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Maximal U(1)Y-violating n-point correlators in N = 4 super-Yang-Mills theory

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jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThis paper concerns a special class of jats:italicn</jats:italic>-point correlation functions of operators in the stress tensor supermultiplet of jats:inline-formulajats:alternativesjats:tex-math$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml=""> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> = 4 supersymmetric SU(jats:italicN</jats:italic>) Yang-Mills theory. These are “maximal U(1)jats:subjats:italicY</jats:italic></jats:sub>-violating” correlators that violate the bonus U(1)jats:subjats:italicY</jats:italic></jats:sub> charge by a maximum of 2(jats:italicn −</jats:italic> 4) units. We will demonstrate that such correlators satisfy SL(2jats:italic,</jats:italic> ℤ)-covariant recursion relations that relate jats:italicn</jats:italic>-point correlators to (jats:italicn −</jats:italic> 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-jats:italicN</jats:italic> expansion of jats:italicn</jats:italic>-point maximal U(1)jats:subjats:italicY</jats:italic></jats:sub>-violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (jats:italicn −</jats:italic> 4) chiral Lagrangian operators, starting from known properties of the jats:italicn</jats:italic> = 4 case. We concentrate on the first three orders in 1/jats:italicN</jats:italic> beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in jats:italicAdS</jats:italic>jats:sub5</jats:sub>jats:italic× S</jats:italic>jats:sup5</jats:sup> at the same orders as jats:italicR</jats:italic>jats:sup4</jats:sup>jats:italic, d</jats:italic>jats:sup4</jats:sup>jats:italicR</jats:italic>jats:sup4</jats:sup> and jats:italicd</jats:italic>jats:sup6</jats:sup>jats:italicR</jats:italic>jats:sup4</jats:sup>. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (jats:italicn −</jats:italic> 4jats:italic,</jats:italic> 4 jats:italic− n</jats:italic>) that are SL(2jats:italic,</jats:italic> ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1)jats:subjats:italicY</jats:italic></jats:sub>-violating jats:italicn</jats:italic>-particle interactions (jats:italicn ></jats:italic> 4) in the low-energy expansion of type IIB superstring amplitudes in jats:italicAdS</jats:italic>jats:sub5</jats:sub>jats:italic× S</jats:italic>jats:sup5</jats:sup>.</jats:p>



1, N Expansion, AdS-CFT Correspondence, Conformal Field Theory, Scattering Amplitudes

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Journal of High Energy Physics

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