REVIEW
Field Theory of Tachyon Matter
High Energy Physics - Theory · Submitted 17 Apr 2002 · 18 references
Pith's verdict: Sen fixes the potential in the DBI tachyon action and shows one choice delivers both near-vacuum properties; the derivations are short, checkable, and the only speculative piece is flagged as a guess.
T0 · AI review
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Referee report
The paper
The paper claims
A single square-root action for the tachyon can reproduce both of its known late-time behaviours: no plane waves near the vacuum, and a pressure that dies off exponentially as the field rolls.
The reading
What carries the argument
The load-bearing object is the square-root Lagrangian $e^{-2T/2}2{-2A}$ with $A_{22}=2_{22}+2_2T2_2T$, the same Born-Infeld structure used for the brane's world-volume gauge field but with the tachyon in place of field strength. The exponential prefactor is the piece that was previously left free and is now fixed: it is what makes the pressure fall off at exactly the rate the string-side computation demands, and what makes the field redefinition $2=e^{-2T/4}$ turn the action into a scale-invariant degree-two functional of $2$, which is the property that forbids plane waves and simultaneously permits the arbitrarily dilute dust configurations.
Extended reading notes
Core claim
The paper proposes the action $S=-2 d^{p+1}x e^{-2T/2}2{1+2^{22}2_22T2_2T}$ for the tachyon on an unstable D$p$-brane near the minimum of its potential, with $2=1$ for the bosonic string and $2=22$ for the superstring. Two checks carry the claim. For homogeneous rolling, conservation of $T_{00}$ forces $2_0T2 1$ at late times, so $T=x^0+Ce^{-2x^0}+2(e^{-22x^0})$, and the pressure computed from the same action becomes $p2-22C e^{-2x^0}$, matching the exponential fall-off known from the string-side analysis. For the absence of plane waves, the author rewrites the action in terms of $2=e^{-2T/4}$, where it is homogeneous of degree two in $2$, and substitutes the ansatz $2=a e^{ik_2x^2}$ into the full equations of motion. The result is $a/2{1-2{16}{2^2}2^{22}k_22k_2}=0$, which has no non-trivial solution for any finite $k_2$; expanding to quadratic order in $k$ recovers the would-be mass-shell condition $-2^{22}k_22k_2=2^2/8$, so the higher-derivative terms are exactly what removes the particle. The author then passes to the Hamiltonian formalism, where $H=2{2^2+e^{-2T}2{1+2_iT2_iT}}$, and exhibits solutions with $2_0T=1$, $2_iT=0$ and $2(x)=f(2 x)$ for an arbitrary function $f$. In terms of $u_2=2_2T$ and $2(x)=2/2_0T$, these obey $2^{22}u_2u_2=-1$ and $2_2(2u^2)=0$, with $T_{22}=2u_2u_2$: the equations of gradient flow for non-interacting dust, with $u_2$ the local velocity four-vector.
Load-bearing premise
The action is claimed to be a good approximation only when second and higher derivatives of the tachyon are small, so corrections such as $(2_22^2T)^2$ inside the square root are dropped without being derived from string field theory or estimated in size.
Editorial extensions
If this is right
- Any spatially homogeneous initial configuration of the tachyon evolves towards the minimum with pressure falling as $e^{-2x^0}$, with the exponent $2=1$ (bosonic) or $2=22$ (superstring) fixed by the exponential prefactor.
- Plane-wave quantization around the tachyon vacuum is impossible in this theory at any momentum, so the would-be tachyon particle of mass $2/2{2}$ exists only in the truncated two-derivative approximation.
- The theory admits classical tachyon-matter configurations whose energy density has arbitrary spatial dependence and can be made arbitrarily small, because the equations are invariant under $T(x)2 2^{-1}T(2x)$.
- Localized lumps of tachyon matter can be boosted to arbitrary velocity, and configurations with different local velocities at different points obey the dust equations $2^{22}u_2u_2=-1$ and $2_2(2u^2)=0$.
- Coupling to gravity, the antisymmetric tensor and the dilaton goes through by replacing $2_{22}$ with $g_{22}+B_{22}$ and multiplying the Lagrangian by $e^{-2}$; the coupling to the Ramond-Ramond $p$-form is guessed to behave as $e^{-T/22}$ at large $T$.
Reading between the lines
- If the dust picture survives quantum corrections, tachyon matter is a candidate for a pressureless component of the universe's energy budget that clusters gravitationally while carrying no pressure, which is the behaviour usually attributed to cold dark matter; the paper stops short of saying so and only notes that quantum effects remain to be studied.
- The absence of plane waves is a statement about the quadratic fluctuation operator, not about the spectrum: it suggests the correct variables near the vacuum are hydrodynamic (energy density and local velocity) rather than particle-like, which would make the tachyon vacuum resemble a fluid rather than an empty state with a mass gap.
- The exponential prefactor's coefficient $2$ is fixed by matching a single number, the late-time pressure exponent; an independent derivation of that exponent from a first-principles worldsheet or string-field calculation would be the sharpest check on the whole construction.
- The guessed Ramond-Ramond coupling in eq. (29) is the most exposed piece: it is presented as an argument from symmetry rather than a boundary-state computation, so a direct calculation of the source produced by the rolling solution would confirm or correct it.
Original abstract
We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: 1) absence of plane-wave solutions around the minimum, and 2) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include non-relativistic matter with arbitrary spatial distribution of energy.
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 propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: 1) absence of plane-wave solutions around the minimum, and 2) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include non-relativistic matter with arbitrary spatial distribution of energy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a field theory for describing the tachyon on a brane-antibrane system near the minimum of the potential. | contribution 1.00 | 0.90 | 0.15 | asserted 0.79 |
| s1 | This field theory realizes two known properties of the tachyon effective action: 1) absence of plane-wave solutions around the minimum, and 2) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. | result 0.70 | 0.63 | 0.34 | asserted 1.00 |
| s2 | Classical solutions in this field theory include non-relativistic matter with arbitrary spatial distribution of energy. | result 0.98 | 0.84 | 0.25 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v4
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References
How the literature uses it
46 arXiv papers cite this in 62 sentences
Papers citing it · 25 sentences without a confident label
Compares with it 2 papers
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Furthermore, the pressure for this system has also been observed to fall off exponentially to zero at late times, much like that in the case of the rolling tachyon in the decay of a non-BPS D$p$-brane to tachyon matter whose equation of state corresponds to that of a pressureless fluid [ref] .
Proper acceleration, geometric tachyon and dynamics of a fundamental string near D$p$ branes · Introduction · 0.84
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Compared with the BCFT approach, physical quantities such as energy-momentum tensor obtained from these EFTs are qualitatively the same as, but slightly different from that in BCFT [ref] – [ref] .
Negative-Tension Branes and Tensionless 1/2 Brane in Boundary Conformal Field Theory · Introduction · 0.95
Cites it as support 3 papers
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However, as was shown in [ref] , the absence of plane wave solutions around the minima of the potential implies that such a perturbative quantisation is not possible.
Mapping Tachyon effective field theory to a subsector of Klein-Gordon theory · Failure of perturbative quantization · 0.98
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[ref] provided good indications that these overlaps between boundary states and test states are invariant under renormalization group flows.
Kondo flow invariants, twisted K-theory and Ramond-Ramond charges · The flat space case · 0.99
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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
Cites it as background 29 papers
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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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The dynamics of tachyon on an unstable D-p-brane in string theory can be described by the following effective action [ref] .
Mapping Tachyon effective field theory to a subsector of Klein-Gordon theory · Introduction · 0.90
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The case of time-like rolling is by now quite well-studied, using boundary state/$$-model methods [ref] , effective field theory models [ref] , and OSFT techniques [ref] .
Light-like tachyon condensation in Open String Field Theory · Introduction · 0.95
Discussion
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