On the Lagrangian formulation of the double copy to cubic order

We investigate the Lagrangian formulation of the double-copy correspondence between gauge theories and gravity, up to the cubic order. Building on the definition of the double-copy field as a convolution of two vectors, we obtain free gravitational Lagrangians as products of two Yang-Mills Lagrangians, in a form amenable to be easily extended to the massive case. We discuss the origin of these results from tensionless strings and show the existence of gauge fixings that mix the two spin-one sectors and lead to an alternative, especially simple, version of the free Lagrangian. We then construct cubic vertices for the full double-copy multiplet, comprising a graviton, a two-form and a scalar particle, by means of the Noether procedure. Both at the free and at the cubic level the result gets uniquely fixed only upon imposing, on top of gauge invariance, a left-right Lorentz symmetry ruling contraction of indices among double-copy fields. Whereas the outcome nicely matches the cubic interactions of $\mathcal{N}=0$ supergravity, including the gauge-invariant coupling between the scalar particle and the two-form, such a twofold Lorentz symmetry seems to conflict with the perturbative reconstruction of space-time geometry.Comment: 28 pages. minor editing, matches published versio

More on holographic correlators: Twisted and dimensionally reduced structures

Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1,2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure \`a la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For $AdS_5\times S^5$ and $AdS_7\times S^4$, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $\mathcal{N}=4$ SYM and the 6d $(2,0)$ theory, finding perfect agreement. For $AdS_4\times S^7$, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.Comment: Minor changes, matches published versio

Gluon scattering in AdS at finite string coupling from localization

We consider gluons scattering in Type IIB string theory on AdS5 × S5/ℤ2 in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d N = 2 USp(2N) gauge theory with SO(8) flavor symmetry and complexified coupling τ. We compute this holographic correlator in the large N and finite τ expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in 1/N and finite τ using supersymmetric localization. In particular, we fix the F4 higher derivative correction to gluon scattering on AdS at finite string coupling τs = τ in terms of Jacobi theta functions, which feature the expected relations between the SL(2, ℤ) duality and the SO(8) triality of the CFT, and match it to the known flat space term. We also use the flat space limit to compute D2F4 corrections of the correlator at finite τ in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a form which is remarkably similar to that of the flat space Veneziano amplitude

Gluon scattering in AdS at finite string coupling from localization

We consider gluons scattering in Type IIB string theory on AdS$_5\times S^5/\mathbb{Z}_2$ in the presence of D7 branes, which is dual to the flavor multiplet correlator in a certain 4d $\mathcal{N}=2$ $USp(2N)$ gauge theory with $SO(8)$ flavor symmetry and complexified coupling $\tau$. We compute this holographic correlator in the large $N$ and finite $\tau$ expansion using constraints from derivatives of the mass deformed sphere free energy, which we compute to all orders in $1/N$ and finite $\tau$ using supersymmetric localization. In particular, we fix the $F^4$ higher derivative correction to gluon scattering on AdS at finite string coupling $\tau_s=\tau$ in terms of Jacobi theta functions, which feature the expected relations between the $SL(2,\mathbb{Z})$ duality and the $SO(8)$ triality of the CFT, and match it to the known flat space term. We also use the flat space limit to compute $D^2F^4$ corrections of the correlator at finite $\tau$ in terms of a non-holomorphic Eisenstein series. At weak string coupling, we find that the AdS correlator takes a form which is remarkably similar to that of the flat space Veneziano amplitude.Comment: 24 pages plus appendice

Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs

We develop the technology for Polyakov-Mellin (PM) bootstrap in one-dimensional conformal field theories (CFT$_1$). By adding appropriate contact terms, we bootstrap various effective field theories in AdS$_2$ and analytically compute the CFT data to one loop. The computation can be extended to higher orders in perturbation theory, if we ignore mixing, for any external dimension. We develop PM bootstrap for $O(N)$ theories and derive the necessary contact terms for such theories (which also involves a new higher gradient contact term absent for $N=1$). We perform cross-checks which include considering the diagonal limit of the $2d$ Ising model in terms of the $1d$ PM blocks. As an independent check of the validity of the results obtained with PM bootstrap, we propose a suitable basis of transcendental functions, which allows to fix the four-point correlators of identical scalar primaries completely, up to a finite number of ambiguities related to the number of contact terms in the PM basis. We perform this analysis both at tree level (with and without exchanges) and at one loop. We also derive expressions for the corresponding CFT data in terms of harmonic sums. Finally, we consider the Regge limit of one-dimensional correlators and derive a precise connection between the latter and the large-twist limit of CFT data. Exploiting this result, we study the crossing equation in the three OPE limits and derive some universal constraints for the large-twist limit of CFT data in Regge-bounded theories with a finite number of exchanges.Comment: 90 pages, 6 figure

Gluon Scattering in AdS from CFT

We present a systematic study of holographic correlators in a vast array of SCFTs with non-maximal superconformal symmetry. These theories include 4d $\mathcal{N}=2$ SCFTs from D3-branes near F-theory singularities, 5d Seiberg exceptional theories and 6d E-string theory, as well as 3d and 4d phenomenological models with probe flavor branes. We consider current multiplets and their generalizations with higher weights, dual to massless and massive super gluons in the bulk. At leading order in the inverse central charge expansion, connected four-point functions of these operators correspond to tree-level gluon scattering amplitudes in AdS. We show that all such tree-level four-point amplitudes in all these theories are fully fixed by symmetries and consistency conditions and explicitly construct them. Our results encode a wealth of SCFT data and exhibit various interesting emergent structures. These include Parisi-Sourlas-like dimensional reductions, hidden conformal symmetry and an AdS version of the color-kinematic duality.Comment: typos corrected, published on JHE

Micro-structured rough surfaces by laser etching for heat transfer enhancement on flush mounted heat sinks

Abstract. The aim of this work is to improve heat transfer performances of ush mounted heat sinks used in electronic cooling. To do this we patterned 1.23 cm2 heat sinks surfaces by micro- structured roughnesses built by laser etching manufacturing technique, and experimentally measured the convective heat transfer enhancements due to dierent patterns. Each roughness diers from the others with regards to the number and the size of the micro-ns (e.g. the micro- n length ranges from 200 to 1100 m). Experimental tests were carried out in forced air cooling regime. In particular fully turbulent ows (heating edge based Reynolds number ranging from 3000 to 17000) were explored. Convective heat transfer coecient of the best micro-structured heat sink is found to be roughly two times compared to the smooth heat sinks one. In addition, surface area roughly doubles with regard to smooth heat sinks, due to the presence of micro-ns. Consequently, patterned heat sinks thermal transmittance [W/K] is found to be roughly four times the smooth heat sinks one. We hope this work may open the way for huge boost in the technology of electronic cooling by innovative manufacturing techniques

In Situ Block Size Distribution Aimed at the Choice of the Design Block for Rockfall Barriers Design: A Case Study along Gardesana Road

When studying rockfall phenomena, a single value of the block volume is not sucient to take into account the natural variability of the geometrical features (orientation, spacing, persistence) of the discontinuity sets. Dierent approaches for obtaining cumulative distributions of potentially detachable block volumes are compared. A highly fractured rock mass outcropping along the western Lake Garda (Italy), consisting of prevailing limestone and interbedded marls, is studied in detail from geological and geostructural points of view. Then, a representative rock face has been selected and analyzed with traditional and non-contact survey methods to identify the main discontinuity sets and to collect spacing samples. Based on these data, in situ block size distributions for dierent combinations of sets are built following statistically-based approaches, without the use of a Discrete Fracture Network (DFN) generator. The validation of the obtained distributions is attempted based on the detached block surveyed at the foot of the slope. However, in this particular case study, the detached blocks cover only a minimal volume range compared to both theoretical values and visible rockfall scars. The fallen rock blocks have a marginal role in design block determination, since their volume depends on geological discontinuities (bedding and fractures) and could be aected by other processes after the detachment (e.g., fragmentation). The procedure here described should be standard practice in the study of rockfall events, and it should be uniform in European standards such as Eurocodes. Future developments should involve the scientific community for setting the percentiles of the probability distribution to be considered for block design definition