The Gravity of Hadrons

PHYSICS IN ACTION dimension can tell you that QCD is asymp- totically free. Other strings with different The gravity of hadrons vibrations or motions, for instance, can describe the properties of states in which two Researchers have calculated the masses of several particles or more gluons are bound together. The duality therefore provides a strict mapping by exploiting a connection between string theory and QCD between each QCD state and a particular dual string. From Nick Evans in the Department of Physics, ICAR In the last few years theorists have turned V University of Southampton, UK AC this new theoretical tool to the question M AN I of whether we can describe the physics of In recent years particle physicists have real- real QCD. But in order to fully account ized that many theories they previously for the plethora of particles that we know thought were distinct are actually copies of to be bound by the strong nuclear force, the one another that describe the same physical dual theory has to be extended so that it phenomena. The most remarkable example includes quarks. of this “duality” has been the connection between string theory and the Standard Something from nothing Model of particle physics. The most versatile construction for inclu- String theory describes the subatomic ding quarks in the gravitational dual was world in terms of lengths and loops of infi- developed by Andreas Karch and co-wor- nitesimal strings that exist in higher spatial kers at the University of Seattle in 2002. dimensions than our familiar three. Differ- Using the same mapping rules between ent vibrations or modes of these strings re- QCD and strings developed for the gluon- present different particle properties, and only dual theory, the researchers included at long distances the strings appear as if a new sector of strings in the gravity theory they are indeed point-like. Crucially, these that had the correct properties, such as modes require the curved space–time of mass, to describe quarks. The next step was general relativity,which is a theory of grav- to find out whether the quarks triggered ity. String theory is thus viewed as a candi- the vacuum of the gluon-only theory to fill date for a “theory of everything” that unites with quark–antiquark pairs. gravity with the three other fundamental Asymptotic freedom has dramatic con- forces of nature: electromagnetism plus the Duality could simplify our understanding of the way sequences for the way QCD describes the weak and the strong nuclear forces. quarks are bound in hadrons such as neutrons. vacuum. You might think that the vacuum The hugely successful Standard Model would simply be empty, but according to describes these three forces in terms of gauge in computing capabilities have enabled re- the uncertainty principle empty space can theories, in which the interactions between searchers to thoroughly test the theory (see borrow a little energy for very short periods elementary particles are mediated by “gauge Physics World July pp22–23). But in 1997 of time. Einstein’s famous mass–energy bosons”. For example, in the gauge theory Juan Maldacena of the Institute for Ad- relation then tells us that this energy can be of electromagnetism – quantum electrody- vanced Study in Princeton conjectured that used to create particles such as a quark– namics or QED – charged particles such as the physics of quarks and gluons could antiquark pair. electrons interact via the exchange of pho- be equally well described in terms of the The strength of the attraction between tons. Gravity,however, is not included in the space–time geometry,black holes and grav- distant quarks means that these “virtual” Standard Model. ity waves of a “dual” string theory. This particles become real and long-lived. The Although there is no firm evidence for dual theory is weakly coupled, rather than vacuum therefore fills rapidly until the string theory or for higher dimensions, dual- strongly coupled like QCD, which means quarks are so close together that asymp- ity proposes that strings might offer a new we know how to calculate observables such totic freedom kicks in and the production description of the gauge theory of the strong as particle masses using it. In other words, of further quark pairs is no longer energet- force: quantum chromodynamics (QCD). Maldacena’s duality suggested that every- ically favourable. The signal we have for thing about the QCD particle spectrum this cut-off behaviour is simply the proton Strongly coupled might be calculable from the dual theory mass, which is 100 times larger than the In QCD the interactions between the six with no more than a pencil and paper! combined mass of its constituent quarks known quarks (up, down, charm, strange, Early work on this correspondence be- (two up quarks and a down quark) due to bottom and top) are mediated by massless tween QCD and string theory was per- their interactions with the mire of vacuum gluons. However, unlike the forces of elec- formed with a mathematical relative of quark pairs. tromagnetism and gravity – which decrease QCD that included only gluons, in order In 2004 James Babington and co-workers rapidly with distance – the strong nuclear to make the calculations simpler. This dual at Humboldt University in Berlin along with force gets stronger the further two quarks are theory,which automatically includes gravity, the present author (and, in a parallel ana- separated. Indeed, the interaction between contains strings that exist in four spatial di- lysis, Martin Kruczenski and co-workers at widely separated quarks is so strong that mensions. As you move in the fourth di- the Perimeter Institute in Canada) showed the quarks can never be freed from one rection of this “anti-de-Sitter” space–time, that one of the extra string distributions another, and are instead confined into pro- lengths in the remaining three directions in- introduced by Karch and co-workers cor- tons, neutrons and other hadrons. On the crease (see Physics World May 2003 pp35–38). responds to a non-zero density of quark– other hand, the strong interaction switches To the surprise of many theorists, the antiquark pairs in the dual theory. In other off completely at very short distances. extra dimension in this dual gravitational words, the gravitational description indeed This “asymptotic freedom” makes the theory turns out to account for the different appeared to describe the QCD vacuum, equations of QCD extremely difficult to length scales in QCD. For example, the den- and theorists could begin to study hadrons solve, and it is only recently that advances sity of strings at different places in the fourth for the first time. 26 physicsweb.org P HYSICS W ORLD A UGUST 2005 PHYSICS IN ACTION The first hadron we looked at was a type N (2600) of meson called a pion, which is a bound HIGHLIGHTS FROM state of either an up or down quark plus an antiquark. In QCD such a state corresponds N (2250) PHYSICSWEB to a small area of space where the quark– N (2190) antiquark density is greater than it is in the N (1700) New look for hydrogen storage vacuum. But the gravitational theory des- mass N (1675) N (2220) Physicists in the US, Canada and cribes the pion as an area of space in which N (1650) Germany have proposed a novel there is an excess in the density of strings that N (1720) technique for storing hydrogen. The N (1680) travels through anti-de-Sitter space like a N (1535) method involves storing the gas between wave. The gravitational technique again N (1520) layers of graphite, and could help in the turned out to be a success, reproducing, for N (939) quest for practical hydrogen-storage example, the experimental observation that 0 2 4 6 devices for fuel cells. John Tse of the the pion mass depends on the square root orbital angular momentum, L University of Saskatchewan and of the mass of the constituent quarks. Mass agreement – using a “gravitational dual” co-workers have shown that thin sheets These results were all obtained in simple theory that can also describe QCD, Stanley Brodsky of carbon atoms spaced between 6–7 Å gravitational duals that contained only one and co-workers were able to predict the masses of apart can store hydrogen at room certain baryons called nucleons, N. These particles type of quark. But formally deriving the 1 temperature and moderate pressures. can have a spin angular momentum of /2 (dashed 3 string theory of a more realistic gravita- curve) or of /2 (solid curve) and each state can also tional dual of QCD – one that includes up, have various values of orbital angular momentum Triple-star status for exoplanet down and strange quarks, for example – has (horizontal axis). For example, the L = 0 state is the A planet with a mass similar to that of turned out to be hard. Recently, however, neutron, N (939), where the number in brackets Jupiter has been discovered orbiting a Stanley Brodsky of Stanford University, represent its mass in mega-electron-volts. The star in the constellation Cygnus. Josh Erlich of Seattle University and Le- observed masses of the nucleons are shown by Maciej Konacki and colleagues found the points. Importantly, the gravitational-dual andro De Rold of the University of Barce- theory correctly predicts that states differing by that the new planet orbits the main star of lona independently took a more practical one unit of L on the solid and dotted curves have a triple-star system every 3.35 days, which approach and simply guessed what the grav- the same mass.

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