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Generalized Riemann curvature corrections to type II supergravity
High Energy Physics - Theory · Submitted 17 Mar 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The new Lagrangian density is then equivalent to the replacement of the generalized Riemann curvature into the expression $t_8t_8R^4$.
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The abstract, sentence by sentence
We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$, is not fully consistent with the S-matrix elements in the superstring theory. In particular, they produce non-zero S-matrix elements for odd number of B-field strengths which are not consistent with the string theory results. Using the consistency of the couplings with the linear T-duality as a guiding principle, we consider all T-duality invariant couplings and fix their coefficients by requiring them to be consistent with the S-matrix elements. The new Lagrangian density is then equivalent to the replacement of the generalized Riemann curvature into the expression $t_8t_8R^4$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$, is not fully consistent with the S-matrix elements in the superstring theory. | result 0.81 | 0.77 | 0.49 | asserted 0.98 |
| s1 | In particular, they produce non-zero S-matrix elements for odd number of B-field strengths which are not consistent with the string theory results. | result 0.93 | 0.42 | 0.16 | asserted 1.00 |
| s2 | Using the consistency of the couplings with the linear T-duality as a guiding principle, we consider all T-duality invariant couplings and fix their coefficients by requiring them to be consistent with the S-matrix elements. | method 0.96 | 0.93 | 0.12 | asserted 0.98 |
| s3 | The new Lagrangian density is then equivalent to the replacement of the generalized Riemann curvature into the expression $t_8t_8R^4$. | result 0.95 | 0.87 | 0.51 | asserted 1.00 |
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The paper
Original abstract
We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$, is not fully consistent with the S-matrix elements in the superstring theory. In particular, they produce non-zero S-matrix elements for odd number of B-field strengths which are not consistent with the string theory results. Using the consistency of the couplings with the linear T-duality as a guiding principle, we consider all T-duality invariant couplings and fix their coefficients by requiring them to be consistent with the S-matrix elements. The new Lagrangian density is then equivalent to the replacement of the generalized Riemann curvature into the expression $t_8t_8R^4$.
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References
How the literature uses it
10 arXiv papers cite this in 17 sentences
Papers citing it · 11 sentences without a confident label
Uses its data or values 1 paper
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The low energy expansion of this S-matrix element produces the following eight-derivative couplings in the string frame [ref] : S_3 ⊃ γ_3/κ^2∫d^10x√(-g) e^-2Φ () S2 where the normalization factor is $γ_3=(3)/2^5$, and the Lagrangian density has the following eight independent terms: () = 1/8_κγ^δβ ^κγτα_μνδτ ^μν_αβ + 1/32_αβκγ ^αβκγ_μνδτ ^μνδτ + 1/16_αβ^δτ ^αβκγ_μνδτ ^μν_κγ - 1/4_κγ^αβ ^κγδ_α_μνδτ ^μντ_β + 1/4 ^α_βκγ_μνδτ ^μβκγ ^ν_α^δτ + 1/8 ^α_β^δτ_μνδτ ^μβκγ ^ν_ακγ + 1/2 ^α_β^κ_γ_μνδτ ^μβδγ ^ν_α^τ_κ + ^α_β^δ_γ_μνδτ ^μβκγ ^ν_α^τ_κL where $_μναβ$ is the linear part of the following tensor: _μναβ = R_μναβ+H_μν[α;β] Here $H_μν[α;β]=1/2∇_βH_μνα-1/2∇_αH_μνβ$.
Minimal gauge invariant couplings at order $\alpha'^3$: NS-NS fields · Constraint from 4-point functions · 0.95
Compares with it 2 papers
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There are only two couplings when there is no B-field, L_3(g,Φ) = 2 R_α^ϵ_γ^ε R^αβγδ R_β^μ_ϵ^ζ R_δζεμ + R_αβ^ϵε R^αβγδ R_γ^μ_ϵ^ζ R_δζεμRRf The couplings in this structure are exactly the couplings that have been found by the S-matrix and sigma-model calculations [ref] provided that one chooses the overall parameter to be $c=-(3)/2^6$.
On NS-NS couplings at order $\alpha'^3$ · Introduction · 0.92
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Writing the effective action as _3 = -2c/κ^2∫d^10x √(-G)e^-2Φ_3S3 where $c$ is the overall parameter, the couplings involving only metric and dilaton are the following: L_3(G,Φ) = 2 R_α^ϵ_γ^ε R^αβγδ R_β^μ_ϵ^ζ R_δζεμ + R_αβ^ϵε R^αβγδ R_γ^μ_ϵ^ζ R_δζεμRRf It is exactly the couplings that have been found by the S-matrix and sigma-model calculations [ref] provided that one chooses the overall parameters to be $c=-(3)/2^6$.
Effective action of type II superstring theories at order $\alpha'^3$: NS-NS couplings · Results · 0.98
Cites it as support 1 paper
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This observation aligns with the fact that the four-point sphere-level S-matrix elements involving one $B$-field and three gravitons, or three $B$-fields and one graviton, are zero in superstring theory (see, for example, [ref] ).
An NS-NS basis for odd-parity couplings at order $\alpha'^3$ · Discussion · 0.96
Cites it as background 2 papers
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The $t_8$ tensor was first defined in [ref] , the contraction of $t_8$ with four arbitrary antisymmetric matrices $M^1, ⋯, M^4$ is t_hkmnpqrsM^1_hkM^2_mnM^3_pqM^4_rs=8(M^1M^2M^3M^4+M^1M^3M^2M^4+M^1M^3M^4M^2) -2(M^1M^2M^3M^4+M^1M^3M^2M^4+M^1M^4M^2M^3)t8 Using this tensor, the coupling $t_8t_8R^4$ can be written as [ref] [For the generalized Riemann curvature trans which does not have all symmetries of the Riemann curvature, the coupling $t_8t_8R̅^4$ has different structure [ref] .] t_8t_8R^4 ≡ t_μ_1⋯μ_8t_ν_1⋯ν_8R_μ_1μ_2_ν_1ν_2R_μ_3μ_4_ν_3ν_4R_μ_5μ_6_ν_5ν_6R_μ_7μ_8_ν_7ν_8 = 3·2^7[R_hkmnR_krnpR_rs_qmR_sh_pq+1/2R_hkmnR_krnpR_rspqR_shqmY3 -1/2R_hkmnR_krmnR_rspqR_shpq -1/4R_hkmnR_krpqR_rs_mnR_sh_pq +1/16R_hkmnR_khpqR_rsmnR_srpq+1/32R_hkmnR_khmnR_rspqR_srpq]Using the linearized Riemann curvature R, one finds the vertex V_R^4(1,2,3,h)_mn = 3·2^7iγ(3)[k_1.φ_2 k_1.φ_3 k_2.ρ_3 k_2.φ_1 k_3.ρ_1 k_3.ρ
S-duality invariant dilaton couplings at order $\alpha'^3$ · Five-point amplitude · 0.85
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For the type II string, the higher derivative corrections at order $𝒪(α'^3)$ have been investigated in [ref] and completed via T-duality in [ref] .
T-duality building blocks for $\alpha'$ string corrections · Introduction · 0.96
What it cites · 5 sentences without a confident label
Cites as support 1 paper
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It has been shown in [ref] that such couplings at four-field level are consistent with the linear T-duality.
Ricci curvature corrections to type II supergravity · Introduction · 0.98
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