Scalar Quartic Couplings in Type IIB Supergravity on $Ad{S}_5\times S^5$

Abstract

All quartic couplings of scalar fields $s^I$ that are dual to extended chiral primary operators in $\mathcal{N}=4$ SYM${}_4$ are derived by using the covariant equations of motion for type IIB supergravity on $Ad{S}_5\times S^5$. It is shown that despite some expectations if one keeps the structure of the cubic terms untouched, the quartic action obtained contains terms with two and four derivatives. It is shown that the quartic action vanishes on shell in the extremal case, e.g. k_1=k_2+k_3+k_4. Consistency of the truncation of the quartic couplings to the massless multiplet of the $\mathcal{N}=8$, d=5 supergravity is proven and the explicit values of the couplings are found. It is argued that the consistency of the KK reduction implies non-renormalization of $n$-point functions of $n-1$ operators dual to the fields from the massless multiplet and one operator dual to a field from a massive multiplet.

Latex, 15 + 46 p, expressions for two couplings are corrected

References in corpus (18)

• On the Holographic Renormalization Group
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• Consistent nonlinear KK reduction of 11d supergravity on $Ad{S}_7\times S_4$ and self-duality in odd dimensions
• Consistency of the $Ad{S}_7\times S_4$ reduction and the origin of self-duality in odd dimensions
• AdS/CFT 4-point functions: How to succeed at z-integrals without really trying
• Extremal Correlators in the AdS/CFT Correspondence
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• On the logarithmic behaviour in N=4 SYM theory
• Some Cubic Couplings in Type IIB Supergravity on $Ad{S}_5\times S^5$ and Three-point Functions in SYM_4 at Large N
• Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• Extremal correlators in four-dimensional SCFT
• AdS_5/CFT_4 Four-point Functions of Chiral Primary Operators: Cubic Vertices
• Near-extremal correlators and vanishing supergravity couplings in AdS/CFT
• Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence
• Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence
• Massive symmetric tensor field on AdS
• On direct and crossed channel asymptotics of four-point functions in AdS/CFT correspondence

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