General scalar exchange in \(\text{AdS}_{d+1}\)

DOI10.1016/S0550-3213(99)00169-8zbMATH Open0949.83070arXivhep-th/9811257OpenAlexW1963491142MaRDI QIDQ1572134

Author name not available (Why is that?)

Publication date: 12 July 2000

Published in: (Search for Journal in Brave)

Abstract: The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space,

A d S_{d + 1}

. The conformal dimensions

D e l t a_{i}

,

i = 1, ..., 4

of the scalar operators and the dimension

D e l t a

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

D e l t a_{i}, D e l t a

, the amplitude can be presented as a multiple derivative of a simple universal function. Results simplify if further conditions hold, such as the inequalities,

D e l t a < D e l t a_{1} + D e l t a_{3}

or

D e l t a < D e l t a_{2} + D e l t a_{4}

. These conditions are satisfied, with

<

replaced by

l e

, in Type IIB supergravity on

A d S_{5} i m e s 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

(l o g)^{2}

singularities in the direct channel.

Full work available at URL: https://arxiv.org/abs/hep-th/9811257

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: General scalar exchange in \(\text{AdS}_{d+1}\)

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1572134)