arXiv subjects

Danilo E. Diaz

Publications and source records attributed to Danilo E. Diaz.

6 recordsLinked to original sources

arXiv2026

Universal relations for two- and three-point functions of the CFT energy-momentum tensor and the Weyl anomaly

We establish universal relations, valid for a generic conformal field theory in even dimension $d\geqslant6$, between the coefficients $\mathcal{A}$, $\mathcal{B}$, $\mathcal{C}$ of the energy-momentum tensor three-point function and the coefficients of the quadratic and cubic terms in the Weyl tensor in the Weyl anomaly. Alternatively, we can replace the three-point function coefficients with the two-point function coefficient $C_T$ and the two energy flux parameters $t_2$ and $t_4$. Our derivation combines well-known holographic results for $C_T$ with more recent holographic results for $t_2$ and $t_4$, along with a newly obtained Chern--Gauss--Bonnet formula for compact Einstein manifolds. This theorem isolates the Weyl-squared and Weyl-cubed contributions in the relation between the Euler density and the $Q$-curvature, allowing us to identify the relevant quadratic and cubic terms unambiguously. We also provide two genuine CFT derivations for $C_T$ based on the renormalization-group running of the $TT$-correlator with respect to the arbitrary but necessary mass scale $μ$. We revisit several examples to illustrate and validate the general result. These include free scalars, GJMS operators, and holographic duals of higher-derivative gravities.

hep-th↗

arXiv2022

GJMS-like operators on symmetric 2-tensors and their gravitational duals

We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$ acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars. We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level, we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $P_{2k}^{(2)}$ in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $P_{2k}^{(1)}$ is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part. Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.

hep-th↗

arXiv2013

AdS Chern-Simons Gravity induces Conformal Gravity

The leitmotif of this paper is the question of whether four- and higher even-dimensional Conformal Gravities do have a Chern-Simons pedigree. We show that Weyl gravity can be obtained as dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauged-fixed, tractor-like) five-dimensional AdS connection. The gauge-fixing and dimensional reduction program admits a readily generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.

gr-qc↗

arXiv2008

Polyakov formulas for GJMS operators from AdS/CFT

We argue that the AdS/CFT calculational prescription for double-trace deformations leads to a holographic derivation of the conformal anomaly, and its conformal primitive, associated to the whole family of conformally covariant powers of the Laplacian (GJMS operators) at the conformal boundary. The bulk side involves a quantum 1-loop correction to the SUGRA action and the boundary counterpart accounts for a sub-leading term in the large-N limit. The sequence of GJMS conformal Laplacians shows up in the two-point function of the CFT operator dual to a bulk scalar field at certain values of its scaling dimension. The restriction to conformally flat boundary metrics reduces the bulk computation to that of volume renormalization which renders the universal type A anomaly. In this way, we directly connect two chief roles of the Q-curvature: the main term in Polyakov formulas on one hand, and its relation to the Poincare metrics of the Fefferman-Graham construction, on the other hand. We find agreement with previously conjectured patterns including a generic and simple formula for the type A anomaly coefficient that matches all reported values in the literature concerning GJMS operators, to our knowledge.

hep-th↗

arXiv2006

On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image

We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of the scalar singlet bilinear is reorganized to make it explicitly crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge fields. We are able to analytically establish the factorized form of the fusion coefficients as well as the two-point function coefficient of the HS currents. We insist in directly computing the free correlators from bulk graphs with the unconventional branch. The three-point function of the scalar bilinear turns out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be precisely related to the CPWs of the boundary dual scalar and its shadow. The flow in the IR by Legendre transforming at leading 1/N, following the pattern of double-trace deformations, and the assumption of degeneracy of the hologram lead to the CPWE of the scalar four-point function at IR. Here we confirm some previous results, obtained from more involved computations of skeleton graphs, as well as extend some of them from d=3 to generic dimension 2<d<4.

hep-th↗

arXiv2004

Propagators and WKB-exactness in the plane wave limit of AdSxS

Green functions for the scalar, spinor and vector fields in a plane wave geometry arising as a Penrose limit of $AdS\times S$ are obtained. The Schwinger-DeWitt technique directly gives the results in the plane wave background, which turns out to be WKB-exact. Therefore the structural similarity with flat space results is unveiled. In addition, based on the local character of the Penrose limit, it is claimed that for getting the correct propagators in the limit one can rely on the first terms of the direct geodesic contribution in the Schwinger-DeWitt expansion of the original propagators . This is explicitly shown for the Einstein Static Universe, which has the same Penrose limit as $AdS\times S$ with equal radii, and for a number of other illustrative cases.

hep-th↗