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Duality Groups, Automorphic Forms and Higher Derivative Corrections
High Energy Physics - Theory · Submitted 29 Nov 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Since the automorphic forms of this theory contain the weights of E_8 we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.
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The abstract, sentence by sentence
We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). This construction is based on the theory of non-linear realizations and we find that the automorphic forms contain the weights of G. We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E_8 occur generalizing previous results of the authors on M-theory. Since the automorphic forms of this theory contain the weights of E_8 we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. | contribution 0.76 | 0.85 | 0.04 | asserted 0.85 |
| s1 | Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. | result 0.83 | 0.93 | 0.40 | asserted 1.00 |
| s2 | We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). | method 0.75 | 0.95 | 0.10 | asserted 1.00 |
| s3 | This construction is based on the theory of non-linear realizations and we find that the automorphic forms contain the weights of G. | result 0.66 | 0.94 | 0.10 | asserted 1.00 |
| s4 | We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E_8 occur generalizing previous results of the authors on M-theory. | result 0.87 | 0.95 | 0.15 | asserted 1.00 |
| s5 | Since the automorphic forms of this theory contain the weights of E_8 we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry. | interpretation 1.00 | 0.65 | 0.51 | hedged possibility 0.77 |
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Original abstract
We study the higher derivative corrections that occur in type II superstring theories in ten dimensions or less. Assuming invariance under a discrete duality group G(Z) we show that the generic functions of the scalar fields that occur can be identified with automorphic forms. We then give a systematic method to construct automorphic forms from a given group G(Z) together with a chosen subgroup H and a linear representation of G(Z). This construction is based on the theory of non-linear realizations and we find that the automorphic forms contain the weights of G. We also carry out the dimensional reduction of the generic higher derivative corrections of the IIB theory to three dimensions and find that the weights of E_8 occur generalizing previous results of the authors on M-theory. Since the automorphic forms of this theory contain the weights of E_8 we can interpret the occurrence of weights in the dimensional reduction as evidence for an underlying U-duality symmetry.
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References
How the literature uses it
14 arXiv papers cite this in 22 sentences
Papers citing it · 14 sentences without a confident label
Cites it as support 1 paper
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Two other spectacular findings provide additional support to the conjecture: * The quantum corrections to $M$-theory are compatible with the $E_10$ algebraic structure, in the sense that they correspond to roots of $E_10$ [ref] (see also [ref] for further discussions and developments). * The massive deformation of type IIA supergravity corresponds to a level 4 root of $E_10$ (or $E_11$) [ref] , a result that can be extended to other deformations of the theory in lower dimensions (see the original works [ref] for entries into this fast growing literature).
Kac-Moody algebras and the structure of cosmological singularities: a new light on the Belinskii-Khalatnikov-Lifshitz analysis · Hidden Symmetries? · 1.00
Cites it as background 6 papers
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Recently, several authors [ref] have initiated an investigation aimed at answering the question of whether or not the U-duality group $U_3$ in three dimensions is preserved also if the tree-level Lagrangian is supplemented by higher order curvature corrections.
U-Duality and the Compactified Gauss-Bonnet Term · Non-Perturbative Completion and Automorphic Forms · 0.88
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Although the coefficients, $^(D)_(p,q)$, have not been determined in generality, a significant amount of information has accumulated for the first three terms for the cases with $D≥6$ (duality groups $E_d+1$ with $d ≤4$) [ref] , and there are various conjectures concerning the coefficient of the $^4$ interaction, $^(D)_(0,0)$, for higher-rank groups [ref] .
Eisenstein series for higher-rank groups and string theory amplitudes · Introduction · 0.80
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In the context of U-duality, the same question arises as to whether higher-derivative interactions, beyond the already well understood gravitational sector, preserve the duality symmetry $G_3()=E_8(8)(ℤ)$ of M-theory compactified on a eight-torus [ref] .
Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality · Introduction and Summary · 0.83
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