Conformal collider physics: energy and charge correlations

By D. Hofman, J. Maldacena. 2008

823 citations recorded by the source corpus.

We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision. We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers. For = 1 superconformal theories the one point function for states created by the R-current or the stress tensor are determined by the two parameters a and c characterizing the conformal anomaly. Demanding that the measured energies are positive we get bounds on a/c. We also give a prescription for computing the energy and charge correlation functions in theories that have a gravity dual. The prescription amounts to probing the falling string state as it crosses the AdS horizon with gravitational shock waves. In the leading, two derivative, gravity approximation the energy is uniformly distributed on the sphere at infinity, with no fluctuations. We compute the stringy corrections and we show that they lead to small, non-gaussian, fluctuations in the energy distribution. Corrections to the one point functions or antenna patterns are related to higher derivative corrections in the bulk.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bef65335e7239d00af42d3606808f735c9e8f156

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In Nuclear and High Energy Physics

Citations in the corpus

Holographic studies of quasi-topological gravity (2010, methodology): “In particular, the new couplings are generalized such that the dual CFT will not be supersymmetric [11] and so this holographic model may provide new insights on non-supersymmetric gauge theories with a conformal fixed point.”
Stringy effects in scrambling (2014, methodology): “[51], we choose to evaluate it on a null slice u = , just to the left of the shock.”
Holographic Lovelock gravities and black holes (2009, background): “Requiring positivity of the energy flux in a four-dimensional CFT places certain constraints on the values of the two parameters which determine the angular distribution of the energy flux, t2 and t4 [11].”
Central charges of 𝒩 = 2 superconformal field theories in four dimensions (2008, background): “In [30] bounds on a/c have been obtained based on a positive energy assumption.”
Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “This property is equivalent to the averaged null energy condition for QFT and has interesting consequences [39].”
On renormalization group flows in four dimensions (2011, background): “2 Interesting bounds on the values a and c may assume at fixed points have been devised recently [7,8].”
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, background): “In recent proofs of the Hofman-Maldacena bounds from bootstrap methods, these operators also make an appearance [43].”
On graviton non-gaussianities during inflation (2011, background): “21) becomes of order one we have causality problems [29–32].”
Searching for long-lived particles beyond the Standard Model at the Large Hadron Collider (2019, background): “simplest case is Anti-de Sitter (AdS)/CFT duality, where events are perfectly spherical [549].”
Holographic GB gravity in arbitrary dimensions (2009, methodology): “Changing the coordinates, it can be shown [18, 25] that the relevant graviton profile is given by Hy1y2(y + = 0, y, y, u) ≃ 1 E2 e −/2 δ(y) δ(u− 1) .”
Holographic Quantum Matter (2016, background): “Remarkably, it can be shown, both from the bulk and also from general QFT arguments, that consistency requires [142; 381; 382; 383; 569]”
Momentum dissipation and effective theories of coherent and incoherent transport (2014, neutral): “However, γ1 is bounded by causality, and must satisfy −1/12 ≤ γ1 ≤ 1/12 [71, 78].”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, positive): “…to be generated by a local operator O acting on the vacuum, the ANEC leads to positivity constraints on 3pt functions 〈OTµνO〉 called “conformal collider bounds” (Hofman and Maldacena, 2008).46 Recently, Cordova and Diab (2018) used the ANEC to argue that primaries of high chirality (large |`− ¯̀”
Emergent spacetime and holographic CFTs (2011, background): “90 The relative scaling of a, c, A,B,C, and CT in the limit CT → ∞ follows, to some extent, from the inequalities derived in [115].”
Light quark energy loss in strongly coupled N=4 supersymmetric Yang-Mills plasma (2008, neutral): “[37].”
TASI Lectures on the Conformal Bootstrap (2016, background): “Examples include bounds from energy positivity [43], dispersion relations [44–47], and causality [48, 49].”