Welcome: QCD Meets Gravity

Transcription

1 Welcome: QCD Meets Gravity December 11, 2017 Zvi Bern 1

2 Welcome To The Mani L. Bhaumik Institute We have a new Institute! Workshop is hosted by Institute. Discussion area not quite ready, so we are going to Caltech on Thur. You can say hello to Mani at Tuesday s conference dinner. Note: He s a laser physicist who loves fundamental theory, so please talk physics him! Speakers: Please send talks to dylan@physics.ucla.edu Please consult web pages for latest schedule 2

3 Scattering Amplitudes QCD and collider physics string theory supergravity N = 4 sym AdS/CFT twistor strings scattering amplitudes mathematics new principles: amplituhedron last year gravity waves this year Healthy fields always produce results of interest to outsiders 3

4 Many topics at workshop KLT, BCJ, and double copy Classical solutions. Talks: Carrasco, Schlotterer, Mizera, Ochirov Talks: Adamo, Schlotterer, Mizera, Ochirov Ambitwistor strings. Generalized unitarity. Supergravity, double copy. Talks: Geyer, Tourkine, Roehrig Talks: Bourjaily, Carrasco Talks: Anastasiou, Carrasco Nagy, Chiodaroli, Parra-Martinez Grassmannians, positive geometry, polytopes. Talks: Bai, He, Huang Gravity waves etc Talks: Buonanno, Rothstein, Guevara, Goldberger, Ridgway 4

5 Gravity waves? LIGO and gravity waves are here to stay. Mature field with a lot of work. Nontrivial to make useful contributions. Why might we be able help out? High orders of gravity perturbation theory is our specialty. We appreciate the challenge. NLO QCD for colliders. The double copy! Simplifying gravity. The time is right. New advances setting up basics. I want to explain why many of us think something important can be done for gravity waves using modern ideas from amplitudes. 5

6 Feynman Diagrams for Gravity Over the years some debate about UV properties of supergravity. Suppose we want to check by calculating: 3 loops 4 loops ~10 20 TERMS ~10 26 TERMS No surprise it has never been calculated via Feynman diagrams. Calculations to settle this seemed utterly hopeless! Seemed destined for dustbin of undecidable questions. 5 loops ~10 31 TERMS More terms than atoms in your brain! Superspace helps, but not enough to make a difference. Standard techniques utterly hopeless.

7 How do we tame gravity perturbation theory? Two principles: 1) Analytic properties. Gauge-invariant on-shell quantities. 2) Take the square root by rewriting as two copies of gauge theory.

8 Analytic Propertes: BCFW Recursion Britto, Cachazo, Feng and Witten (BCFW) Physical scattering amplitudes constructed from on-shell physical scattering amplitudes with fewer particles! on-shell gauge invariant amplitude Works by making clever use of Cauchy s residue theorem Same construction works in gravity. Brandhuber, Travaglini, Spence; Cachazo, Svrcek; Benincasa, Boucher-Veronneau, Cachazo; Arkani-Hamed and Kaplan, Hall 8

9 Analytic Properties: Modern Unitarity Method E 2 = p 2 + m 2 Two-particle cut: Three-particle cut: on-shell ZB, Dixon, Dunbar and Kosower Systematic assembly of complete amplitudes from other amplitudes. Works for any number of particles or loops. Generalized unitarity cut as a practical tool. leading singularity on-shell ZB, Dixon and Kosower; ZB, Morgan; Britto, Cachazo, Feng; Ossala,Pittau,Papadopoulos; Ellis, Kunszt, Melnikov; Forde; Badger and many others Ideas used throughout workshop. Application of these ideas to post-newtonian approximation. See talk by Guevara Talks by Bourjaily, Carrasco, Chiodaroli, etc 9

10 A New Way to Think About Gravity Kawai-Lewellen-Tye string relations in low-energy limit: gravity KLT (1985) gauge theory color ordered Pattern gives explicit all-leg form Gravity is obtainable from gauge theory. Standard QFT offers no hint why this is possible. 10

11 Gravity vs Gauge Theory Consider the Einstein gravity Lagrangian curvature Flat-space metric graviton field metric Infinite number of interactions + giant mess Compare to gauge-theory Lagrangian on which QCD is based Only three and four point interactions Gravity seems so much more complicated than gauge theory. Does not look related! How do KLT relations come about? 11

12 Three Vertices Standard Feynman diagram approach. Three-gluon vertex: Three-graviton vertex: About 100 terms in three vertex Naïve conclusion: Gravity is a nasty mess. KLT formulas proves this is not correct way to look at gravity 12

13 Simplicity of Gravity Amplitudes People were looking at gravity amplitudes the wrong way. On-shell viewpoint much more powerful. On-shell three vertices contains all information: Yang-Mills gauge theory: Einstein gravity: square of Yang-Mills vertex. Using modern methods, any gravity scattering amplitude constructible solely from on-shell 3 vertex. Higher-point vertices irrelevant! Simplest manifestation of double copy 13

14 Gravity From Gauge Theory? How does the Einstein action reflect KLT factorization? Consider all possible field redefinitions and gauge fixing. ZB and Grant (1999) Lorentz indices factorize but no KLT in sight. Not satisfactory. More recent work: Order by order BCJ double copy Lagrangian. ZB, Dennen, Huang, Kiermaier (2004); Tolotti, Weinzierl (2013) All orders Lorentz index factorization in compact Lagrangian. Cheung and Remmen (2016) Lorentz index factorization!

15 Duality Between Color and Kinematics Consider five-point tree amplitude: A tree 5 = X15 i=1 c i n i Q i p 2 i ZB, Carrasco, Johansson (BCJ) color factor kinematic numerator factor Feynman propagators c c 2 = f a 3a 4 b f ba2c f ca 1a 5 1 = f a 3a 4 b f ba5c f ca 1a 2 c 3 = f a 3a 4 b f ba1c f ca 2a 5 c 1 + c 2 + c 3 =0 n 1 + n 2 + n 3 =0 At tree level can always find a rearrangement so color and kinematics satisfy the same algebraic constraint equations. Loop level remains a conjecture. BCJ, Bjerrum-Bohr, Feng, Damgaard, Vanhove, ; Mafra, Stieberger, Schlotterer; Tye and Zhang; Feng, Huang, Jia; Chen, Du, Feng; Du, Feng, Fu; Naculich, Nastase, Schnitzer O Connell and Montiero; Bjerrum-Bohr, Damgaard, O Connell and Montiero; O Connell, Montiero, White, etc. 15

16 Gravity Loop Integrands from Gauge Theory BCJ Ideas conjectured to generalize to loops: color factor (k) (i) (j) If you have a set of duality satisfying numerators. To get: gauge theory color factor simply take gravity theory kinematic numerator kinematic numerator c k n k Gravity loop integrands follow from gauge theory! 16

17 Simplest constructions: Gravity From Gauge Theory N = 8 sugra: (N = 4 sym) (N = 4 sym) N = 5 sugra: (N = 4 sym) (N = 1 sym) N = 4 sugra: (N = 4 sym) (N = 0 sym) Spectrum controlled by simple tensor product of gauge theories. More sophisticated lower-susy cases: QCD, magical supergravities, Einstein-YM with and without Higgsing, twin supergravities. Anastasiou, Bornsten, Duff; Duff, Hughs, Nagy; Johansson and Ochirov; Carrasco, Chiodaroli, Günaydin and Roiban; ZB, Davies, Dennen, Huang and Nohle; Nohle; Chiodaroli, Günaydin, Johansson, Roiban. A. Anastasiou, L. Borsten, M.J. Duff, M.J. Hughes, Marrani, Nagy, Zoccali. Many other theories in double-copy story, including open and closed string theory, NLSM, Dirac Born Infeld, Galileon and Z theory. Cachazo, He, Yuan; Chen Du, Broedel, Schlotterer and Stieberger; Carrasco, Mafra, Schlotterer; Talks from Anastasiou, Nagy, Chiodaroli, etc 17

18 Real Gravity? Natural double copy of gluons: 2 x 2 = 4 Graviton, dilaton, antisymmetric tensor (or axion) Supergravity theories typically have dilatons and axions, so OK. What about real world problems with no susy? Insert graviton physical state projectors into unitarity cuts: Used to reanalyze 2 loop UV divergence of pure Einstein gravity to show its value is content free. Calculate renorm. scale instead. ZB, Cheung, Chi, Dixon,Nohle; ZB, Chi, Dixon, Edison An alternative is to use ghosts. Johansson and Ochirov For gravity waves, already some nice work on dealing with dilaton annoyance. Luna, Nicholson, O'Connell, White. 18

19 Generalized Double Copies New method, bypasses this: Start with naïve double copy of any correct sym integrand: c i! n i BCJ representation can be hard to find. Not a BCJ representation See Mogul and Carrasco talks. Systematic corrections in terms of BCJ discrepancy function n i + n j + n k = J ijk BCJ discrepancy function (1) (2) propagators cancel trivially BCJ representation not required for double copy. ZB, Carrasco, Chen, Johansson, Roiban, Zeng (2017) Generalized double copy works for 5 loop N = 8 sugra problem. Ideas might be helpful to gravity wave problem. 19

20 Double Copy and Classical Solutions Luna, Monteiro, O Connell and White; Luna, Monteiro, Nicholsen, O Connell and White; Ridgway and Wise; Goldberger and Ridgway; Tim Adamo, Casali, Mason, Nekovar; Cachazo and Guevara Schwarzchild and Kerr black holes. Taub-NUT spaces Solutions with cosmological constant. Radiation from accelerating black hole. 3 point functions and curved backgrounds Post-Newtonian approximation It may be possible to extend this to more general cases. Recent papers explain possible application to gravity waves. Goldberger and Ridgway; Luna, Monteiro, Nicholson, Ochirov, O'Connell, Westerberg, White; Goldberger, Prabhu, Thompson Talks from Ochirov, Adamo, Casali, Guevara, Goldberger, Ridgway 20

21 Outlook Besides all the other topics, it will be great fun to discuss possible applications to gravity waves. What are the challenges to having a fully functioning double-copy formalism at required PN orders? What are gravity-wave issues, where we might actually be able to contribute in short term? Gravity wave review talks from Buonanno and Rothstein Thursday: a day of gravity wave discussions. 21