In search of a unified theory

The most efficient solution to date for unifying gravitation and quantum mechanics is the superstrings theory, which is currently being formed by researchers as the ones linked to a FAPESP Thematic Project

By Fábio de Castro

Agência FAPESP – The theory of general relativity explains gravity. Quantum mechanics explains nuclear forces and electromagnetism. Reconciling the two theories is one of the greatest challenges for physics.

The most efficient solution to date for unifying gravitation and quantum mechanics is the superstrings theory, which is currently being formed. In the last 20 years, international efforts to promote advances in this area have had major participation from researchers linked to the Thematic Project: “Research and learning on the strings theory,” financed by FAPESP.
 
Under the coordination of Nathan Jacob Berkovits, professor at Universidade Estadual Paulista’s (Unesp) Theoretical Physics Institute (IFT), the project is the third on the topic since 2000. In that year, Berkovits presented an innovative mathematical formulation developed over 15 years, which is known as “pure spinors.”  

This formalism has been important in the last decade to facilitate the calculations related to the theory of superstrings. In 2009, Berkovits received the Third World Academy of Sciences (TWAS) Award in Physics, recognizing this body of work.

Developed as of the 1960s, the superstrings theory is a physical model in which the fundamental components of matter are not the points with negligible dimensions that characterize subatomic particles in traditional physics, but rather extensive unidimensional objects similar to a cord. Depending on the “tone” of the vibration of these cords, they correspond to each subatomic particle.

According to Berkovits, the Thematic Project, which involves a series of international partnerships, has explored application for pure spinors on several fronts of development in the superstring theory.

“The superstring theory is the most successful attempt to unify gravitation and quantum mechanics, theories that are very difficult to reconcile. Theoretical physicists are also dreaming that a superstring theory can unify all fundamental forces and particles of nature, but this, for the time being, is just a dream,” comments Berkovits in an interview with Agência FAPESP.

The advances in the theoretical field, nevertheless, are very real. Pure spinor formalism has been the most appropriate tool for studying the AdS/CFT (Anti-de-Sitter space/conformal field theory) correspondence – also known as the Maldacena duality.

This duality, proposed by Argentine scientist Juan Maldacena in 1997, gave an unprecedented boost to the superstrings theory and research on quantum gravitation. The article in which Maldacena proposes this duality has had more the 3,000 citations and  became one of the major conceptual breakthroughs in the physical theory in the 90s.

“In addition to working on the application of pure spinors to study AdS/CFT correspondence, we have advanced application of this formalism on other fronts, like scattering amplitudes,” says Berkovits.

The study of superstring scattering – which is related to particle scattering – encounters major difficulties when the particles involved are fermions. All elementary particles of matter are fermions or bosons, which have half-integer or integers spins, respectively, and obey different statistical mechanics.

“With the application of pure spinor formalism, the study of superstring scattering involving fermions is no more difficult than cases that involve boson. Another area in which we are utilizing pure spinor formalism is in the string field theory, which is still in the initial phases of development,” he explains.

According to Berkovits, when the theoretical physicist describes a particle, s/he employs a variable that describes its position. When it involves a particle with spin – like photons or electrons – the position variable is not enough to describe it.

“There are several ways to describe spin and the most traditional was the formalism of Ramond-Neveu-Schwarz, conceived in 1973. Later in 1980, the Green-Schwarz formalism was developed. It was a new means of describing spin and offered a few advantages. But it also brought with it some disadvantages as well: the Green-Schwarz formalism did not maintain Lorentz invariance, an important property related to space-time  rotations,” he notes.

Since 1980 theoretical physicists have been trying resolve the problems with Green-Schwarz formalism.  The year 2000 marked a breakthrough with the pure spinor formalism, resolving the question of describing particle spin in a manner that maintained all the symmetries in the theory of relativity.

International community

It is estimated that there are currently 2,000 researchers actively studying the theory of superstrings. Berkovits has worked with roughly 50 of them. The Thematic Project, which he coordinates, benefits from the international connections of its participating researchers.

“In addition to the studies conducted by our post-doctoral and post-graduate students, we have many collaborations abroad. We have a series of specialists that collaborate with us and participate in the congresses that we organize. On the other hand, we frequently send students to work with international teams and participate in events,” says the researcher, winner of the 2009 Physics Award from the Third World Academy of Sciences (TWAS).

The group directly involved with the Thematic Project currently has a post-doctoral student, three doctoral students, three master’s students and one intern. Two researchers recently hired by IFT are also participants in the project. Other students have also been members of the group and are now working in other universities in Brazil and abroad.

“We are contributing to the formation of a community involved in researching the theory of superstrings. It is an important and fertile frontier, that still has only a few people [working on it] in Brazil, compared to  the rest of the world, he affirms.

Interest in the area, however, is on the rise. Proof of this is the high numbers attending the event held by IFT and Unesco’s International Centre for Theoretical Physics (ICTP). “We received more than 200 registration requests and we could only accept half,” says Berkovits.

The course entitled ICTP-Capes Latin American String School boasted the presence of the world’s leading researchers in the area, including Juan Maldacena and the American national Joe Polchinski- both winners of the Dirac Medal– the most import award in physics after the Nobel Prize.