*image: Andrew J. Hanson/Wikimedia Commons*)

# Brazilian scientist makes key contributions to advances in superstring theory

#### February 25, 2015

**By José Tadeu Arantes**

**Agência FAPESP** – All the experiments in high-energy physics that have been performed in recent decades have confirmed the so-called “Standard Model” of particle physics, a theoretical construct that describes the structure and behavior of matter at the atomic and subatomic scales.

Several scientists who contributed to the development of the model have been awarded the Nobel Prize in Physics, including the UK’s Peter Higgs, who postulated the famous Higgs boson and won the prize together with Belgium’s François Englert in 2013.

This success, however, can also be regarded as an impasse because important problems in the Standard Model remain unsolved.

The most important of these, and an issue that is frequently cited, is the impossibility of unifying the four fundamental interactions in nature (the gravitational, electromagnetic, weak nuclear and strong nuclear forces) in a single framework owing to the incompatibility between the general theory of relativity (which describes the gravitational interaction) and quantum theory (which describes the other three interactions).

Several proposals have been presented in the search for alternatives to the Standard Model by the new generation of physicists, but the proposal that has lasted the longest and that has proved to be the most promising is superstring theory, which replaces the Standard Model’s concept of point particles with the idea of tiny vibrating strings. According to this theory, different string vibrations or “excitation modes” give rise to the various particle types.

Superstring theory has been reformulated several times since it was first proposed in the early 1970s. One of the researchers who has actively contributed to its development is Nathan Berkovits, full professor at the Theoretical Physics Institute of São Paulo State University (IFT-UNESP) in Brazil. Berkovits was born in the United States and is a naturalized Brazilian citizen.

In 2009 Berkovits won the annual physics prize awarded by The World Academy of Sciences (TWAS) for his research on superstring theory. Since 2011 he has headed the ICTP South American Institute for Fundamental Research (ICTP-SAIFR), established by the Abdus Salam International Center for Theoretical Physics (ICTP), which is based in Trieste, Italy, in partnership with UNESP and FAPESP.

He currently leads the Thematic Project “**ICTP South American Institute for Fundamental Research: a regional center for theoretical physics**,” which is supported by FAPESP. In 2014 he concluded a **Thematic Project** on research and learning in string theory.

In an interview given to **Agência FAPESP**, Berkovits outlined the state of the art in superstring theory and described his contributions to knowledge in this field.

*Agência FAPESP** – Why is it so important to construct a theory that is capable of overcoming the contradiction between general relativity and quantum mechanics?*

**Nathan Berkovits** – Although general relativity is used to describe the macrocosm, at the interstellar and intergalactic scales, and quantum mechanics is used to describe the microcosm, at the atomic and subatomic scales, reconciling the two is not irrelevant, especially if we want to understand the primordial universe. According to the Big Bang theory, the universe was of subatomic size in the fractions of a second that followed the initial instant. The scale at which quantum mechanics affects the gravitational interaction is so small that we can’t even dream of building accelerators that are capable of detecting it, but such information may eventually be obtained from cosmological observations of the young universe.

*Agência FAPESP** – And is superstring theory a promising alternative to overcome this contradiction?*

**Berkovits** – Yes, because the theory states that different string vibrations describe different particles. So superstring theory can not only unify gravity with the other interactions but also unify all particles. Superstring theory is very far from being experimentally verifiable but it has given rise to several ideas that have been useful in other areas of physics and mathematics. One such idea is the concept of supersymmetry.

*Agência FAPESP** – Could you explain this concept?*

**Berkovits **– The concept of supersymmetry relates fermionic particles, which constitute matter, to bosonic particles, which transmit the interactions or forces between the constituents of matter. Although fermions and bosons are quite different, these two types of particle can be related through supersymmetry. According to this concept, for every fermion there must be a corresponding boson, i.e., a supersymmetric particle, and vice versa. This concept arose in the 1970s, in string theory, hence the term superstring. An important property of theories with supersymmetry is that the contradictions with quantum mechanics are attenuated owing to the possibility of cancellation between fermionic and bosonic particles. For this reason, even physicists who don’t work with superstring theory have become highly interested in supersymmetry. Researchers at the Large Hadron Collider in Geneva are actively looking for evidence of supersymmetry, a concept that has proved to be applicable to various areas of physics and mathematics.

*Agência FAPESP **– One of the difficulties with superstring theory is the large number of dimensions that space must have in order for us to be able to describe it.*

**Berkovits **– True. The mathematical formalism of superstring theory uses ten-dimensional space. You might well wonder why we observe only four of these ten dimensions. There are at least two answers to that question. One is that the other six dimensions are so small that we can’t detect them. The model that says this is called compactification. Another answer is that matter can’t occupy all the dimensions of the universe, only its surface. The universe is a ten-dimensional object with a four-dimensional surface, and particles such as electrons and photons are confined to this surface. Only gravitons, which transmit the gravitational interaction, are free to move through the entire universe. This surface is termed a brane, by analogy to a membrane, the two-dimensional surface of a three-dimensional object. So we have brane theory, too.

*Agência FAPESP** – What recent developments in superstring theory would you highlight?*

**Berkovits **– The concept of duality was an important step. In this context, duality means bringing together two quite different theories that are used to describe the same thing. The most significant example of such a duality is the AdS-CFT correspondence, which relates a quantum theory of gravitation with a field theory. This correspondence was conjectured in 1997 by the Argentinian physicist Juan Maldacena, at the Institute of Advanced Studies at Princeton in the United States. Later on, he presented several types of evidence to prove it, at the same time as other researchers. It refers to the correspondence between a quantum theory of gravitation in anti de Sitter (AdS) space and a supersymmetric Yang-Mills field theory, which is an example of a conformal field theory (CFT). The AdS-CFT correspondence has been one of the most active topics in high-energy physics in the last 15 years and has triggered applications in other areas, such as heavy-ion physics and the physics of superconductivity.

*Agência FAPESP **– You’ve also contributed, haven’t you?*

**Berkovits **– I’ve been doing research on this for some 25 years now, focusing on an effort to understand supersymmetry in superstring theory and applying this understanding to the study of the AdS-CFT correspondence. The conventional formalism for the superstring, the RNS formalism (an acronym for the last names of Pierre Ramond, André Neveu and John Schwarz), was developed in the 1970s. However, supersymmetry was hidden in it. In the 1980s, Michael Green and Schwarz developed an alternative formalism, called GS after them, but its quantization was complicated. The problem remained open until 2000, when I proposed a new formalism, with manifest supersymmetry and simple quantization. This new apparatus is known as “pure spinor formalism” because it involves not only vector variables that describe space-time but also spinor variables.

*Agência FAPESP** – What is a spinor?*

**Berkovits **– It’s a mathematical tool. Perhaps spinors will be more comprehensible if we compare them with vectors, another mathematical tool. To describe any point in space-time, we use a vector with four dimensions, three for space (height, width and length, for example) and one for time. We can think of reality as having more than four dimensions, and the vector will have as many components as there are dimensions. A spinor can describe magnitudes other than position in space-time. Take an electron, for example. It’s not enough to know its location in space-time. You also need to know its spin, i.e., which axis it’s spinning along. The spinor provides this description. So it carries more information than the vector.

*Agência FAPESP** – How was your new formalism received?*

**Berkovits **– In 2000, shortly after the start of my first **Thematic Project** supported by FAPESP, I wrote a paper entitled “Super-Poincaré covariant quantization of the superstring.” It was published in the *Journal of High Energy Physics* (JHEP) and generated over 400 citations. Several research groups around the world are now working with the pure spinor formalism.

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