%0 Journal Article %1 Papadodimas2011Correlation %A Papadodimas, Kyriakos %A Raju, Suvrat %D 2011 %K arxiv, higher-spin %T Correlation Functions in Holographic Minimal Models %U http://arxiv.org/abs/1108.3077 %X We compute exact three and four point functions in the W\_N minimal models that were recently conjectured to be dual to a higher spin theory in AdS\_3. The boundary theory has a large number of light operators that are not only invisible in the bulk but grow exponentially with N even at small conformal dimensions. Nevertheless, we provide evidence that this theory can be understood in a 1/N expansion since our correlators look like free-field correlators corrected by a power series in 1/N . However, on examining these corrections we find that the four point function of the two bulk scalar fields is corrected at leading order in 1/N through the contribution of one of the additional light operators in an OPE channel. This suggests that, to correctly reproduce even tree-level correlators on the boundary, the bulk theory needs to be modified by the inclusion of additional fields. As a technical by-product of our analysis, we describe two separate methods -- including a Coulomb gas type free-field formalism -- that may be used to compute correlation functions in this theory.

@article{Papadodimas2011Correlation, abstract = {{We compute exact three and four point functions in the W\_N minimal models that were recently conjectured to be dual to a higher spin theory in AdS\_3. The boundary theory has a large number of light operators that are not only invisible in the bulk but grow exponentially with N even at small conformal dimensions. Nevertheless, we provide evidence that this theory can be understood in a 1/N expansion since our correlators look like free-field correlators corrected by a power series in 1/N . However, on examining these corrections we find that the four point function of the two bulk scalar fields is corrected at leading order in 1/N through the contribution of one of the additional light operators in an OPE channel. This suggests that, to correctly reproduce even tree-level correlators on the boundary, the bulk theory needs to be modified by the inclusion of additional fields. As a technical by-product of our analysis, we describe two separate methods -- including a Coulomb gas type free-field formalism -- that may be used to compute correlation functions in this theory.}}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Papadodimas, Kyriakos and Raju, Suvrat}, biburl = {https://www.bibsonomy.org/bibtex/266a7f3b7b6d514f818527e900d1d2399/acastro}, citeulike-article-id = {9678670}, citeulike-linkout-0 = {http://arxiv.org/abs/1108.3077}, citeulike-linkout-1 = {http://arxiv.org/pdf/1108.3077}, day = 15, eprint = {1108.3077}, interhash = {3830e5533ce17a26aa1cbca982c7e1e2}, intrahash = {66a7f3b7b6d514f818527e900d1d2399}, keywords = {arxiv, higher-spin}, month = aug, posted-at = {2011-08-18 02:22:18}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Correlation Functions in Holographic Minimal Models}}, url = {http://arxiv.org/abs/1108.3077}, year = 2011 }