REVIEW
Rolling Tachyon
High Energy Physics - Theory · Submitted 22 Mar 2002 · 38 references
Pith's verdict: The paper that opened the rolling-tachyon literature: the construction and the smooth-vs-singular split hold up, and the soft spots are mostly the ones Sen flags himself.
T0 · AI review
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Referee report
The paper
The paper claims
Sen argues that an unstable D-brane's rolling tachyon has a smooth late-time energy-momentum tensor on the stable side of the potential, while the unstable side produces a finite-time singularity.
The reading
What carries the argument
The load-bearing device is the Wick rotation between the real-time boundary deformation $cosh X^0$ and the Euclidean deformation $cos X$. The Euclidean version is a solvable boundary conformal field theory: its boundary state is a sum over Virasoro Ishibashi states dressed by an $SU(2)$ rotation matrix with angle $pi tilde{lambda}$, and at $tilde{lambda}=pm 1/2$ it reduces to known arrays of Dirichlet branes. Rotating $Xto -iX^0$ turns the $cos(nX)$ terms into $cosh(nx^0)$ terms and produces the source functions $f(x^0)$ and $g(x^0)$ for closed-string fields. This is what lets the paper make statements about arbitrarily late times without controlling the infinite-derivative string field action directly.
Extended reading notes
Core claim
The central claim is that the classical decay of an unstable D-brane is a well-defined time-dependent solution of open string field theory, not merely a formal expansion. Sen constructs the solution order by order in the initial tachyon displacement $lambda$, with leading term $T(x^0)=lambda cosh(x^0)$ in bosonic string theory, and argues that the operator $cosh(X^0)$ is exactly marginal because its Wick rotation $cos(X)$ is a known marginal boundary deformation. The associated world-sheet theory is a free scalar with boundary term $tilde{lambda}int dt,cosh X^0(t)$, and its boundary state is obtained by inverse-Wick-rotating the known boundary state of the $cos X$ deformation. The oscillator-free part of that state yields $f(x^0)=1/(1+e^{x^0}sin(pi tilde{lambda}))+1/(1+e^{-x^0}sin(pi tilde{lambda}))-1$, finite for all $x^0$ when $tilde{lambda}>0$ and singular at $x^0=ln(-1/sin(pi tilde{lambda}))$ when $tilde{lambda}<0$. The conserved combination $f+g=1+cos(2pi tilde{lambda})$ is interpreted as the energy density, so the sign of the deformation controls whether the late-time energy-momentum tensor is smooth or singular.
Load-bearing premise
The load-bearing premise is that the solvable boundary conformal field theory with boundary term $tilde{lambda}int dt,cosh X^0$ is the correct continuation of the string field theory solution beyond the radius of convergence of the $lambda$ expansion—the paper itself estimates that expansion as reliable only for $x^0<ln(1/|lambda|)$—and that its parameter $tilde{lambda}$ is related to the string field theory displacement $lambda$ by the asserted functional relation used in the energy check.
Editorial extensions
If this is right
- Open string field theory admits a two-parameter family of classical tachyon-roll solutions labelled by initial position and velocity, despite the infinite number of time derivatives in the action.
- The decay is universal: it depends only on the time coordinate and the universal tachyon sector, not on the details of the $c=25$ matter theory.
- The energy density remains localized on the original brane plane, so the decay does not produce conventional closed-string radiation carrying energy away.
- For bosonic D-branes, pushing the tachyon toward the local minimum gives a smooth asymptotic energy-momentum tensor, while pushing it toward the unbounded side gives a finite-time singularity.
- At $tilde{lambda}=1/2$ the total energy vanishes and the configuration does not evolve, matching the tachyon vacuum.
Reading between the lines
- The smooth-versus-singular split is a sharp target for numerical string field theory: tracking the energy density at late times for positive and negative initial displacements would test the boundary-state continuation where the power series has already broken down.
- Because the closed-string tachyon source $f(x^0)$ vanishes asymptotically while $g(x^0)$ remains nonzero, the late-time object may be a static graviton/dilaton source rather than a decaying tachyon; working out its precise stress tensor would clarify what remnant, if any, the brane leaves behind.
- If the same Wick-rotation method extends to the superstring boundary term $tilde{lambda}int dt,sigma_1otimespsi^0sinh X^0$, an explicit boundary state there would show whether the bosonic smooth-versus-singular dichotomy survives supersymmetry.
- The finite-time singularity for negative $tilde{lambda}$ may signal a breakdown of the boundary conformal field theory rather than a physical crunch, so distinguishing the two would require a UV completion of the world-sheet description.
Original abstract
We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time derivatives, and hence it is not a priori clear how to set up the initial value problem, the theory contains a family of time dependent solutions characterized by the initial position and velocity of the tachyon field. We write down the world-sheet action of the boundary conformal field theories associated with these solutions and study the corresponding boundary states. For D-branes in bosonic string theory, the energy momentum tensor of the system evolves asymptotically towards a finite limit if we push the tachyon in the direction in which the potential has a local minimum, but hits a singularity if we push it in the direction where the potential is unbounded from below.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time derivatives, and hence it is not a priori clear how to set up the initial value problem, the theory contains a family of time dependent solutions characterized by the initial position and velocity of the tachyon field. We write down the world-sheet action of the boundary conformal field theories associated with these solutions and study the corresponding boundary states. For D-branes in bosonic string theory, the energy momentum tensor of the system evolves asymptotically towards a finite limit if we push the tachyon in the direction in which the potential has a local minimum, but hits a singularity if we push it in the direction where the potential is unbounded from below.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. | contribution 0.99 | 0.83 | 0.11 | asserted 0.82 |
| s1 | Despite the fact that the string field theory action contains infinite number of time derivatives, and hence it is not a priori clear how to set up the initial value problem, the theory contains a family of time dependent solutions characterized by the initial position and velocity of the tachyon field. | result 0.82 | 0.66 | 0.21 | asserted 1.00 |
| s2 | We write down the world-sheet action of the boundary conformal field theories associated with these solutions and study the corresponding boundary states. | contribution 0.73 | 0.93 | 0.06 | asserted 0.98 |
| s3 | For D-branes in bosonic string theory, the energy momentum tensor of the system evolves asymptotically towards a finite limit if we push the tachyon in the direction in which the potential has a local minimum, but hits a singularity if we push it in the direction where the potential is unbounded from below. | result 1.00 | 0.83 | 0.43 | asserted 0.98 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
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- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
112 arXiv papers cite this in 168 sentences
Papers citing it · 89 sentences without a confident label
Uses its method or tool 2 papers
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We will follow the approach of [ref] and first expand $_n$ as a power series, in powers of the boundary interaction.
N-point functions in rolling tachyon background · Boundary amplitudes in timelike Liouville theory · 1.00
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An alternative route is through the boundary states [ref] .
Tachyon solutions in boundary and cubic string field theory · Rolling solution of bosonic boundary SFT · 0.91
Compares with it 4 papers
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However, when we perform the string worldsheet theory analysis (along the lines of [ref] ), surprisingly we find that the result is almost the same as ([ref]), with maximum 1% relative deviation.
Disk Partition Function and Oscillatory Rolling Tachyons · Introduction · 0.99
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Our results imply, in particular, that the boundary state $|(Ψ)⟩$ calculated from the known rolling tachyon solutions of open string field theory coincides with the BCFT boundary state discussed in [ref] .
The boundary state from open string fields · Introduction · 0.95
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By comparing the action ([ref]) with the open string tachyon effective action given in [ref] , we get the tachyon potential as $V(T) = τ_f√(1+ l^2/R^2)/H(R(T))$ which is different than that given in [ref] .
Fundamental String (Membrane) Orbiting D5(M5)-branes · F-string Orbiting a stack of D5-branes · 0.93
Cites it as support 3 papers
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A spacelike brane, or an S-brane, in Minkowski spacetime cannot preserve any SUSY [ref] .
BPS Wilson loops in Minkowski spacetime and Euclidean space · Conclusion and discussion · 0.99
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However, this is not the case, and this is in accordance with the fact that time-dependent rolling solutions are distinct from the vacuum solution [ref] .
Mapping Tachyon effective field theory to a subsector of Klein-Gordon theory · Coherent state and initial D-brane system · 0.96
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Therefore, the attractor is stable against various potential shapes and cosmic red-shifts; and 2) after the tachyon condenses into cold matter form [ref] , tachyon matter gets red-shifted to sub-dominated without ruining the desired inflation phase.
Kinetically stabilized inflation · Introduction · 0.96
Cites it as background 65 papers
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Among the models connected to the Dark Energy for the present article we will consider a scalar field given by a relativistic Lagrangian and called Tachyonic field [ref] .
Interaction between Generalized Varying Chaplygin gas and Tachyonic Fluid · Introduction · 0.99
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Introduction The condensation of the tachyonic mode (or modes) present in an unstable brane system in string theory was found to lead to pressureless tachyon matter [ref] .
The energy-momentum tensor of perturbed tachyon matter · Introduction · 0.96
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These models were introduced in [ref] , and their cosmological consequences have been previously studied in detail in [ref] .
Varying Alpha Generalized Dirac-Born-Infeld Models · Tachyon field · 0.94
Discussion
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