Integrability, One-point Functions and Tests of AdS/dCFT

Charlotte Kristjansen

Niels Bohr Inst., Copenhagen

Thu, Nov. 08th 2018, 14:15

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

\noindent ``Integrability meeting ENS/IPhT'' \\ \\ We consider a defect version of the gauge/gravity correspondence (AdS/dCFT) where N=4 SYM has gauge groups of different ranks on the two sides of a co-dimension one defect and where the dual string theory picture is that of a probe-brane set-up of either D3-D5 or D3-D7 type with either background gauge field flux or non-trivial instanton number. The main results obtained concerning one-point functions of the above AdS/dCFT are reviewed. First, we present a closed formula for tree-level one-point functions of all conformal operators constructed from the scalar fields of N=4 SYM in the case of the D3-D5 set-up. Using the language of integrability, the one-point functions are expressed in terms of the spin chain rapidities of the conformal operators in question. Important ingredients in the formula are the Gaudin determinant, various Baxter polynomials as well as quantities closely related to the transfer matrix of the integrable spin chain involved. We furthermore present a closed one-loop order formula for one-point functions in the SU(2) sub-sector of the same set-up. Subsequently, we discuss the status of similar studies for the D3-D7 set-up. Finally, we present a positive test of AdS/dCFT at the next to leading order in a certain double scaling parameter both for the half supersymmetric D3-D5 probe brane set-up and for a non-supersymmetric D3-D7 probe brane set-up. \\ \\ (IPhT organizers: Ivan Kostov and Didina Serban)

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