Abstract
The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space, AdS d+1 . The conformal dimensions δ i , i = 1, … , 4 of the scalar operators and the dimension Δ of the exchanged field are arbitrary, constrained only to obey the unitarity bound. Techniques similar to those developed earlier for gauge boson exchange are used, but results are generally more complicated. However, for integer Δ i , Δ the amplitude can be presented as a multiple derivative of a simple universal function. Results simplify if further conditions hold, such as the inequalities, Δ < Δ 1 + Δ 3 or Δ < Δ 2 + Δ 4. These conditions are satisfied, with < replaced by ⩽ in Type IIB supergravity on AdS 5 x S 5 because of selection rules from SO(6) symmetry. A new form of interaction is suggested for the marginal case of the inequalities. The short distance asymptotics of the amplitudes are studied. In the direct channel the leading singular term agrees with the double operator product expansion. Logarithmic singularities occur at sub-leading order in the direct channel but at leading order in the crossed channel. When the inequalities above are violated, there are also (log) 2 singularities in the direct channel.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
