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The Dilaton Theorem and Closed String Backgrounds
High Energy Physics - Theory · Submitted 8 Nov 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus the ``dilaton theorem'', familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.
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The abstract, sentence by sentence
The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. It is given by the action of the BRST operator on another state $\x$, but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and $\x$ insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of $\x$. Surprisingly, the ghost number anomaly makes this a trivial deformation. While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. Thus the ``dilaton theorem'', familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. | background 0.54 | 0.24 | 0.07 | asserted 1.00 |
| s1 | It is given by the action of the BRST operator on another state $\x$, but remains nontrivial in the semirelative BRST cohomology. | background 0.49 | 0.42 | 0.05 | asserted 1.00 |
| s2 | When local coordinates arise from metrics we show that dilaton and $\x$ insertions compute Riemannian curvature and geodesic curvature respectively. | result 0.90 | 0.86 | 0.05 | asserted 1.00 |
| s3 | A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of $\x$. | result 0.35 | 0.70 | 0.06 | asserted 0.99 |
| s4 | Surprisingly, the ghost number anomaly makes this a trivial deformation. | result 0.92 | 0.71 | 0.07 | asserted 1.00 |
| s5 | While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. | interpretation 0.85 | 0.77 | 0.33 | asserted 1.00 |
| s6 | We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. | result 0.49 | 0.89 | 0.32 | asserted 1.00 |
| s7 | Thus the ``dilaton theorem'', familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action. | interpretation 0.55 | 0.78 | 0.76 | asserted 1.00 |
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Original abstract
The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. It is given by the action of the BRST operator on another state $\x$, but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and $\x$ insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of $\x$. Surprisingly, the ghost number anomaly makes this a trivial deformation. While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. Thus the ``dilaton theorem'', familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.
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References
How the literature uses it
18 arXiv papers cite this in 38 sentences
Papers citing it · 29 sentences without a confident label
Builds on it 1 paper
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This can be generalized to an expression for the string field that describes a constant dilaton shift around a nontrivial background solution $Ψ$ [ref] , of the form K_Ψ= Q_B ϰ- Ψ+ [Ψ⊗ϰ] + ⋯, where $⋯$ stands for higher order terms in $Ψ$.
Conformal Perturbation Theory and Tachyon-Dilaton Eschatology via String Fields · Decoupling the linear dilaton sector · 0.91
Uses its method or tool 4 papers
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If \(p_a\) is a special puncture and the metric is written locally as \(ds=ρ^w_a(w_a,w̅_a)|dw_a|\), then the Bergman–Zwiebach prescription [ref] fixes the local coordinate \(w_a\) up to constant phase by [equation] Equivalently, the metric determines a normalized local-coordinate map \(z=g_a(w_a)\) at each special puncture.
Closed String Field Theory in 25.99 Dimensions · States, Operators, and Metric-Adapted Special Coordinates · 0.85
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Given $Q$, the nilpotent BRST operator, $Ψ$, the ghost-two closed string field, $κ$, a coupling constant proportional to the closed string coupling, $ω$, the symplectic form, and $L_n(...)$ denoting Grassmann-odd string products, the starting point is a tree-level closed, bosonic string field theory action given by [equation] A result in [ref] was used, where a field variation “U” that rescales the coupling constant $κ$ was shown to exist: [equation] Using this variation of the string field, (a) the variation of the closed string field theory action is zero, and (b) that variation produces the action time a constant different than one, implying that the on-shell action vanishes: [equation]
de Sitter in String Theory vs. Gibbons & Hawking · A bosonic string field theory argument · 0.88
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In [ref] Bergman and Zwiebach find an expression for the form that one needs to integrate in order to compute the amplitude with one ghost dilaton (see [ref] for a derivation). ω_D = d ξ∧d ξ̅ (_ξ̅ β_4 + _ξβ̅_̅4̅) This means that ⟨T,T,T,D⟩= -1/2πi t^3 d ∮_ℛ ( -d ξ β_4 + dξ̅ β̅_̅4̅) + O(y) where we used the complex version of the Stokes theorem ∫_Ωd ξ∧d ξ̅ (_ξ f(ξ,ξ̅) + _ξ̅ g(ξ,ξ̅)) = ∮_Ω (d ξ̅ f(ξ,ξ̅) - d ξ g(ξ,ξ̅)) .
Closed string tachyon condensation revisited · Elementary contributions to dilaton amplitudes · 0.88
Cites it as support 1 paper
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This expectation is further compounded by the recent result of Erler on the vanishing of the on-shell closed SFT action [ref] , based on the dilaton theorem [ref] , which indicates that the only contribution to the on-shell action comes from the boundary.
Boundary terms in string field theory · Introduction · 1.00
Cites it as background 3 papers
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In string theory, soft dilaton theorem tells us that if in a given amplitude we insert a zero momentum dilaton vertex operator, we get back the same amplitude up to a constant of proportionality [ref] .
A New Term in Type II Effective Action · Introduction · 0.98
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In fact, it is unclear if this solution can ever accommodate a local worldsheet CFT description in the conventional sense.[A related concept in SFT is the background independence [ref] , which asserts that different SFTs described by different string couplings or worldsheet CFTs sharing the moduli space are related to each other by string field redefinitions.
A Worldsheet Description of Flux Compactifications · Introduction · 0.95
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For example, it has been established that the on-shell action vanishes up to boundary terms in closed string field theory [ref] , thanks to the dilaton theorem [ref] .
Topological recursion for hyperbolic string field theory · Discussion · 0.87
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