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Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings
High Energy Physics - Theory · Submitted 7 Jun 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.
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The abstract, sentence by sentence
In the first part of this paper, we calculate the disk-level S-matrix elements of one RR, one NSNS and one NS vertex operators, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. We show that the massless poles of the amplitude at low energy are fully consistent with the known D-brane couplings at order $\alpha'^2$ which involve one RR or NSNS and two NS fields. Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order $\alpha'^2$. Some of these terms are reproduced by the Taylor expansion and the pull-back of two closed string couplings, some other couplings are reproduced by linear graviton in the second fundamental form and by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed and two open string couplings. In the second part, we write all independent covariant contractions of one RR, one NSNS and one NS fields with unknown coefficients. We then constrain the couplings to be consistent with the linear T-duality and with the above contact terms. Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the first part of this paper, we calculate the disk-level S-matrix elements of one RR, one NSNS and one NS vertex operators, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. | contribution 0.82 | 0.94 | 0.09 | asserted 0.98 |
| s1 | We show that the massless poles of the amplitude at low energy are fully consistent with the known D-brane couplings at order $\alpha'^2$ which involve one RR or NSNS and two NS fields. | result 0.99 | 0.88 | 0.12 | asserted 0.96 |
| s2 | Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order $\alpha'^2$. | result 0.75 | 0.96 | 0.10 | asserted 1.00 |
| s3 | Some of these terms are reproduced by the Taylor expansion and the pull-back of two closed string couplings, some other couplings are reproduced by linear graviton in the second fundamental form and by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed and two open string couplings. | result 0.69 | 0.80 | 0.09 | asserted 0.99 |
| s4 | In the second part, we write all independent covariant contractions of one RR, one NSNS and one NS fields with unknown coefficients. | method 0.79 | 0.96 | 0.04 | asserted 0.99 |
| s5 | We then constrain the couplings to be consistent with the linear T-duality and with the above contact terms. | method 0.95 | 0.93 | 0.06 | asserted 0.96 |
| s6 | Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients. | result 0.98 | 0.97 | 0.65 | asserted 1.00 |
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The paper
Original abstract
In the first part of this paper, we calculate the disk-level S-matrix elements of one RR, one NSNS and one NS vertex operators, and show that they are consistent with the amplitudes that have been recently found by applying various Ward identities. We show that the massless poles of the amplitude at low energy are fully consistent with the known D-brane couplings at order $\alpha'^2$ which involve one RR or NSNS and two NS fields. Subtracting the massless poles, we then find the contact terms of one RR, one NSNS and one NS fields at order $\alpha'^2$. Some of these terms are reproduced by the Taylor expansion and the pull-back of two closed string couplings, some other couplings are reproduced by linear graviton in the second fundamental form and by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed and two open string couplings. In the second part, we write all independent covariant contractions of one RR, one NSNS and one NS fields with unknown coefficients. We then constrain the couplings to be consistent with the linear T-duality and with the above contact terms. Interestingly, we have found that up to total derivative terms and Bianchi identities, these constraints uniquely fix all the unknown coefficients.
Human review
How the literature uses it
6 arXiv papers cite this in 14 sentences
Papers citing it · 11 sentences without a confident label
Builds on it 2 papers
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In this section, we summarize all flux corrections to D-branes in superstring theory from the papers [ref] that are non-vanishing for the KS throat, extend them to the NS5-brane and evaluate them at the tip of the KS throat.
$\alpha'$ corrections to KPV: An uplifting story · Flux corrections on the NS5-brane · 0.91
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We do so by extending the leading order calculation of the potential of a nonabelian $D3$-brane stack of [ref] to include the next-to-leading order commutator corrections as well as the same set of $α'$ corrections [ref] which has been encountered in [ref] but here as corrections to $D3$-branes.
Higher order corrections to KPV: The nonabelian brane stack perspective · Introduction · 1.00
Cites it as background 1 paper
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Moreover, there are $α'$ corrections to the CS action which are computed in [ref] .
$\alpha'$ corrections to KPV: An uplifting story · Flux corrections that vanish for the KS set up · 0.80
What it cites · 43 sentences without a confident label
Uses the method or tool of 2 papers
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To find the correlator of $ψ$, one should use the Wick-like rule for the correlation function involving an arbitrary number of $ψ$'s and two $S$'s [ref] .
On RR couplings on D-branes at order $O(\alpha'^2)$ · The S-matrix element in string theory · 0.97
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In this subsection, using the Mathematica package "xAct" [ref] , we write all contractions of one massless RR, one NSNS and one NS fields in which each field has at most two derivatives.
xTras: a field-theory inspired xAct package for Mathematica · All contractions of one RR, one NSNS and one NS fields · 1.00
Uses data or values from 3 papers
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The explicit form of these integrals have been found in [ref] , _1 = 4(z̅_1 z̅_2+z_1( z_2-z̅_1+z̅_2)+z_2(z̅_1-2z̅_2) /z_12 z_31 z_2 1̅ z_3 1̅ z_12̅ z_2 2̅ z_1̅ 2̅K _2 = 2z_22̅/z_12 z_32 z_2 1̅ z_1 2̅ z_32̅ z_1̅ 2̅K = 2z_11̅/z_12 z_13 z_2 1̅ z_3 1̅ z_12̅ z_1̅ 2̅Kint where $z_ij=z_i-z_j$ and $z_3=x_3$.
Ramond-Ramond S-matrix elements from T-dual Ward identity · The S-matrix element in string theory · 0.91
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The explicit form of these integrals have been found in [ref] , _1 = 4(z̅_1 z̅_2+z_1( z_2-z̅_1+z̅_2)+z_2(z̅_1-2z̅_2) /z_12 z_31 z_2 1̅ z_3 1̅ z_12̅ z_2 2̅ z_1̅ 2̅K _2 = 2z_22̅/z_12 z_32 z_2 1̅ z_1 2̅ z_32̅ z_1̅ 2̅K = 2z_11̅/z_12 z_13 z_2 1̅ z_3 1̅ z_12̅ z_1̅ 2̅Kint where $z_ij=z_i-z_j$ and $z_3=x_3$.
Tree-level S-matrix elements from S-duality · The S-matrix element in string theory · 0.91
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Then the $α'$ expansion produce the following expansions [ref] : = 2/p_1.p_3-π^2/3p_3.D.p_3+⋯ _1 = -2/3p_1.p_3-8/3p_1.D.p_1+4/3 π^2 p_1.p_3+1/2 π^2 p_3.D.p_3-1/6 π^2 p_1.D.p_1 +16 π^2 (p_2.p_3)^2/3 p_3.D.p_3 +⋯ _2 = -2/p_1.p_3+π^2/3p_1.D.p_1+⋯expand where dots refer to the terms with more than two momenta.
Towards extending the Chern-Simons couplings at order $O(\alpha'^2)$ · Contact terms at low energy · 0.92
Compares with 1 paper
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We have explicitly calculated the amplitude amp23 for RR $(p-1)$-form and found exactly the result in ext1 with the following expressions for the two integrals: _3 = 2 (x_3 (z̅_1+z_1-2 z_2)+z_2 z̅_1+z_1 (z_2-2 z̅_1)) (x_3 (z̅_1-2 z̅_2+z_1)-2 z_1 z̅_1+(z̅_1+z_1) z̅_2)/3 (z_1-z_2) (z_1-z̅_1) (z_2-z̅_1) (z_1-z̅_2) (z̅_1-z̅_2) (x_3-z_1) (x_3-z_2) (x_3-z̅_1) (x_3-z̅_2)K _4 = 4 (z̅_1 z̅_2+z_1 (-2 z̅_1+z̅_2+z_2)+z_2 (z̅_1-2 z̅_2))/3 (z_2-z_1) (z_1-z̅_1) (z_2-z̅_1) (z_1-z̅_2) (z̅_1-z̅_2) (x_3-z_2) (x_3-z̅_2)Kint2 The following relation between the integrals $_2$, $_3$, $_4$ has been found in [ref] : 3p_3Vp_3 _4+6p_2p_3_3+2p_1Np_3_2 = 0rel2 By using $α'$ expansions for the integrals int2 we have checked it to the first order of $α'$.
Ramond-Ramond S-matrix elements from T-dual Ward identity · The S-matrix element in string theory · 0.84
Cites as support 2 papers
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To see this, we note that, in the type II super string theories, the consistency of NS-NS couplings at order $α'^2$ on the world volume of O-plane with the standard Buscher rules, produces unique couplings which are consistent with S-matrix elements [ref] .
Higher Derivative Corrections to O-plane Actions: NS-NS Sector · T-duality constraint · 0.98
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To see this, we note that, in the type II super string theories, the consistency of NS-NS couplings at order $α'^2$ on the world volume of O-plane with the standard Buscher rules, produces unique couplings which are consistent with S-matrix elements [ref] .
T-duality of O-plane action at order $ \alpha'^2$ · T-duality constraint · 0.98
Cites as background 9 papers
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The curvature corrections to the WS action have been found in [ref] by requiring that the chiral anomaly on the world volume of intersecting D-branes (I-brane) cancels with the anomalous variation of the WS action.
Anomalies, Branes, and Currents · Introduction and Results · 0.96
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The curvature corrections to the WS action have been found in [ref] by requiring that the chiral anomaly on the world volume of intersecting D-branes (I-brane) cancels with the anomalous variation of the WS action.
I-Brane Inflow and Anomalous Couplings on D-Branes · Introduction and Results · 0.96
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The T-duality transformations on massless field at the leading order of $α'$ are given by the Buscher rules [ref] .
T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds · T-duality constraint · 0.89
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