Three-point functions at strong coupling in the BMN limit

Abstract

We consider structure constants of single-trace operators at strong coupling in planar N = 4 SYM theory using the hexagon formalism. We concentrate on heavy-heavylight correlators where the heavy operators are BMN operators, with large R-charges and finite anomalous dimensions, and the light one is a finite-charge chiral primary operator. They describe the couplings between two highly boosted strings and a supergravity mode in the bulk dual. In the hexagon framework, two sums over virtual magnons are needed to bind the hexagons together around the light operator. We evaluate these sums explicitly at strong coupling, for a certain choice of BMN operators, and show that they factorise into a ratio of Gamma functions and a simple stringy prefactor. The former originates from giant mirror magnons scanning the AdS geometry while the latter stems from small fluctuations around the BMN vacuum. The resulting structure constants have poles at positions where an enhanced mixing with double-trace operators is expected and zeros whenever the process is forbidden by supersymmetry. We also discuss the transition to the classical regime, when the length of the light operator scales like the string tension, where we observe similitudes with the Neumann coefficients of the pp-wave String Field Theory vertex.

One-loop amplitudes in AdS5×S5 supergravity from $$ \mathcal{N} $$ = 4 SYM at strong coupling

“…The two factors giving the numerator of (54) in the RHS are both O(1/N 2 ) whereas the factor in the denominator is leading in large N, thus the RHS is O(1/N 4 ) as we stated already in (45). The formula (54) may be proven by simply using (51) on both sides and then using (53) and (52) on the RHS to cancel the denominator.…”

“…Future directions include a more detailed investigation of the Mellin space representation of our one-loop functions, which would extend the analysis of 2222 in [11], as well as the possibility of pushing our bootstrap program to two loops. It would be fascinating if the results we obtain in the large N expansion could be compared (possibly taking into account also the α ′ corrections) to the results based on integrable methods [50][51][52][53][54]. We also emphasise that our fresh new look at free N = 4 SYM, especially our understanding of single particle operators and generalised tree-level functions, suggests a different way to approach the mysterious six-dimensional (2, 0) theory, which has been recently studied from a holographic perspective in several papers [55][56][57][58].…”

Liouville theory, AdS2 string, and three-point functions

“…Unfortunately, the WKB expansion turned out to be less powerful here and will not fix the ambiguity completely. Instead, we need to carefully discuss the analytic properties of the Wronskians in order to determine the CDD ambiguity 21 . This was for instance demonstrated in [4].…”

“…The former pole crosses the contour from the inside to the outside while the latter pole crosses the contour from the outside to the inside. 21 Note that in general the multiplication of the CDD-like factors will modify the analytic property of the Wronskians (as a function of the spectral parameter). Therefore, if one can determine the analytic property of the Wronskian by some other means, one will be able to fix the CDD ambiguities.…”

“…Recently, part of the classical string result was rederived from the non-perturbative approach called the hexagon formalism in[19] 24. It was recently shown that functions with similar properties can be obtained from the hexagon formalism at strong coupling[21] 25 In[22], they also introduced the twistorial generalization of the DOZZ formula. This is closely related to our final formula (111).…”