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<p>The circle compactification of M-theory is dual to type IIA string theory, requiring that the dimensional reduction of the M-theory couplings <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(({t}_{8}{t}_{8}-\frac{1}{4}{\epsilon }_{8}{\epsilon }_{8}){R}^{4}\)</EquationSource> </InlineEquation> must reproduce the type IIA one-loop effective action at order <i>α′</i><sup>3</sup>, including contributions from the metric, dilaton, and RR one-form. Through compactification, we obtain 1,276 couplings involving Riemann, Ricci, and Ricci scalar tensors, along with first and second derivatives of the dilaton and RR one-form. By employing field redefinitions, we reduce these to a basis of 359 independent couplings. Crucially, we observe that the dilaton cannot be entirely removed from the couplings via field redefinitions, even in the pure metric-dilaton sector. We validate our results by showing exact agreement between all four-field couplings and the corresponding string-theory S-matrix elements in the string frame.</p><p>Further, upon compactifying on K3, we demonstrate that the resulting six-dimensional <i>α′</i> couplings at one-loop level transform under S-duality into the tree-level <i>α′</i> couplings of heterotic string theory on <i>T</i><sup>4</sup>. This match necessitates carefully chosen field redefinitions for both the type IIA (on K3) and heterotic (on <i>T</i><sup>4</sup>) sectors, providing a stringent test of the duality.</p>

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Type IIA supergravity at one loop: α′3 terms in the metric-dilaton-RR one-form sector

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  • 发表日期：

    2025年11月18日

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  • Mohammad R. Garousi

摘要

The circle compactification of M-theory is dual to type IIA string theory, requiring that the dimensional reduction of the M-theory couplings \(({t}_{8}{t}_{8}-\frac{1}{4}{\epsilon }_{8}{\epsilon }_{8}){R}^{4}\) must reproduce the type IIA one-loop effective action at order α′3, including contributions from the metric, dilaton, and RR one-form. Through compactification, we obtain 1,276 couplings involving Riemann, Ricci, and Ricci scalar tensors, along with first and second derivatives of the dilaton and RR one-form. By employing field redefinitions, we reduce these to a basis of 359 independent couplings. Crucially, we observe that the dilaton cannot be entirely removed from the couplings via field redefinitions, even in the pure metric-dilaton sector. We validate our results by showing exact agreement between all four-field couplings and the corresponding string-theory S-matrix elements in the string frame.

Further, upon compactifying on K3, we demonstrate that the resulting six-dimensional α′ couplings at one-loop level transform under S-duality into the tree-level α′ couplings of heterotic string theory on T4. This match necessitates carefully chosen field redefinitions for both the type IIA (on K3) and heterotic (on T4) sectors, providing a stringent test of the duality.