String Theory and Nonplanar AdS/CFT – Public Talk and Seminar by Robert de Mello Koch

On Tuesday the 15th, Robert de Mello Koch graced the AIMS/Science Out Loud scene with his public talk entitled “From Spacetime and Quantum Mechanics to String Theory”. In his brilliant overview of string theory, in which important props such as a soccer ball and his son’s pants were used for demonstration, he explained how Einstein’s theory of relativity and quantum mechanics could not be married together in one theory but that string theory could hold the answer to unification.

In string theory, every particle is made up of tiny (~10-34m!) vibrating strings, which can either be open (such as in the case of electromagnetism) or closed (such as for gravity). One of the beautiful things about string theory is that there seems to be a duality between electromagnetism and gravity, which Robert further detailed in his seminar.

On the 14th, Robert gave us an enlightening seminar on his latest work in string theory. AdS/CFT correspondence is a conjectured equivalence between a string theory with gravity defined on an anti de Sitter (AdS) space and a conformal quantum field theory (CFT). The example Robert worked with was the correspondence between quantum gravity on AdS5 × S5 space and a supersymmetric N = 4 Yang–Mills gauge theory.

In this work, Robert et al. computed anomalous dimensions of operators in a large N (but non-planar) limit in N=4 super Yang-Mills theory, using the AdS/CFT correspondence.

They asked the question, how do you test AdS/CFT correspondence, perhaps in areas that are not at first obvious? Robert et al. applied the correspondence to the problem of quantising membranes. A D-brane is simply defined as a place where an open string ends. We cannot study a D-brane directly because we don’t know how to deal with dynamical boundary conditions. So in string theory, we cannot quantify the membrane. What about posing the same question in a Yang-Mills theory and then using the AdS/CFT correspondence to answer the question in string theory?

Understandably, the same question in a Yang-Mills theory is very difficult. We could consider a simple example: a giant graviton. A giant graviton is just a spherical D-brane. The strings that might start and end on it would be bounded and so the energy in the vibrational modes of the strings is quantised. In fact, we would expect these strings to behave just like harmonic oscillators. When Robert et al. solved the system in the Yang-Mills theory, they got exactly a harmonic oscillator solution with the right frequencies, perhaps more evidence that AdS/CFT correspondence is correct.

What does this tell you about membranes? Well this work was done in the large N limit, but it could now be extended by including 1/N corrections. The solution in the Yang-Mills theory produces the Hamiltonian of the membranes in the string theory, which can tell you how the membranes are interacting.

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