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Is N=8 Supergravity Finite?

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Is N=8 Supergravity Finite? Do We Need String Theory to Quantize Gravity? Lance Dixon (CERN & SLAC) in collaboration with Z. Bern, J.J. Carrasco, H. Johansson, R. Roiban Theory Colloquium University of Padova and INFN Padova 3 February 2011 Gravity Governs the Very Big Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 2 But Per Particle It Is Very Weak Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 3 Quantum Mechanics Rules the Very Small Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 4 How Can Gravity And Quantum Mechanics Coexist? • Since Einstein, physicists have sought to unify all the fundamental forces and particles in the universe. • 3 of 4 forces – strong, weak and electromagnetic – have been put on a common footing, fully quantum mechanical and relativistic, and subject to a multitude of experimental tests. • Gravity is very different. • Conventional wisdom for 25 years: The only way to make gravity consistent with quantum mechanics is if all elementary particles are really oscillation modes of strings. • Here I want to describe another possible way that quantum gravity might work, without strings, with only point-like particles. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 5 Hawking Radiation • Involves both quantum mechanics and gravity • Particles produced in curved spacetime near a black hole • Very well accepted theoretically, although also poses paradoxes • However, main effect is not quantum gravity – spacetime geometry is treated classically, not as fluctuating Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 6 Quantum Space-Time Foam • This is quantum gravity – geometry has quantum fluctuations • But very hard to treat quantitatively • We will do something simpler – bounce gravitons off each other • Gravitons are quantized plane-wave ripples of space-time Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 7 Quantum Foam Constrained A Little • Some models of quantum gravity predict a tiny violation of Lorentz invariance, resulting in different speeds of light for different photon energies: dt/L = dE/MPlanck • Fermi Gamma-ray Space Telescope (Padova, SLAC,…) measured photon arrival times from g-ray burst 7 billion light years away to be < 1 second. Contradicts (barely) this specific kind of deviation. Fermi GBM/LAT collaboration, arXiv:0908.1832 Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 8 Electromagnetism • Force holding atoms together • Electricity, magnetism, light, radio waves, ... • Carried by photon, a packet of light – plane-wave ripple of electromagnetic field Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 9 Quantum ElectroDynamics (QED) • The quantum mechanical, special relativistic, theory of electromagnetism • Describes interactions of photons and electrons to incredible accuracy Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 10 QED – A Very Precise Theory • Sum up all Feynman diagrams at each order (number of closed loops) • Successive orders suppressed by a small number, the fine structure constant: g + e e3 = ea e5 = ea2 + anomalous magnetic moment of electron – computed to four loops, order a4 Kinoshita et al. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 11 Standard Model • Describes all elementary forces except gravity in same basic framework as QED • Forces carried by spin 1 vector bosons: g W+ W- Z0 g • Finite, testable predictions for all quantities (after renormalization) „t Hooft-Veltman Nobel Prize 1999 n g electromagnetism (QED) weak strong (QCD) Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 12 Gravity Is Very Different E&M a vector force, Gravity a tensor force, carried by carried by spin 1 photon g spin 2 graviton h End view Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 13 Gravitons Are Real No direct detection of gravitational waves yet But radiated power in binary pulsar system is precisely accounted for by orbital decay NASA, K. Thorne & T. Carnahan Hulse, Taylor 1974-1983 Nobel 1993 LIGO, Hanford, WA Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 14 Those Were Classical Waves But in quantum mechanics GRAVITY NASA, K. Thorne & T. Carnahan We can (in theory) scatter gravitons off each other, and see how different quantum gravity theories behave. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 15 Gravity Is Very Different Coulomb‟s Law for Newton‟s Law of electrostatic force universal gravitation Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 16 Per Particle, Gravity Is Very Weak 1044 for 2 electrons Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 17 Graviton Scattering – Strictly a Gedanken Experiment • Even the leading term is unobservably small, let alone quantum corrections! • Like QED, sum up all Feynman q diagrams at each loop order (number of closed loops) • Successive orders should be suppressed by a very small number, at least when energies are small: Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 18 Graviton Scattering Amplitude q (24 more) Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 19 Compare Photon & Graviton Scattering In both cases, have to do a sum over all possible quantum fluctuations an integral over relativistic four-momentum p flowing around the loop: But the form of Newton‟s Law, boosted relativistically to high energies generically implies two powers worse behavior in p per loop in gravity than in QED Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 20 Compare Photon & Graviton Scattering In QED, the integrals “barely” converge – in fact, there are divergences (in other diagrams) but the divergences can systematically be removed by renormalization Feynman, Tomonaga, Schwinger, Nobel 1965 In gravity, the integrals look hopelessly divergent. In fact, one loop amplitude in pure gravity is finite ‟t Hooft, Veltman 1974 But at two loops there is a divergence which cannot be removed by renormalization – and all predictive power is lost Goroff, Sagnotti 1986; van de Ven, 1992 Pure gravity is nonrenormalizable Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 21 Meanwhile, String Theory Came Along Newton (1680) Replacing particles with strings spreads out the interactions in spacetime, which damps the integrals in momentum space, making them finite. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 22 String Theory Has Many Virtues – But Also Some Problems The String “Landscape” 10500? ground states (vacua) to choose from predicting new phenomena unambiguously is a big challenge (unless string length scale is very nearby) Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 23 Is String Theory Necessary for a Finite Theory of Quantum Gravity? • String theory cures the divergences of quantum gravity by introducing a new length scale, the string scale, at which particles are no longer pointlike. • Is this necessary? Or could enough (super)symmetry allow a point-particle quantum gravity theory to be finite? • If the latter is true, even if in a “toy model”, it would have a big impact on how we think about quantum gravity. • There are other proposed alternatives to string theory: - Simplicial lattice regularization (Regge) e.g. Hamber, Williams - Asymptotic safety program Niedermaier, Reuter, Liv. Rev. Rel. 9, 5 - UV theory could be Lorentz asymmetric, but renormalizable Hořava, 0812.4287, 0901.3775 - Loop quantum gravity A. Ashtekar et al. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 24 About Supersymmetry • Relates particles with integer spin (bosons) to particles with ½ integer spin (fermions) • Phenomenological version ( supersymmetry) predicts a host of new particles to be discovered at the LHC Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 25 “Toy model” we have been studying: Supergravity DeWit, Freedman (1977); Cremmer, Julia, Scherk (1978); Cremmer, Julia (1978,1979) 28 = 256 particles, all massless • The eight supersymmetries relate all states to each other, ½ unit of helicity at a time • Most supersymmetry allowed, for maximum spin of 2 • Unique theory, but very complicated-looking interactions Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 26 Is ( ) supergravity finite? A question that has been asked many times, over many years. “Reports of the death of supergravity are exaggerations. One year everyone believed that supergravity was finite. The next year the fashion changed and everyone said that supergravity was bound to have divergences even though none had actually been found.” S. Hawking (1994) Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 27 Supergravity vs. String Theory String vibrations imply an infinite tower of particle states with increasingly large mass Lowest, massless states of one string theory (closed type II superstring) identical to those of N=8 supergravity. Low-energy limit of interactions also the same; but high energy behavior is very different due to massive states Still, can get hints from string theory (and M theory) about the possible behavior of N=8 supergravity: • No divergences until 9 loops? (No divergences at all?) Green Russo Vanhove (2006-7) • No divergences until 7
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