In this paper we present a new and simple analytic solution for tachyon condensation in open bosonic string field theory. Unlike the B_0 gauge solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious "phantom" counter term, this new solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.
We discuss classical solutions of a graviton-dilaton-B_{μν}-tachyon system. Both constant tachyon solutions, including AdS_3 solutions, and space-dependent tachyon solutions are investigated, and their possible implications to closed string tachyon condensation are argued. The stability issue of the AdS_3 solutions is also discussed.
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.
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.
We study closed string tachyon condensation using the RG flow of the worldsheet theory. In many cases the worldsheet theory enjoys N=2 supersymmetry, which provides analytic control over the flow, due to non-renormalization theorems. Moreover, Mirror symmetry sheds light on the RG flow in such cases. We discuss the relevant tachyon condensation in the context of both compact and non-compact situations which lead to very different conclusions. Furthermore, the tachyon condensation leads to non-trivial dualities for non-supersymmetric probe theories.
In this paper we will construct all BPS and non-BPS D-branes in Type IIA and Type IIB theories from tachyon condensation. We also propose form of Wess-Zumino term for non-BPS D-brane and we will show that tachyon condensation in this term leads to standard Wess-Zumino term for BPS D-brane.
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.
In this paper we will study the quantum field theory of fluctuation modes around the classical solution that describes tachyon condensation on unstable D-brane.We will calculate the number of particle produced near the beginning of the rolling tachyon process. We will perform this calculation for different tachyon effective actions and we will find that the rate of the particle production strongly depends on the form of the effective action used for the description of the early stage of the tachyon condensation.
We discuss the tachyon condensation in a single unstable D-brane in the framework of boundary state formulation. The boundary state in the background of the tachyon condensation and the NS B-field is explicitly constructed. We show in both commutative theory and noncommutative theory that the unstable D-branes behaves like an extended object and eventually reduces to the lower dimensional D-branes as the system approaches the infrared fixed point. We clarify the relationship between the commutative field theoretical description of the tachyon condensation and the noncommutative one.
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.
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 construct an effective action describing brane-antibrane system containing N D-branes and N \bar{D}-branes. BPS equations for remaining D-branes after tachyon condensation are derived and their properties are investigated. The value of the D-brane tension and the number of brane bound states are discussed.
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.
Using the boundary state formalism we obtain the partition function corresponding to a dynamical (rotating-moving) D$p$-brane in the presence of electromagnetic and tachyonic background fields in the superstring theory. The instability of such D$p$-brane due to the tachyon condensation is investigated.
We investigate quasilocal tachyon condensation by using gravity/gauge duality. In order to cure the IR divergence due to a tachyon, we introduce two regularization schemes: AdS space and a d=10 Schwarzschild black hole in a cavity. These provide stable canonical ensembles and thus are good candidates for the endpoint of tachyon condensation. Introducing the Cardy-Verlinde formula, we establish the on-shell gravity/gauge duality. We propose that the stringy geometry resulting from the off-shell tachyon dynamics matches onto the off-shell AdS black hole, where "off-shell" means non-equilibrium c…
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 find an exact solution, with a nonzero net D-brane charge, in the boundary string field theory of brane-anti-brane pairs on a torus. We explicitly take the T-dual of this configuration. The Nahm-transformation of the instantons is derived from the tachyon condensation.
We extend the recent computation of the tachyon potential by Berkovits, Sen and Zwiebach by including level two fields and keeping up to level four terms in the action. We find 90.5% of the expected result.
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%.
Using boundary string field theory we study the decay of unstable D-branes to lower dimensional D-branes via the tachyon condensation at one loop level. We analyze one loop divergences and use the Fischler-Susskind mechanism to cancel divergences arising at the boundary of moduli space. The tachyon action up to the second derivative is obtained and a logarithmic correction to the tachyon potential is written down explicitly. Multiple D-branes is also considered and the role of the boundary fermions is highlighted.
We study a system of N D3-branes in which open string tachyons survive in the low energy alpha' -> 0 limit. We compute the height of the tachyon potential both in the weak and strong couplings by using N=4 super Yang-Mills and the dual AdS_5 descriptions respectively. We find an exact agreement between the two descriptions in the large N limit. This provides an example of gravitational duals of open string tachyon condensation.
String propagation on a cone with deficit angle $2π(1-{1\over N})$ is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.
The decay of rotated brane configurations and the corresponding condensation of tachyons is discussed. In a certain IIB orbifold case a heuristic argument about the mass of the state living on the fixed plane is made. When the rotation angle is $π$ this mass agrees with that obtained by Sen.
We construct non-supersymmetric $p$-brane solutions of type II supergravities in arbitrary dimensions ($d$) delocalized in one of the spatial transverse directions. By a Wick rotation we convert these solutions into Euclidean $p$-branes delocalized in the transverse time-like direction. The former solutions in $d=10$ nicely interpolate between the $(p+1)$-dimensional non-BPS D-branes and the $p$-dimensional BPS D-branes very similar to the picture of tachyon condensation for the tachyonic kink solution on the non-BPS D-branes. On the other hand the latter solutions interpolate between the $(p+…
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.
We study a configuration in matrix theory carying longitudinal fivebrane charge, i.e. a D0-D4 bound state. We calculate the one-loop effective potential between a D0-D4 bound state and a D0-anti-D4 bound state and compare our results to a supergravity calculation. Next, we identify the tachyonic fluctuations in the D0-D4 and D0-anti-D4 system. We analyse classically the action for these tachyons and find solutions to the equations of motion corresponding to tachyon condensation.
We construct a model describing BPS brane-systems using low energy effective theory of brane-antibrane system. Both parallel branes and intersecting branes can be treated by this model. After tachyon condensation, the dynamics of fluctuations around such brane-systems is supersymmetric if the degrees of freedom are restricted on the branes. The form of the tachyon potential and the application of this model to the black hole physics are discussed.
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.
Quantum theory of 2d gravity is examined by including a special quantum correction, which corresponds to the open string loop corrections and provides a new conformal anomaly for the corresponding $σ$ model. This anomaly leads to the condensation of the tachyon, and the resultant effective theory implies a possibility of extending the 2d gravity to the case of $c>1$.
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 perform canonical quantization of the open string on a unstable D-brane in the background of the tachyon condensation. Evaluating the Polyakov path-integral on a stripe, we obtain the field theoretical propagator in the open string theory. As the condensation occurs the string field theory is continuously deformed. At the infrared fixed point of the condensation, the open string field on the unstable D-brane transmutes to that on the lower dimensional D-brane with the correct D-brane tension.
We consider $tt^*$ equations appearing in the study of localized tachyon condensations. They are described by various Toda system when we consider the condensation by the lowest tachyon corresponding to the monomial $xy$. The tachyon potential is calculated as a solution to these equations. The Toda system appearing in the deformation of $\C^2/\Z_n$ by $xy$ is identical to that of $D_n$ singularity deformed by $x$. For $\C^3/\Z_n$ with $xyz$ deformation, we find only generic non-simple form, similar to the case appearing in $\C/\Z_5\to \C/\Z_3$ and we discuss the difficulties in these cases.
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.
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 show that the p-dimensional noncommutative Yang--Mills model corresponding to a (p-1)-brane allows solutions which correspond to lower branes. This may be interpreted as the Morita equivalence of noncommutative planes of various dimensions.
We construct the exact noncommutative solutions on tori. This gives an exact description of tachyon condensation on bosonic D-branes, non-BPS D-branes and brane-antibrane systems. We obtain various bound states of D-branes after the tachyon condensation. Our results show that these solutions can be generated by applying the gauge Morita equivalence between the constant curvature projective modules. We argue that there is a general framework of the noncommutative geometry based on the notion of Morita equivalence which underlies this specific example.
We consider a sphaleron solution in field theory that provides a toy model for unstable D-branes of string theory. We investigate the tachyon condensation on a Dp-brane. The localized modes, including a tachyon, arise in the spectrum of a sphaleron solution of a ϕ^4 field theory on M^{p+1}\times S^1. We use these modes to find a multiscalar tachyon potential living on the sphaleron world-volume. A complete cancelation between brane tension and the minimum of the tachyon potential is found as the size of the circle becomes small.
We show that the decay of the D2-\bar{D2} system with large worldvolume magnetic fields can be described in noncommutative gauge theory. Tachyon condensation in this system describes the annihilation of D2-\bar{D2} into $D0$-branes. From the 2+1 dimensional point of view, this is the decay of a nonabelian magnetic flux into vortices. The semiclassical approximation is valid over a long period of the decay. Our analysis allows us to clarify earlier results in the literature related to tachyon condensation and noncommutative gauge theory.
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.
We construct the explicit boundary state description of the vortex-type (codimension two) tachyon condensation in brane-antibrane systems generalizing the known result of the kink-type (Frau et al. hep-th/9903123). In this description we show how the RR-charge of the lower dimensional D-branes emerges. We also investigate the tachyon condensation in T^4/Z_2 orbifold and find that the twisted sector can be treated almost in the same way as the untwisted sector from the viewpoint of the boundary state. Further we discuss the higher codimension cases.
Intersecting D-brane models and their T-dual magnetic compactifications provide an attractive framework for particle physics, allowing for chiral fermions and supersymmetry breaking. Generically, magnetic compactifications have tachyons that are usually removed by Wilson lines. However, quantum corrections prevent local minima for Wilson lines. We therefore study tachyon condensation in the simplest case, the magnetic compactification of type I string theory on a torus to eight dimensions. We find that tachyon condensation restores supersymmetry, which is broken by the magnetic flux, and we co…
We study quantum corrections at the one loop level in open superstring tachyon condensation using the boundary string field theory (BSFT) method. We find that the tachyon field action has the same form as at the disc level, but with a renormalized effective coupling $λ' =g_s^{ren}e^{-T^2/4}$ ($g_s^{ren}$ is the renormalized dimensionless closed string coupling, $e^{-T^2/4}$ is the tachyonic field expectation value) and with an effective string tension. This result is in agreement with that based on general analysis of loop effects.
The c=1 matrix model, with or without a type 0 hat, has an exact quantum solution corresponding to closed string tachyon condensation along a null surface. The condensation occurs, and spacetime dissolves, at a finite retarded time on I^+. The outgoing quantum state of tachyon fluctuations in this time-dependent background is computed using both the collective field and exact fermion pictures. Perturbative particle production induced by the moving tachyon wall is shown to be similar to that induced by a soft moving mirror. Hence, despite the fact that I^+ for the tachyon is geodesicaly incompl…
The study of open string tachyon condensation in string field theory can be drastically simplified by making an appropriate choice of coordinates on the space of string fields. We show that a very natural coordinate system is suggested by the connection between the worldsheet renormalization group and spacetime physics. In this system only one field, the tachyon, condenses while all other fields have vanishing expectation values. These coordinates are also well-suited to the study of D-branes as solitons. We use them to show that the tension of the D25-brane is cancelled by tachyon condensatio…
In this thesis we review the fundamental framework of boundary string field theory (BSFT) and apply it to the tachyon condensation on non-BPS systems in the superstring theory. The boundary string field theory can be regarded as a natural extension of the nonlinear sigma model. By using this theory we can describe the tachyon condensation exactly and also obtain the effective actions on non-BPS systems consisting of the Dirac-Born-Infeld type action and the Wess-Zumino type action. Especially the Wess-Zumino action is written by superconnection and coincides with the mathematical argument by K…
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.
D0-branes are unstable in the presence of an R-R field strength background. A fuzzy two-sphere is classically stable under such a background, this phenomenon being called the Myers effect. We analyze this effect from the viewpoint of tachyon condensation. It is explicitly shown that a fuzzy two-sphere is realized by the condensation of tachyons which appear from strings connecting different D0-branes. The formation of a fuzzy $CP^{2}$ is also investigated by considering the SU(3) invariant R-R field strength background. We find that the dynamics of the D-branes depends on the properties of the…
The gauge invariance of open string field theory is considered from the point of view of level truncation, and applications to the tachyon condensation problem are discussed. We show that the region of validity of Feynman-Siegel gauge can be accurately determined using the level truncation method. We then show that singularities previously found in the tachyon effective potential are gauge artifacts arising from the boundary of the region of validity of Feynman-Siegel gauge. The problem of finding the stable vacuum and tachyon potential without fixing Feynman-Siegel gauge is addressed.
We analyze how lower-dimensional bosonic D-branes further decay, using the boundary string field theory. Especially we find that the effective tachyon potential of the lower-dimensional D-brane has the same profile as that of D25-brane.
We study the evolution of stable D-branes of C/Z_n and twisted circle theories in the process of closed string tachyon condensation. We interpret the fractional branes in these backgrounds as type II branes wrapping (`blown up') cycles, and trace the evolution of the corresponding cycles under tachyon condensation. We also study RG flows of the corresponding N=2 boundary conformal field theories. We find flows along which fractional D-branes either disappear or evolve into other fractional D-branes, and other flows along which bulk branes either disappear or evolve into stable branes.
We describe timelike linear dilaton backgrounds of supercritical string theories as time-dependent Dynamical Cobordisms in string theory, with their spacelike singularity as a boundary defining the beginning of time. We propose and provide compelling evidence that its microscopic interpretation corresponds to a region of (a strong coupling version of) closed tachyon condensation. We argue that this beginning of time is closely related to (and shares the same scaling behaviour as) the bubbles of nothing obtained in a weakly coupled background with lightlike tachyon condensation. As an intermedi…
The open string tachyon and U(1) gauge field as longitudinal fluctuations and the velocity as transverse fluctuation of an arbitrary dimensional D-brane are considered as boundary deformations of a closed superstring free action. The path integral approach will be applied to calculate the corresponding generalized boundary states using supersymmetrized boundary actions. Obtaining the disk partition functions from the boundary states and studying the effect of tachyon condensation on both of them in the NSNS and RR sectors, leads to results that differ from the established ones.
We study the tachyon condensation on the D-brane--antiD-brane system from the supergravity point of view. The non-supersymmetric supergravity solutions with symmetry ISO($p,1$) $\times$ SO($9-p$) are known to be characterized by three parameters. By interpreting this solution as coincident $N$ D$p$-branes and ${\bar N}$ ${\bar {\rm D}}p$-branes we give, for the first time, an explicit representation of the three parameters of supergravity solutions in terms of $N, \bar N$ and the tachyon vev. We demonstrate that the solution and the corresponding ADM mass capture all the required properties an…
The amplitudes in perturbative open string theory are examined as functions of the tachyon condensate parameter. The boundary state formalism demonstrates the decoupling of the open string modes at the non-perturbative minima of the tachyon potential via a degeneration of open world-sheets and identifies an independence of the coupling constants $g_s$ and $g_{YM}$ at general values of the tachyon condensate. The closed sector is generated at the quantum level; it is also generated at the classical level through the condensation of the propagating open string modes on the D-brane degrees of fre…
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.
In superstring theory of type II, the separated brane-antibrane pair admits a bi-fundamental tachyon in its open string spectrum, for any separation less than the critical distance. The dynamics of this system would be described by the Garousi's effective action for any non-zero separation. Our study shows however that the domain of validity of this action only includes space-like tachyon condensation. Previous studies led by Bagchi and Sen showed that, in a partial sub-critical domain, exists a conformal field theory (CFT), which describes a dynamical condensation at static distance, called r…
We study some aspects of localized tachyon condensation on non-supersymmetric orbifolds of the form $\BC^2/\BZ_n$ and $\BC^3/\BZ_n$. We discuss the gauged linear sigma models for these orbifolds. We show how several features of the decay of orbifolds of $\BC^3$ can be realised in terms of orbifolds of $\BC^2$.
We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.
We generalize our study of the tachyon condensation on the brane-antibrane system [hep-th/0403147] to the intersecting brane-antibrane system. The supergravity solutions of the intersecting brane-antibrane system are characterized by five parameters. We relate these parameters to the microscopic physical parameters, namely, the number of D$p$-branes ($N_1$), the number of ${\bar {\rm D}}p$-branes (${\bar N}_1$), the number of D$(p-4)$-branes ($N_2)$, the number of ${\bar{\rm D}}(p-4)$-branes (${\bar N}_2$) and the tachyon vev $T$. We show that the solution and the ADM mass capture all the requ…
The level truncation approach to string field theory is used to study the zero-momentum action for vector excitations on a bosonic D-brane which has been annihilated by tachyon condensation. It is shown that in the true vacuum the translation zero modes associated with transverse scalars on the D-brane are lifted by spontaneous generation of mass terms. Similarly, the U(1) gauge field on the brane develops a nonzero mass term.
