# Dual of shockwaves As reviewed and studied in [[2017#Afkhami-Jeddi, Hartman, Kundu, Tajdini]], there are three ways of creating [[0117 Shockwave|shockwaves]] from the CFT perspective. 1. insert momentum-space operator smeared against a wavepacket profile 2. insert a heavy local operator $\phi$ with $\Delta_\phi\gg 1$ at a single point 3. complexified wavepacket These states differ microscopically but appear the same for probes avoiding the delta function at the shockwave source. ## Refs - method 1 (inserting momentum-space operator smeared against a wavepacket profile) - [[2006#Cornalba, Costa, Penedones, Schiappa (a)]] - [[2006#Cornalba, Costa, Penedones, Schiappa (b)]] - [[2007#Cornalba, Costa, Penedones]] - method 2 (insert a heavy local operator $\phi$ with $\Delta_\phi\gg 1$ at a single point) - [[2013#Nozaki, Numasawa, Takayagani]] - [[2014#Asplund, Bernamonti, Galli, Hartman]] - [[2015#Hartman, Jain, Kundu]] - [[2014#Roberts, Stanford, Susskind]] - method 3 (complexified wavepacket) - [[2016#Afkhami-Jeddi, Hartman, Kundu, Tajdini]] - shockwave and [[0030 Operator product expansion|OPE]] - [[2017#Afkhami-Jeddi, Hartman, Kundu, Tajdini]] - causality - [[2016#Hartman, Kundu, Tajdini]]: ANEC from causality - [[2017#Afkhami-Jeddi, Hartman, Kundu, Tajdini]] - locality - [[2017#Chen, Fitzpatrick, Kaplan, Li]] - related - [[2015#Hartman, Jain, Kundu]] shock waves but *in CFT* ## Method 2: local heavy operators - insert a scalar primary operator $\psi$ near $\mathrm{i}\infty$ - e.g. a real Lorentzian shock wave metric is dual to $|\Psi\rangle=\psi\left(u=\frac{\mathrm{i} \Delta_{\psi}}{2 E}, v=\frac{2 \mathrm{i} z_{0}^{2} E}{\Delta_{\psi}}\right)|0\rangle$ - require $1\ll\Delta_\psi\ll E$ ## Correlator - $G_{\text {Eik }}(z, \bar{z})=\frac{\Gamma(2 \Delta)}{\Gamma^{2}(\Delta-1)} \int_{H_{3}} \frac{d^{3} \mathbf{x}}{(-2 \mathbf{q} \cdot \mathbf{x}+h(\mathbf{x} \cdot \mathbf{p})+i \epsilon)^{2 \Delta}}$ - leading eikonal [[2006#Cornalba, Costa, Penedones, Schiappa (a)]] - all order eikonal [[2019#Fitzpatrick, Huang, Li]] eqn.31 and later as an expansion - QFT on shockwave background? [[Klimcik1988]]