irene valenzuela, agreed a theoretical physicist from the Department of Theoretical Physics at the Autonomous University of Madrid. "One of the questions is whether or not string theory is the only theory of quantum gravity," he said. "This goes in the direction that string theory is unique."

Other commentators felt this was too bold a leap, and noted reservations about the way the calculation was done.

## Einstein corrected

The number that Vieira, Guerrieri and Penedones calculated is the minimum possible value of $latex\alpha$ (alpha). Roughly speaking, $latex\alpha$ is the size of the first and largest mathematical term you must add to Albert Einstein's gravity equations to describe, for example, an interaction between two gravitons: the putative quantum units of gravity.

Einstein's 1915 general theory of relativity describes gravity as curves in the space-time continuum created by matter and energy. He perfectly describes behavior on a large scale, like a planet orbiting a star. But when matter is packed into very small spaces, general relativity is short-circuited. "There has to be some correction for Einstein's gravity," he said.Simon Caron Huot, theoretical physicist from McGill University.

Physicists can organize their lack of knowledge about the microscopic nature of gravity using a scheme developed by in the 1960skenneth wilsonmiStefan Weinberg: They simply add a number of possible "corrections" to general relativity that may become important at short distances. Suppose you want to predict the probability that two gravitons will interact in a certain way. They start with the standard mathematical concept of relativity and then add new concepts (using all relevant variables as building blocks) that become more important as distances get smaller. These fictitious terms are preceded by unknown numbers called $latex\alpha$, $latex\beta$, $latex\gamma$, etc. that define its size. "Different theories of quantum gravity will lead to different corrections," said Vieira, who has joint appointments at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and the International Center for Theoretical Physics in São Paulo, Brazil. "So these fixes are our first opportunity to differentiate between these possibilities."

In practice, $latex\alpha$ has only been computed explicitly in string theory, and even then only for highly symmetric 10-dimensional universes. The English String Theoristgreen michaeland colleagues found in the 1990s that in such worlds $latex\alpha$ must be at least 0.1389. In a given stringy universe it may be larger; how much higher depends on the string's coupling constant, or the tendency of a string to spontaneously split in two. (This coupling constant varies between versions of string theory, but all versions are tied to one main framework called M-theory, in which string coupling constants correspond to different positions in an extra 11th dimension.)

Meanwhile, alternative ideas about quantum gravity cannot yet make predictions about $latex\alpha$. And because physicists can't actually detect gravitons (gravity is very weak), they couldn't measure $latex\alpha$ directly to investigate and test theories of quantum gravity.

Then, a few years ago, Penedones, Vieira, and Guerrieri started talking about using the bootstrap method to constrain what can happen in particle interactions. You firstsuccessfully applied the approachto particles called pions. "We said, okay, this works great, so why not use gravity?" Guerrieri said.

## tearing up the border

The trick of using accepted truths to limit unknown possibilities was invented by particle physicists in the 1960s, then forgotten and revived to fantastic effect in the last decade by researchers with supercomputers capable of solving the awesome formulas Bootstrap is prone to.

Guerrieri, Vieira, and Penedones wanted to determine what $latex\alpha$ must be to satisfy two consistency constraints. The first, called unitarity, states that the probabilities of different outcomes must always add up to 100%. The second, known as Lorentz invariance, states that the same laws of physics must apply from all points of view.

The trio specifically looked at the range of $latex\alpha$ values allowed by these two principles in 10D supersymmetric universes. The calculation is not only simple enough to perform in this scenario (this is currently not the case for $latex\alpha$ in 4D universes like ours), but also allowed them to extend their initialized range with the theory's prediction of strings. Compare Latex \alpha$ in this 10D configuration is 0.1389 or higher.

Unitarity and Lorentz invariance place the following constraints on what can happen when two gravitons interact: When gravitons come together and dissipate, they can separate as two gravitons, or split into three gravitons, or any number of gravitons or other particles. they transform. Increasing the energies of the approaching gravitons changes the probability that they will emerge from the encounter as two gravitons, but consistency requires that the probability never exceed 100%. Lorentz invariance means that the probability cannot depend on how an observer is moving relative to the gravitons, which limits the form of the equations. Together, the rules create a complicated initialized expression that $latex\alpha$ must satisfy. Guerrieri, Penedones, and Vieira programmed the Perimeter Institute's computer clusters to solve for values that make the interactions of two gravitons uniform and Lorentz invariant.

The computer spit out its lower bound for $latex\alpha$: 0.14, plus or minus one hundredth, an extremely close and potentially exact match to the 0.1389 lower bound of string theory. In other words, string theory seems to span the entire space of allowed $latex\alpha$ values, at least in the 10D position where the researchers checked. "It was a big surprise," Vieira said.

## 10 dimensional matches

What can numerical randomness mean? According to Simmons-Duffin, whose work helped fuel Bootstrap's revival a few years ago, "They are trying to solve a fundamental and important problem. Namely, to what extent does string theory as we know it cover the space of all possible theories of quantum gravity?

String theory emerged in the 1960s as a putative picture of the fibrous glue that holds together composite particles called mesons. Over time, a different description became popular for this purpose, but years later it was discovered that string theory could have higher goals: if strings are small, so small that they look like points, they could serve as elementary building blocks. of the nature. Electrons, photons, etc., would all be the same type of fundamental string played in different ways. The selling point of the theory is that it provides a quantum mechanical description of gravity: a graviton is a string or closed loop in its lowest energy mode of vibration, with an equal number of waves propagating clockwise and counterclockwise. around the loop. This resource is behind the macroscopic properties of gravity, such as the corkscrew polarization of gravitational waves.

But combining the theory with all other aspects of reality requires some work. To get rid of the negative energies that would correspond to nonphysical particles faster than luminals, string theory needs a property called supersymmetry that doubles the number of vibrational modes of strings. Each vibratory mode that corresponds to a particle of matter must be accompanied by another mode that corresponds to a particle of force. String theory also requires the existence of 10 dimensions of space-time for strings to move. However, we did not find any supersymmetric companion particles, and our universe appears in 4D with three spatial dimensions and one temporal dimension. The data points present a problem.

If string theory describes our world, supersymmetry must break here. This means that the associated particles, if any, must be much heavier than the known group of particles, too heavy to lump together in experiments. And if there really are 10 dimensions, six must be coiled so small that we are imperceptible to them: tight little knots of additional directions that you can access at any point in space. These "packed" dimensions in a 4D-like universe can have any number of possible arrangements, all of which affect strings (and numbers like $latex\alpha$) differently.

Broken supersymmetry and unseen dimensions have led many quantum gravity researchers to seek or favor alternative, nonfibrous ideas. But until now, competing approaches have had trouble producing the kind of concrete calculations about things like graviton interactions that string theory can do.

Some physicists hope that string theory will automatically win hearts and minds because it is the only microscopic description of gravity that is logically consistent. If researchers can prove what is sometimes called "string universality," a monopoly of string theories among viable fundamental theories of nature, we have no choice but to believe in hidden dimensions and an inaudible string orchestra. .

For string theorists, the new bootstrap calculus opens a path to eventually proving the universality of strings, and the journey is off to a good start.

Other researchers disagree with these implications.Astrid Eichhorn, a theoretical physicist at the University of Southern Denmark and the University of Heidelberg who specializes in a nonlinear approach called asymptotically safe quantum gravity, told me: "I would look at the relevant scenario to find evidence for or against a quantum theory. particular of gravity collect "four-dimensional and non-supersymmetric universes" as this "better describes our world, at least so far".

Eichhorn pointed out that there may be uniform, Lorentz-invariant descriptions of gravitons in 4D that are meaningless in 10D. "Only with this configuration choice, one can rule out alternative quantum gravity approaches" that are viable, he said.

Acknowledging that the universality of strings can only be held in 10 dimensions, Vieira said: "It could be that in 10D with supersymmetry there is only string theory, and when you go to 4D there will be many theories." I doubt."

However, another criticism is that even if string theory saturates the range of allowed values of $latex\alpha$ in the 10-dimensional scenario the researchers studied, that does not prevent other theories from falling within the allowed range. "I don't see any practical way to conclude that string theory is the only answer," he said.André Tolleytun Imperial College London.

## just the beginning

Assessing the importance of chance becomes easier when starters can generalize similar results and extend to more settings. "Right now, many, many people are pursuing these ideas in different variations," he said.Alejandro Schibojedow, theoretical physicist at CERN, the European laboratory for particle physics.

Guerrieri, Penedones, and Vieira have already performed a "dual" bootstrap computation that bounds $latex\alpha$ from below and discards solutions smaller than the minimum rather than solving for usable values of $latex\alpha$ above the bound, like they did. before. This double calculation shows that their computer groups simply did not miss the minimum allowed values of $latex\alpha$, which would amount to other viable theories of quantum gravity beyond the scope of string theory.

They also plan to initialize the lower bound for worlds with nine large dimensions, where string theory calculations are still under scrutiny (since only one dimension is curled up), to look for more evidence of correlation. In addition to $latex\alpha$, bootstrappers also want to calculate $latex\beta$ and $latex\gamma$, the allowable magnitudes of the second and third largest quantum gravity corrections, and have ideas on how to do more difficult calculations. calculations on worlds where supersymmetry is broken or absent as it appears in reality. In this way, they will attempt to circumscribe the space of allowed quantum gravity theories, testing the universality of strings in the process.

claudia from ramm, a theorist at Imperial College, emphasized the need to be "agnostic" and found that bootstrap principles are useful for exploring more ideas than just string theory. She and Tolley used positivity, the rule that probabilities are always positive, toconstrain a theory called massive gravity, which may or may not be a realization of string theory. They discovered potentially testable consequences, showing that massive gravity is positive only when certain exotic particles exist. De Rham sees bootstrap principles and positive frontiers as "one of the most exciting research developments right now" in fundamental physics.

"No one did this job of taking everything we know, making it consistent and putting it all together," Zhiboedov said. It was "exciting," he added, that theorists had to work "at a very basic level."

*Editor's Note: Penedones and Vieira are members of the Simons Collaboration on the Nonperturbative Bootstrap, a research program supported and funded by the Simons Foundation*independent publishing magazine*. Funding decisions by the Simons Foundation do not affect our reporting.*