REVIEW
Tachyon Condensation on the Brane Antibrane System
High Energy Physics - Theory · Submitted 26 May 1998 · 16 references
Pith's verdict: The founding argument for tachyon condensation on brane–antibrane pairs: a clean, explicit physics argument with one load-bearing continuity step the paper itself hedges.
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Referee report
The paper
The paper claims
Sen argues that at the minimum of the tachyon potential on a coincident D-brane/anti-D-brane pair, the negative potential energy exactly cancels the combined brane tension, leaving a zero-energy configuration with space-time supersymmetry.
The reading
What carries the argument
The load-bearing device is a T-duality plus 't Hooft-twist argument that converts a strongly coupled, tachyonic question into a weakly coupled gauge-theory minimization. The magnetic flux on each wrapped brane is chosen so that the D0-brane charges add, and T-duality on both circles interchanges 0-brane and 2-brane charge, turning the anti-brane's flux into the opposite sign. The resulting $U(2)$ gauge theory on the dual torus has a background field $A_2 = 2pi x_1 sigma_3/Ṽ$ with twisted boundary conditions set by $Omega_1 = exp(i x_2 sigma_3/Ṙ_2)$, $Omega_2 = 1$. Because there is no obstruction to removing the twist, a gauge transformation $g(x_1,x_2)$ exists making both transition functions the identity while remaining periodic, so the lowest-energy configuration has vanishing field strength for both the $U(1)$ and $SU(2)$ parts. That vanishing field strength is what fixes the minimum energy at exactly twice the single-brane tension, i.e. at the BPS bound, and the continuity of BPS saturation is what carries that value back to the physical large-radius brane-antibrane system.
Extended reading notes
Core claim
The paper claims that at the classical minimum of the tachyonic potential the negative energy density of the potential exactly cancels the sum of the tensions of the brane and the anti-brane, so that the energy per unit area of the pair vanishes. The argument proceeds by deforming the problem into a regime where the answer is computable. A D2-brane and anti-D2-brane are wrapped on a torus $T^2$ with one unit of magnetic flux each, chosen so that each carries $+1$ unit of D0-brane charge, with field strength $F_{12} = 2V^{-1}$ in units where $V$ is the torus area. In the limit of small radii the system is T-dualized to a large dual torus, where it is described by a supersymmetric $U(2)$ gauge theory with a background gauge field lying entirely in the $SU(2)$ part, subject to 't Hooft twisted boundary conditions. The tachyonic modes of the original string theory reappear as the statement that this constant-field-strength configuration is not the lowest-energy field configuration allowed by those boundary conditions. Because $SU(2)$ is simply connected, a gauge transformation exists that makes the twist trivial, after which the minimum is plainly zero field strength and the mass is just the sum of the two D2-brane tensions, $M = 2R_1R_2/ĝ$, saturating the BPS bound. Sen then invokes continuity: a configuration that saturates the BPS bound at the classical minimum should keep saturating it as the parameters are varied, so the mass formula survives the trip back to the original variables, giving $M = 2/g$ and an energy per unit area $1/(2pi^2 R_1 R_2 g)$ that goes to zero as the torus grows. The paper closes with a proposal that the same logic identifies the stable non-BPS $SO(32)$ spinor of type I theory with a tachyonic kink on a D-string/anti-D-string pair.
Load-bearing premise
The argument assumes that a configuration sitting exactly on the BPS bound at the computable small-radius end continues to sit exactly on that bound as the radii are varied continuously back to the physical large-radius regime, with no phase transition or loss of the state along the way.
Editorial extensions
If this is right
- The endpoint of brane-antibrane annihilation is a zero-energy, zero-tension configuration, so the process does not leave behind a positive-energy remnant and the space-time supersymmetry broken by the brane-antibrane pair is restored.
- The tachyon potential's depth is fixed to equal the sum of the brane tensions, which turns a statement about the potential into a quantitative identity that any microscopic computation of the tachyon potential must reproduce.
- In type I string theory, a kink in the tachyon field on a D-string/anti-D-string pair, where the tachyon runs from $-T_0$ to $+T_0$, is identified as a candidate for the stable non-BPS $SO(32)$ spinor state, with the anti-periodicity needed around a compact circle supplied by a relative $Z_2$ Wilson line.
- The argument is presented as extending to other D$p$-branes, not just the D2-brane worked out explicitly, since only the wrapping and flux bookkeeping changes.
- Wound D-string bound states carrying both spinorial and winding charge acquire a natural description as tachyon kinks on the wrapped pair.
Reading between the lines
- The continuity step is doing more work than its one-line justification suggests: BPS saturation is being assumed to survive an interpolation that passes through a region where the effective description changes from a weakly coupled gauge theory to a strongly coupled string theory, and a reader could reasonably want the moduli-space metric checked along that path.
- If the cancellation is exact, the tachyon potential must be bounded below and its minimum must be reached at finite field value; a potential that runs away to zero energy only asymptotically would leave a residual negative energy density and spoil the conclusion, so the shape of the potential away from the minimum is a hidden input.
- The same flux-and-twist bookkeeping suggests a sharper check: the mass of the twisted-sector ground state on the dual torus can be computed at finite $\tilde R_i$, and matching its large-radius limit against the brane tensions would test the continuity assumption rather than assume it.
- The type I kink proposal makes a concrete prediction about the quantum numbers of a stable non-BPS state, which neighbouring work on wound D-string bound states could confirm or exclude.
Original abstract
A coincident D-brane - anti-D-brane pair has a tachyonic mode. We present an argument showing that at the classical minimum of the tachyonic potential the negative energy density associated with the potential exactly cancels the sum of the tension of the brane and the anti-brane, thereby giving a configuration of zero energy density and restoring space-time supersymmetry.
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
A coincident D-brane - anti-D-brane pair has a tachyonic mode. We present an argument showing that at the classical minimum of the tachyonic potential the negative energy density associated with the potential exactly cancels the sum of the tension of the brane and the anti-brane, thereby giving a configuration of zero energy density and restoring space-time supersymmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A coincident D-brane - anti-D-brane pair has a tachyonic mode. | background 1.00 | 0.14 | 0.04 | asserted 1.00 |
| s1 | We present an argument showing that at the classical minimum of the tachyonic potential the negative energy density associated with the potential exactly cancels the sum of the tension of the brane and the anti-brane, thereby giving a configuration of zero energy density and restoring space-time supersymmetry. | result 0.83 | 0.89 | 0.92 | asserted 1.00 |
What was examined, and what was not
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References
How later papers used it
98 later papers cite it
2 later papers by other authors are listed below: 1 used its method or tool and 1 cited it as support.
Uses its method or tool 1 of 4 papers with this label
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Recast T-branes in this paper's tachyon condensation picture.
T-branes as branes within branes (2014) · 0.89 · paraphrased: the licence does not allow quoting
Cites it as support 1 of 6 papers with this label
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However, following Sen's conjecture [ref] , a non-BPS brane with the tachyon condensed in its tachyon vacuum corresponds to not having any brane at all.
Connecting flux vacua through scalar field excursions (2023) · Non-BPS branes as domain walls · 0.95
How the literature uses it
95 arXiv papers cite this in 120 sentences
Papers citing it · 87 sentences without a confident label
Uses its method or tool 4 papers
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In this paper, we recast T-branes in Sen's tachyon condensation picture [ref] .
T-branes as branes within branes · Introduction · 0.89
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In order to concretely analyze the 3d $𝒩=2$ theories that arise from M-theory geometric engineering on ccDV fourfolds, we will make ample use of the formalism furnished by tachyon condensation [ref] .
M-theory geometric engineering for rank-0 3d $\mathcal{N}=2$ theories · Tachyon condensation formalism · 1.00
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To arrive at this action, we followed the analysis of GHY [ref] (also, [ref] ), whose own starting point was Sen's effective action for the final state of the decay of unstable $D$-branes at the end of tachyon condensation and near the minimum of the tachyon potential where it vanishes [ref] .
Kerr Black hole mimickers sourced by a string fluid · Lagrangian and equations of motion · 0.81
Compares with it 1 paper
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From the conservation equation ([ref]) we then know that the density of quintessence scales in the range $a^-6$ to $a^0$, while for the scalar the range is restricted to $a^-3$ and $a^0$.[This is the same range accessible to the simplest DBI tachyon model [ref] , but our equation of motion differs from that case.] This property suggests that the scalar may play the role of both dark matter (scaling approximately as $a^-3$) and dark energy (scaling approximately as $a^0$).
Unified dark energy and dark matter from a scalar field different from quintessence · Dynamical equations · 0.91
Cites it as support 3 papers
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Using these relations, we have calculated the ADM mass and have shown that the solution and the ADM mass capture all the required properties and give a correct description of the tachyon condensation [ref] as advocated by Sen [ref] on the D-$D̅$ system.
On Brane-Antibrane Forces · Introduction · 0.96
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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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This projection is also corroborated in superstring theories [ref] and evident in the first [ref] and second [ref] quantizations in string theories [ref] .
Phenomenology of Strong Interactions -- Towards an Effective Theory for Low Energy QCD · Introduction · 0.97
Cites it as background 24 papers
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The starting point for the analysis in [ref] is Sen's effective action for the decay of unstable $D$-branes; specifically, at the end of tachyon condensation and near the minimum of the tachyon potential, where it is vanishing [ref] .
Frozen stars: Black hole mimickers sourced by a string fluid · Born-Infeld effective Lagrangian and BIons · 0.84
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It has been known for a while that all physically consistent D-branes in type IIB can be described as the by-product of tachyon condensation between D9's and anti-D9's [ref] .
T-branes as branes within branes · D7-branes as D9/anti-D9 tachyon condensates · 0.85
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Meanwhile, in non-supersymmetric cases one of the most remarkable progress is the open string tachyon condensation [ref] .
Gravitational Dual of Tachyon Condensation · Introduction · 0.99
Discussion
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