field theory combined with the modified level truncation scheme.
We construct a classical solution in the GSO(-) sector in the framework of a Wess-Zumino-Witten-like open superstring field theory on a non-BPS D-brane. We use an su(2) supercurrent, which is obtained by compactifying a direction to a circle with the critical radius, in order to get analytical tachyonic lump solutions to the equation of motion. By investigating the action expanded around a solution we find that it represents a deformation from a non-BPS D-brane to a D-brane-anti-D-brane system at the critical value of a parameter which is contained in classical solutions. Although such a proce…
The lump solution of ϕ^3 field theory provides a toy model for unstable D-branes of bosonic string theory. The field theory living on this lump is itself a cubic field theory involving a tachyon, two additional scalar fields, and a scalar field continuum. Its action can be written explicitly because the fluctuation spectrum of the lump turns out to be governed by a solvable Schroedinger equation; the \ell=3 case of a series of reflectionless potentials. We study the multiscalar tachyon potential both exactly and in the level expansion, obtaining insight into issues of convergence, branches of …
We study a simple model of p-adic closed and open strings. It sheds some light on the dynamics of tachyon condensation for both types of strings. We calculate the effect of static and decaying D-brane configurations on the closed string background. For closed string tachyons we find lumps analogous to D-branes. By studying their fluctuation spectrum and the D-branes they admit, we argue that closed string lumps should be interpreted as spacetimes of lower dimensionality described by some noncritical p-adic string theory.
We study soliton solutions in scalar field theory with a variety of unbounded potentials. A subset of these potentials have Gaussian lump solutions and their fluctuation spectrum is governed by the harmonic oscillator problem. These lumps are unstable with one tachyonic mode. Soliton solutions in several other classes of potentials are stable and are of kink type. The problem of the stability of these solutions is related to a supersymmetric quantum mechanics problem. The fluctuation spectrum is not equispaced and does not contain any tachyonic mode. The lowest energy mode is the massless Gold…
Renormalization group analysis of boundary conformal field theory on bosonic D25-brane is used to study tachyon condensation. Placing the lump on a finite circle and triggering only the first three tachyon modes, the theory flows to nearby IR fixed point representing lumps that are extended object with definite profile. The boundary entropy corresponding to the D24-brane tension is calculated in the leading order in perturbative analysis which decreases under RG flow and agrees with the expected result to an accuracy of 8%. Multicritical behaviour of the IR theory suggests that the end point o…
Assuming that around the tachyon vacuum the kinetic term of cubic open string field theory is made purely of ghost operators we are led to gauge invariant actions which manifestly implement the absence of open string dynamics around this vacuum. We test this proposal by showing the existence of lump solutions of arbitrary codimension in this string field theory. The key ingredients in this analysis are certain assumptions about the analyticity properties of tachyon Green's functions. With the help of some further assumptions about the properties of these Green's functions, we also calculate th…
We study the fluctuation modes for lump solutions of the tachyon effective potential in p-adic open string theory. We find a discrete spectrum with equally spaced mass squared levels. We also find that the interactions derived from this field theory are consistent with p-adic string amplitudes for excited string states.
We construct the stress tensors for the p-adic string model and for the pure tachyonic sector of open string field theory by naive metric covariantization of the action. Then we give the concrete energy density of a lump solution of the p-adic model. In the cubic open bosonic string field theory, we also give the energy density of a lump solution and pressure evolution of a rolling tachyon solution.
It has been conjectured that an extremum of the tachyon potential of a bosonic D-brane represents the vacuum without any D-brane, and that various tachyonic lump solutions represent D-branes of lower dimension. We show that the tree level effective action of p-adic string theory, the expression for which is known exactly, provides an explicit realisation of these conjectures.
We study how the effect of closed-string tachyon condensation can enter into the on-shell effective action of open-string tachyons in the bosonic case. We also consider open-string one-loop quantum corrections to the on-shell action. We use a sigma-model approach with boundary terms, and we utilize some results of boundary string field theory (BSFT) to define the on-shell effective action. We regard D-instanton-like objects with appropriate weight as closed-string tachyon tadpoles, and we insert them into worldsheets to analyze the effect of closed-string tachyons.
Symplectic structure in open string field theory II: Sliding lump
CEICO, FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Center for Quantum Mathematics and Physics (QMAP), Department of Physics & Astronomy, University of California, Davis（加州大学戴维斯分校量子数学与物理中心）
We study lump solutions in nonlocal toy models and their cosmological applications. These models are motivated by a description of D-brane decay within string field theory framework. In order to find cosmological solutions we use the simplest local approximation keeping only second derivative terms in nonlocal dynamics. We study a validity of this approximation in flat background where time lump solutions can be written explicitly. We work out the validity of this approximation. We show that our models at large time exhibit the phantom behaviour similar to the case of the string kink.
We show an explicit relation between an RG flow of a two-dimensional gravity and an on-shell tachyon condensation in the corresponding string theory, in the case when the string theory is supercritical. The shape of the tachyon potential in this case can, in principle, be obtained by examining various RG flows. We also argue that the shape of tachyon potential for a (sub)critical string can be obtained by analyzing a supercritical string which is obtained from the (sub)critical string.
We construct Dp-branes in bosonic string theory as unstable lumps in a truncated string field theory of open strings on a D25-brane. We find that the lowest level truncation gives good quantitative agreement with the predicted D-brane tension and low-lying spectrum of the D-brane for sufficiently large p and study the effect of the next level corrections for p=24. We show that a U(1) gauge field zero mode on the D-brane arises through a mechanism reminiscent of the Randall-Sundrum mechanism for gravity.
We consider the tachyon potentials in closed and open-closed string theories. In doing so, we apply technique which proved to be useful in studying the open string tachyon potentials to the problem of interest.
We discuss various issues concerning the behaviors near the boundary (σ=0,π) and the midpoint (σ=π/2) of the open string coordinate X(σ) and its conjugate momentum P(σ)=-iδ/δX(σ) 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 v…
We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two--dimensional world-sheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.
We discuss fluctuations on solitons in the dilaton/graviton/tachyon system using the low energy effective field theory approach. It is shown that closed string solitons are free of tachyons in this approximation, regardless of the exact shape of the tachyon potential.
The results conjectured here are based on tachyon condensation in compactified bosonic strings. They can in fact be proven from compactification alone, but this step was not treated consistently here. The proof is given in a new version of the paper: hep-th/0106235
We investigate the string field theory around the tachyon vacuum. A pure gauge form of the solution is constructed at the tachyon vacuum. For a special choice of the gauge function for the pure gauge form, marginal deformation from the tachyon vacuum is allowed due to the nontrivial roles of Schnabl's analytic vacuum solution. We obtain an exact rolling tachyon solution which describes the late time behaviors of D-brane decay.
These notes are an expanded version of a review lecture on closed string tachyon condensation at the RTN workshop in Copenhagen in September 2003. We begin with a lightning review of open string tachyon condensation, and then proceed to review recent results on localized closed string tachyon condensation, focusing on two simple systems, C/Z_n orbifolds and twisted circle compactifications.
I review the physical properties of different vacua in the background independent open string field theory. Talk presented at Strings 2001, Mumbai, India, http://theory.theory.tifr.res.in/strings/Proceedings/#sha-s.
We investigate spectrum of open strings on D-branes after tachyon condensation in bosonic string theory. We calculate 1-loop partition function of the string and show that its limiting forms coincide with partition functions of open strings with different boundary conditions.
We describe numerical methods for constructing lump solutions in open string field theory. According to Sen, these lumps represent lower dimensional Dp-Branes and numerical evaluation of their energy can be compared with the expected value for the tension. We take particular care of all higher derivative terms inherent in Witten's version of open string field theory. The importance of these terms for off shell phenomena is argued in the text. Detailed numerical calculations done for the case of general $p$ brane show very good agreement with Sen's conjectured value. This gives credence to the …
In this paper we propose tachyon effective actions for unstable D-branes in superstring and bosonic string theories in the presence of the linear dilaton background.
In this short note we apply Schrodinger picture description of the minisuperspace approach to the closed string tachyon condensation. We will calculate the rate of produced closed string and we will show that the density of high massive closed string modes reaches the string density in time of order one in string units.
Closed string tachyons have long been somewhat mysterious. We note that there is often a regime in the classical moduli space in which one can systematically compute the effective action for such fields. In this regime, the tachyon is light, and cannot be integrated out. Instead, one must consider the combined dynamics of gravitons, moduli, tachyons and other light fields. We compute the action and find that the quartic term for the tachyon is positive in the field definition where the tachyon has no derivative coupling to the radion. We study the evolution of isotropic, homogeneous configurat…
We discuss tachyon configuration for the unoriented bosonic string theory which produces a bosonic string theory with SO(32) gauge symmetry in ten dimensions. It is closely related to the tachyon condensation scenario proposed by A. Sen. We also give the boundary state description of the tachyon condensation process, with some emphasis on the rôle of orbifold conformal field theory.
We compute the D0-brane tension in string field theory by representing it as a tachyon lump of the D1-brane compactified on a circle of radius $R$. To this aim, we calculate the lump solution in level truncation up to level L=8. The normalized D0-brane tension is independent on $R$. The compactification radius is therefore chosen in order to cancel the subleading correction $1/L^2$. We show that an optimal radius $R^*$ indeed exists and that at $R^*$ the theoretical prediction for the tension is reproduced at the level of $10^{-5}$. As a byproduct of our calculation we also discuss the determi…
We study a bosonic open string coupled to a tachyonic background field $T[X]$ and find that the tachyon field can effectively be replaced by a configuration of D-branes placed at either the zeros or the critical points of $T[X]$, depending on our choice of boundary conditions. This dual picture of the open string tachyon is explored in detail for the explicit case when the tachyonic field is quadratic.
Open string field theory in the level truncation approximation is considered. It is shown that the energy conservation law determines the existence of rolling tachyon solution. The coupling of the open string field theory action to a Friedmann-Robertson-Walker metric is considered and as a result the new time dependent rolling tachyon solution is presented and possible cosmological consequences are discussed.
The boundary string field theory approach is used to evaluate the one-loop tachyon potential. We first discuss the boundary condition at the two boundaries on annulus diagram and then the exact form of corrected potentials at zero and high temperature are obtained. The profile of the tachyon potential is found to be temperature independent and tachyon will condense at high temperature. Our investigations also provide an easy way to prove the universality of the tachyon potential, even if the string is in the thermal background.
We analyze the tachyon field in the bosonic open string theory in a constant B-field background using the background independent open string field theory. We show that in the large noncommutativity limit the action of tachyon field is given exactly by the potential term which has the same form as in the case without B-field but the product of tachyon field is taken to be the star product.
A discrete symmetry of the string field tachyon condensate noted by Hata and Shinohara is identified as a discrete subgroup of an SU(1,1) symmetry acting on the ghost coordinates. This symmetry, known from early studies of free gauge invariant string field actions, extends to off-shell interactions only for very restricted kinds of string vertices, among them the associative vertex of cubic string field theory. It follows that the string field relevant for tachyon condensation can be trimmed down to SU(1,1) singlets.
In this paper we propose the toy model of the closed string tachyon effective action that has marginal tachyon profile as its exact solution in case of constant or linear dilaton background. Then we will apply this model for description of two dimensional bosonic string theory. We will find that the background configuration with the spatial dependent linear dilaton, flat spacetime metric and marginal tachyon profile is the exact solution of our model even if we take into account backreaction of tachyon on dilaton and metric.
In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits' superstring field theory. In chapter 4, we look for exact solutions in a toy model. Unpublished result: we use conservation laws to calculate the level (4,8) approximation of the tachyon potential in Berkovits' superstring field theory. We verify Sen's conjecture up to 94.4%.
An F-theory dual of a nonsupersymmetric orientifold is considered. It is argued that the condensation of both open and closed string tachyons in the orientifold corresponds to the annihilation of branes and anti-branes in the F-theory dual. The end-point of tachyon condensation is thus expected to be the vacuum of Type-IIB superstring. Some speculations are presented about the F-theory dual of the bosonic string and tachyon condensation thereof.
A new family of non critical bosonic string backgrounds in arbitrary space time dimension $D$ and with $ISO(1,D-2)$ Poincaré invariance are presented. The metric warping factor and dilaton agree asymptotically with the linear dilaton background. The closed string tachyon equation of motion enjoys, in the linear approximation, an exact solution of ``kink'' type interpolating between different expectation values. A renormalization group flow interpretation ,based on a closed string tachyon potential of type $-T^{2}e^{-T}$, is suggested.
We construct a class of CFT's which describe space-dependent closed string tachyon backgrounds, as the IR limit of GLSM's in which the FI-parameter is promoted to a superfield. Whole process of tachyon condensation is described by a single CFT. We apply this construction to several examples, in which target space is deformed drastically, and the dilaton background may vary, as a tachyon condenses.
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 evidence confirming these conjectures is reviewed.
A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one transverse direction compactified on a circle admits various unstable D-brane systems, - some with geometric instability arising out of being placed at a point of unstable equilibrium in space and some with the usual open string tachyonic instability but no geometric instability. We discuss the effect of NS 5-branes on the descent relations among these branes and their physical interpretation in the T-dual ALF spaces. We argue that if the tachyon potential controlling these descent relations obeys certain conditions, t…
We use open string field theory to study the dynamics of unstable branes in the bosonic string theory, in the background of a generic linear dilaton. We find a simple exact solution describing a dynamical interpolation between the perturbative vacuum and the recently discovered nonperturbative tachyon vacuum. In our solution, the open string tachyon increases exponentially along a null direction, after which nonlinearities set in and cause the solution to asymptote to a static state. In particular, the wild oscillations of the open string fields which plague the time-like rolling tachyon solut…
We construct a vertex operator which describes an emission of the ground-state tachyon of the closed string out of the noncommutative open string. Such a vertex operator is shown to exist only when the momentum of the closed-string tachyon is subject to some constraints coming from the background $B$ field. The vertex operator has a multiplicative coupling constant $g(σ)$ which depends on $σ$ as $g(σ)=\sin^2 σ$ in $0 \le σ\le π$. This behavior is the same as in the ordinary B=0 case.
We study decay of a flat unstable D$p$-brane in the context of boundary string field theory action. Three types of homogeneous rolling tachyons are obtained without and with Born-Infeld type electromagnetic field.
We investigate real-time tachyon dynamics of unstable D-brane carrying fundamental string charge. We construct the boundary state relevant for rolling of modulated tachyon with gauge fields excited on the world-volume, and study spatial distribution of the fundamental string charge and current as the D-brane decays. We find that, in contrast to homogeneous tachyon rolling, spatial modulation of the tachyon field triggers density wave of strings when electric field is turned on, and of string anti-string pairs when magnetic field is turned on. We show that the energy density and the fundamental…
We discuss the problem of tachyon condensation in the framework of background independent open string field theory. We show, in particular, that the computation of the string field theory action simplifies considerably if one looks at closed string backgrounds with a large B field, and can be carried out exactly for a generic tachyon profile. We confirm previous results on the form of the exact tachyon potential, and we find, within this framework, solitonic solutions which correspond to lower dimensional unstable branes.
The ratios of the masses of D(p-d) branes to the masses of Dp in open bosonic string field theory are computed within the modified level truncation approximation of Moeller, Sen and Zweibach. At the lowest non-trivial truncation requiring the addition of new primary states, we find evidence of rapid convergence to the expected result for 1<d<7 providing additional evidence for the consistency of this approximation.
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.
We analyse the condensation of closed string tachyons on the $C/Z_N$ orbifold. We construct the potential for the tachyons upto the quartic interaction term in the large $N$ limit. In this limit there are near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory. We argue that higher point interaction terms are are also of the same order in 1/N as the quartic term and are necessary for existence of the minimum of the tachy…
We argue that the rolling-tachyon solution in cubic OSFT proceeds at late times to precisely the analytic tachyon-vacuum solution constructed by Schnabl. In addition, we demonstrate the relationship between the rolling-tachyon solution and the standard BCFT description by showing that there is a finite gauge transformation which relates the two.
By a toroidal compactification with a vortex like configuration of tachyon fields, the unoriented bosonic string in 26 dimensions becomes equivalent to 10 dimensional string theory with gauge group $SO(32)\times G$ where $G$ has rank 16. The reduction from SO(8192) to SO(32) is induced by the action of non-abelian Wilson lines which twists the tachyon. The additional enhanced gauge symmetry $G$ appears from closed string sector by Frenkel-Kac construction. We also examine the consistency of the tachyon condensation.
The spacetime physics of bulk closed string tachyon condensation is studied at the level of a two-derivative effective action. We derive the unique perturbative tachyon potential consistent with a full class of linearized tachyonic deformations of supercritical string theory. The solutions of interest deform a general linear dilaton background by the insertion of purely exponential tachyon vertex operators. In spacetime, the evolution of the tachyon drives an accelerated contraction of the universe and, absent higher-order corrections, the theory collapses to a cosmological singularity in fini…
We consider tachyon condensation in unstable ten-dimensional heterotic string theory with gauge group E8. In the background of a lightlike linear dilaton rolling to weak coupling, we find an exact solution in which the theory decays to a stable ground state. The final state represents a new, modular-invariant perturbative string theory, tachyon-free in nine spacetime dimensions with a spacelike dilaton gradient, E8 gauge group and no spacetime supersymmetry.
