002707099 001__ 2707099
002707099 005__ 20231004075904.0
002707099 0248_ $$aoai:cds.cern.ch:2707099$$pcerncds:CERN$$pcerncds:CERN:FULLTEXT$$pcerncds:FULLTEXT
002707099 0247_ $$2DOI$$9bibmatch$$a10.1007/JHEP08(2020)031
002707099 037__ $$9arXiv$$aarXiv:1912.11100$$chep-th
002707099 037__ $$aCERN-TH-2019-230
002707099 035__ $$9arXiv$$aoai:arXiv.org:1912.11100
002707099 035__ $$9Inspire$$aoai:inspirehep.net:1773032$$d2023-10-03T08:48:06Z$$h2023-10-04T02:18:11Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002707099 035__ $$9Inspire$$a1773032
002707099 041__ $$aeng
002707099 100__ $$aPenedones, Joao$$jORCID:0000-0003-0345-4836$$tGRID:grid.5333.6$$uEPFL, Lausanne, FSL$$vFields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
002707099 245__ $$9arXiv$$aNonperturbative Mellin Amplitudes: Existence, Properties, Applications
002707099 269__ $$c2019-12-23
002707099 260__ $$c2020-08-06
002707099 300__ $$a119 p
002707099 500__ $$9arXiv$$aThe erroneous claims regarding the consistency of certain AdS EFTs
are corrected
002707099 520__ $$9arXiv$$aWe argue that nonperturbative CFT correlation functions admit a Mellin amplitude representation. Perturbative Mellin representation readily follows. We discuss the main properties of nonperturbative CFT Mellin amplitudes: subtractions, analyticity, unitarity, Polyakov conditions and polynomial boundedness at infinity. Mellin amplitudes are particularly simple for large N CFTs and 2D rational CFTs. We discuss these examples to illustrate our general discussion. We consider subtracted dispersion relations for Mellin amplitudes and use them to derive bootstrap bounds on CFTs. We combine crossing, dispersion relations and Polyakov conditions to write down a set of extremal functionals that act on the OPE data. We check these functionals using the known 3d Ising model OPE data and other known bootstrap constraints. We then apply them to holographic theories.
002707099 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002707099 540__ $$3publication$$aCC-BY-4.0$$fSCOAP3$$uhttps://creativecommons.org/licenses/by/4.0/
002707099 542__ $$3publication$$dThe Authors$$g2020
002707099 595__ $$aCERN-TH
002707099 65017 $$2arXiv$$ahep-th
002707099 65017 $$2SzGeCERN$$aParticle Physics - Theory
002707099 690C_ $$aCERN
002707099 690C_ $$aARTICLE
002707099 700__ $$aSilva, Joao A.$$jORCID:0000-0003-2491-5769$$tGRID:grid.5333.6$$uEPFL, Lausanne, FSL$$vFields and Strings Laboratory, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
002707099 700__ $$aZhiboedov, Alexander$$tGRID:grid.9132.9$$uCERN$$vCERN, Theoretical Physics Department, 1211 Geneva 23, Switzerland
002707099 773__ $$c031$$pJHEP$$v2008$$y2020
002707099 8564_ $$82219624$$s1771637$$uhttp://cds.cern.ch/record/2707099/files/1912.11100.pdf$$yFulltext
002707099 8564_ $$82219625$$s9583$$uhttp://cds.cern.ch/record/2707099/files/leadingtwist2.png$$y00008 Same as figure \ref{fig:leadtwist1} but with an extended range of twists $\tau$ plotted.
002707099 8564_ $$82219626$$s2250$$uhttp://cds.cern.ch/record/2707099/files/phi3triangle2.png$$y00015 The shaded triangles represent the regions where we can put the integration contours for each of the integrals in (\ref{Mellin for diagram phi3}). If we want to gather all three contours into a single deformed contour, then we run into the problem of having pinches. For example, consider the point in the picture where $\Re(\gamma_{14})=0$ and $\Re(\gamma_{14})=\frac{\Delta}{2}$. In order to have a deformed contour, the contour must pass to the right of $\Re(\gamma_{12})=\frac{\Delta}{2}$, above $\Re(\gamma_{14})=0$ and below $\Re (\gamma_{13})=\frac{\Delta}{2}$. This is impossible without introducing some regularization of the integrals.
002707099 8564_ $$82219627$$s9301$$uhttp://cds.cern.ch/record/2707099/files/schannel.png$$y00016 Conditions (\ref{alpha beta}) are verified in the pink and grey region. They are not verified in the white region. The s-channel OPE does not converge at special points that connect the grey and the pink region at $(- \pi, \pi)$, $(- \pi, -\pi)$, $( \pi, -\pi)$, $( \pi, \pi)$. This reflects the fact that when continuing from the grey to the pink region we necessarily cross the $[1, \infty]$ cut in the $z$ or $\bar{z}$ plane. Therefore, the $s$-channel OPE cannot be used in the pink region.
002707099 8564_ $$82219628$$s1740$$uhttp://cds.cern.ch/record/2707099/files/phi3diagrams.png$$y00013 The connected piece of $\langle \phi \phi \phi \phi \rangle$ at tree level. To first order in $\epsilon$, the scalar $\phi$ has dimension $\Delta=2 + \frac{5}{9} \epsilon$.
002707099 8564_ $$82219629$$s3406$$uhttp://cds.cern.ch/record/2707099/files/contour1.png$$y00004 Deformed integration contour $\mathcal{C}$. Firstly, we integrate over $\gamma_{14}$ as shown on the left keeping $\gamma_{12}$ fixed. Secondly, we integrate over $\gamma_{12}$ as shown on the right. Pinching occurs if, as $\epsilon \to 0$, a pole marked with a black cross collides with a pole marked with a blue dot on the $\gamma_{12}$ complex plane.
002707099 8564_ $$82219630$$s4927$$uhttp://cds.cern.ch/record/2707099/files/4dminscal.png$$y00009 We consider a scalar minimally coupled to gravity in $AdS_5$ or $CFT_4$. We imagine that the gravitational coupling is weak, or, equivalently, $c_T \gg 1$. The $\alpha$-functional (\ref{eq:magicfunctionals}) can be applied to $1 < \Delta < 1.5$. We plot the sum given by (\ref{eq:holostress}). We find that the sum is always negative within the region of applicability of the functional.
002707099 8564_ $$82219631$$s1613$$uhttp://cds.cern.ch/record/2707099/files/phi3triangle.png$$y00014 According to expression (\ref{Mellin diagram 2}), the contour must be placed to the right of $\Re (\gamma_{12})=1$, above $\Re (\gamma_{14})=0$ and to the bottom of $Re (\gamma_{13})=0$. We are thus led to the shaded triangle in this figure.
002707099 8564_ $$82219632$$s3866$$uhttp://cds.cern.ch/record/2707099/files/3dminscal.png$$y00010 We consider a scalar minimally coupled to gravity in $AdS_4$ or $CFT_3$. We imagine that the gravitational coupling is weak, or, equivalently, $c_T \gg 1$. The $\alpha$-functional (\ref{eq:magicfunctionals}) can be applied to ${1 \over 2} < \Delta < {3 \over 4}$. We plot the sum given by (\ref{eq:holostress}). We find that the sum is always negative within the region of applicability of the functional.
002707099 8564_ $$82219633$$s20474$$uhttp://cds.cern.ch/record/2707099/files/rhombusOPE.png$$y00003 We use red, blue and grey to colour the regions where the ${\cal O}(x_1) \times {\cal O}(x_2)$, ${\cal O}(x_1) \times {\cal O}(x_4)$ and ${\cal O}(x_1) \times {\cal O}(x_3)$ OPE channels converge respectively.
002707099 8564_ $$82219634$$s3317$$uhttp://cds.cern.ch/record/2707099/files/leadingtwist.png$$y00007 When acting on operators with spin the functionals $\alpha_{\tau, J,m}$ are negative for operators with twist $\tau < 2 \Delta_\sigma$ and non-negative for $\tau > 2 \Delta_\sigma$ with double zeros at the position of double trace operators $\tau_n = 2 \Delta_{\sigma}+2 n$ with $n \geq 1$. Here we plot the result for $J=2$. Different colors correspond to the contribution of descendants labeled by $m$. The external dimension is set to its numerical value in the 3d Ising model $\Delta_{\sigma} \simeq 0.518$.
002707099 8564_ $$82219635$$s1685$$uhttp://cds.cern.ch/record/2707099/files/LandauDiagram.png$$y00011 Example of a boundary Landau diagram.
002707099 8564_ $$82219636$$s3504$$uhttp://cds.cern.ch/record/2707099/files/Regge.png$$y00005 Kinematics (\ref{coordinates}). The Regge limit corresponds to taking $t' \to \infty$. In this limit $x_{34}^2 \to 0$.
002707099 8564_ $$82219637$$s2911$$uhttp://cds.cern.ch/record/2707099/files/cylinderpicture.png$$y00001 Cylinder picture of points $1$, $3$ and $4$. The point at $(t=0, \phi=\pi)$ should be identified with the point at $(t=0, \phi=-\pi)$. The colored area signifies regions where point $2$ is spacelike separated from three other points and no light-cones has been crossed. Note that the colored region is a double cover in the cross ratio space. Indeed changing $t_2 \to - t_2$ does not change the cross ratios (\ref{crossratiosspecial}).
002707099 8564_ $$82219638$$s2108$$uhttp://cds.cern.ch/record/2707099/files/singlevariableMellin.png$$y00012 Singularities in the complex plane of $s$. Blue balls represent the poles of $\psi(s)$, black crosses represent the poles of $\tilde{\psi}(s)$. Notice that we can gather the two straight contours $C_1$ and $C_2$ into a bent contour $C$, that separates poles to the left from poles to the right.
002707099 8564_ $$82219639$$s2643$$uhttp://cds.cern.ch/record/2707099/files/rhombus.png$$y00002 Sectorial domain $\Theta_{CFT}$ of analyticity of a generic CFT correlation function $F(u,v)$.
002707099 8564_ $$82219640$$s20608$$uhttp://cds.cern.ch/record/2707099/files/scalarsfunc.png$$y00006 Functionals $\alpha_{\tau, 0,m}$ as a function of twist $\tau$. They are non-negative with double zeros at the position of double trace operators $\tau_n = 2 \Delta_{\sigma}+2 n$. Different colors correspond to the contribution of descendants labeled by $m$. The external dimension is set to its numerical value in the 3d Ising model $\Delta_{\sigma} \simeq 0.518$.
002707099 8564_ $$82219641$$s1990$$uhttp://cds.cern.ch/record/2707099/files/pictureLorentzian.png$$y00000 We divide the region $u, v >0$ into $4$ regions coloured in blue, pink, red and grey. The regions are separated by the curves $v=(1-\sqrt{u})^2$ and $v=(1+\sqrt{u})^2$ or, equiavelntly, $z = \bar z$. In the grey region $z$ and $\bar{z}$ are the complex conjugate of each other. In the colored regions $z$ and $\bar{z}$ are real and independent variables. In the red region we have that $z, \bar{z} \in (-\infty, 0)$. In the blue and pink regions we have that $z, \bar{z} \in (0,1)$ and $z, \bar{z} \in (1,\infty)$ respectively.
002707099 8564_ $$82242857$$s1600992$$uhttp://cds.cern.ch/record/2707099/files/scoap3-fulltext.pdf$$yArticle from SCOAP3
002707099 8564_ $$82335257$$s1600992$$uhttp://cds.cern.ch/record/2707099/files/scoap.pdf$$yArticle from SCOAP3
002707099 960__ $$a13
002707099 980__ $$aARTICLE