Holographic Three-point Functions Research Articles

Holographic three-point functions from higher curvature gravities in arbitrary dimensions

The three-point function of the energy-momentum tensor in a conformal field theory is completely determined by three parameters, called A, B, C. We carry out a holographic calculation of these three parameters in general d≥4 dimensions from higher curvature gravities up to and including the quartic order. The result is valid both for massless and perturbative higher curvature gravities. It is known that in four dimensional conformal field theory (CFT) the a-charge is a linear combination of A, B, C, our result reproduces this but also shows that a similar relation does not exist for general d>4. We then compute the Weyl anomaly in d=6 and found all the three c-charges are linear combinations of A, B, C, which is consistent with that the a-charge is not. We also find the previously conjectured relation between t2, t4, h′′ does not hold in general massless gravities. Published by the American Physical Society 2024

Orbit averaging coherent states: holographic three-point functions of AdS giant gravitons

We study correlation functions of two AdS giant gravitons in AdS5 × S5 and a BPS supergravity mode using holography. In the gauge theory these are described by BPS correlators of Schur polynomials of fully-symmetric representations and a single trace operator. We find full agreement between the semiclassical gravity and gauge theory computations at large N, for both diagonal and off-diagonal structure constants. Our analysis in mathcal{N} = 4 SYM provides a simpler derivation to the results in the literature, and it can be readily generalized to operators describing bound states of AdS giant gravitons as well as bubbling geometries.

Spectral flow and string correlators in AdS3× S3× T4

We consider three-point correlation functions for superstrings propagating in AdS3 × S3 × T4. In the RNS formalism, these generically involve correlators with current insertions. When vertex operators with non-trivial spectral flow charges are present, their complicated OPEs with the currents imply that standard methods can not be used to compute such correlators. Here we develop techniques for computing all m-basis correlators of the supersymmetric model. We then show how, in some cases, these results can be translated to the x-basis. We obtain a new family of holographic three-point functions involving spacetime chiral primaries living in spectrally flowed sectors of the worldsheet CFT. These match precisely the predictions from the holographic dual at the symmetric product orbifold point. Finally, we also consider long strings and compute the probability amplitude associated with the process describing the emission/absorption of fundamental string quanta.

Giant gravitons on AdS 4 × $ \mathbb{C} $ P3 and their holographic three-point functions

We find a simple parametrization of the anti-symmetric giant graviton in AdS_4 x CP^3, first constructed in arXiv:1108.3084 [hep-th], dual to the anti-symmetric Schur polynomial involving two bi-fundamental complex scalar fields of ABJM theory. Using this parametrization we evaluate in a semi-classical approach the three-point function of two such giant gravitons and one point-like graviton considering both extremal and non-extremal configurations. We likewise discuss the case of the symmetric giant graviton in AdS_4 x CP^3. Finally, we provide an expression for the planar three-point function of chiral primary operators in ABJM at strong coupling and find that the results for the giant graviton three-point functions reduce to this expression in the point-like limit.

Holographic three-point functions for short operators

We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. The interaction position is determined by saddle point, which is equivalent to conservation of the canonical momentum for the interacting particles, and leads to conservation of their conformal charges. We further show that for large dimensions the rms size of the interaction region is small compared to the radius of curvature of the AdS space, but still large compared to the string Compton wave-length. Hence, one can approximate the string vertex operators as flat-space vertex operators with a definite momentum, which depends on the conformal and R-charges of the operator. We then argue that the string vertex operator dual to a primary operator is chosen by satisfying a twisted version of Q^L=Q^R, up to spurious terms. This leads to a unique choice for a scalar vertex operator with the appropriate charges at the first massive level. We then comment on some features of the corresponding three-point functions, including the application of these results to Konishi operators.

Three-point correlation functions of giant magnons with finite size

We compute holographic three-point correlation functions or structure constants of a zero-momentum dilaton operator and two (dyonic) giant magnon string states with a finite-size length in the semiclassical approximation. We show that the semiclassical structure constants match exactly with the three-point functions between two su(2) magnon single trace operators with finite size and the Lagrangian in the large ʼt Hooft coupling constant limit. A special limit J≫λ of our result is compared with the relevant result based on the Lüscher corrections.

Holographic three-point functions of giant gravitons

Working within the AdS/CFT correspondence we calculate the three-point function of two giant gravitons and one pointlike graviton using methods of semiclassical string theory and considering both the case where the giant gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3 in AdS_5. We likewise calculate the correlation function in N=4 SYM using two Schur polynomials and a single trace chiral primary. We find that the gauge and string theory results have structural similarities but do not match perfectly, and interpret this in terms of the Schur polynomials' inability to interpolate between dual giant and pointlike gravitons.

Holographic three-point functions of semiclassical states

We calculate the holographic three-point functions in \( \mathcal{N} = 4 \) super-Yang-Mills theory in the case when two of the operators are semiclassical and one is dual to a supergravity mode. We further discuss the transition to the regime when all three operators are semiclassical.

Holographic three-point functions: one step beyond the tradition

Within the program of holographic renormalization, we discuss the computation of three-point correlation functions along RG flows. We illustrate the procedure in two simple cases. In an RG flow to the Coulomb branch of N=4 SYM theory we derive a compact and finite expression for the three-point function of lowest CPOs dual to inert scalars. In the GPPZ flow, that captures some features of N=1 SYM theory, we identify two new logarithmically divergent counterterms and compute the three-point function with insertion of two inert scalars and one active scalar that mixes with the stress tensor. By amputating the external legs at the mass poles we extract the finite and scheme independent trilinear couplings of the corresponding superglueballs. Finally we outline the procedure for computing three-point functions with insertions of the stress tensor as well as of (broken) R-symmetry currents.

New results on holographic three-point functions

We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE for the active scalar emerges rather simply and makes it possible to use the Green's function method to deal with (quadratic) interaction terms. We thus fill a gap for active scalar operators, whose three-point functions have been inaccessible so far, and derive a general, explicitly Bose symmetric formula thereof. As an application we compute the relevant three-point function along the GPPZ flow and extract the irreducible trilinear couplings of the corresponding superglueballs by amputating the external legs on-shell.