{"arxiv_id":"1303.4034","incoming":{"papers":10,"sentences":17,"groups":[{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2006.09193","title":"Minimal gauge invariant couplings at order $\\alpha'^3$: NS-NS fields","url":"/paper/2006.09193","section":"Constraint from 4-point functions","sentence":"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 $H_μν[α;β]=1/2∇_βH_μνα-1/2∇_αH_μνβ$.","intent_p":0.95,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2012.15091","title":"On NS-NS couplings at order $\\alpha'^3$","url":"/paper/2012.15091","section":"Introduction","sentence":"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 $c=-(3)/2^6$.","intent_p":0.92,"contests_p":null},{"arxiv_id":"2011.02753","title":"Effective action of type II superstring theories at order $\\alpha'^3$: NS-NS couplings","url":"/paper/2011.02753","section":"Results","sentence":"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 $c=-(3)/2^6$.","intent_p":0.98,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2402.16496","title":"An NS-NS basis for odd-parity couplings at order $\\alpha'^3$","url":"/paper/2402.16496","section":"Discussion","sentence":"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] ).","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1306.6851","title":"S-duality invariant dilaton couplings at order $\\alpha'^3$","url":"/paper/1306.6851","section":"Five-point amplitude","sentence":"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","intent_p":0.85,"contests_p":null},{"arxiv_id":"2210.16593","title":"T-duality building blocks for $\\alpha'$ string corrections","url":"/paper/2210.16593","section":"Introduction","sentence":"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] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":11},"outgoing":{"papers":4,"sentences":7,"groups":[{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1210.4379","title":"Ricci curvature corrections to type II supergravity","url":"/paper/1210.4379","section":"Introduction","sentence":"It has been shown in [ref] that such couplings at four-field level are consistent with the linear T-duality.","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":5},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1303.4034"}}