Week 08.03.2009 – 14.03.2009

We first quickly review some basic facts about quantum theories in 1+5 dimensions with 2,0 superconformal symmetry. They arise as decoupled subsectors of string or M theories on space times containing certain defects like branes or singularities. By compactification, they are also related to Yang-Mills theories in lower dimensions. We then describe, in somewhat more detail, recent work on these theories considered on a spatial five torus. In particular, one may determine the spectrum of vacuum states, and also learn much about the spectrum of BPS states. Hopefully, this will eventually be helpful for giving a definition of these mysterious theories.

The results are separate, and apparently paradoxical, and have implications for physics. First, when two exponentials compete, their interference can be dominated by the contribution with smaller exponent. Second, repeated differentiation of almost all functions in a wide class generates trigonometric oscillations ('almost all functions tend to cosx'). Third, it is possible to find band-limited functions that oscillate arbitrarily faster than their fastest Fourier component ('superoscillations').

We review a duality between N=4 super Yang-Mills and a string theory in AdS5xS5 background and integrability arising in both theories. New results conserning finite length operators/short strings will be presented.

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I will discuss the wavefunctions for open strings in warped compactifications, and in particular for D7-branes in warped Calabi-Yau orientifolds, which provide a string theory realizations of the Randall-Sundrum scenario. I will show how certain background fluxes, necessary in the presence of warping, couple to the fermionic wavefunctions and qualitatively change their behavior. Finally, the warped Kahler potential for the D7-brane light modes will be discussed, as well as a proposal to embed it in the full open+closed Kahler potential.

This is the first lecture of a short course on flux compactifications. For more information on the course and the schedule, please visit http://www.strings.ph.qmw.ac.uk/index.htm and follow the link to the Graduate Program in String/Field Theory.