Integrated Calendar

We want to make a “non-biological” system which can self-replicate. The idea is to design particles with specific and reversible and irreversible interactions, introduce seed motifs, and cycle the system in such a way that a copy is made. Repeating the cycle would double the number of offspring in each generation leading to exponential growth. Using the chemistry of DNA either on colloids or on DNA tiles makes the specific recognition part easy. In the case of DNA tiles we have in fact replicated the seed at least to the third generation. The DNA linkers can also be self-protected so that particles don’t interact unless they are held together for sufficient time – a nano-contact glue, and we have discovered a new type of topological interaction associated with concatenation of DNA loops which gives a Velcro-like binding. Chemical modification of the DNA allows us to permanently crosslink hybridized strands for irreversible bonds and a new type of photolithography. We have designed and produced colloidal particles that use novel “lock and key” geometries to get specific and reversible physical interactions. We have also investigated the limits of distinct specific interactions that we can DNA encode on a single particle, how 'polygamous' it can be made, and find that it is entropically and combinatorially restricted to ~100 mates.

Integrability has already led to remarkable explicit results in planar AdS5/CFT4, and holds the promise for more. I shall review some of these developments, starting from the initial evidence of integrability at weak coupling, followed by the all-loop S-matrix, and its implications for large and small operators. Time permitting, I shall present some of my own recent work on integrable twists in AdS/CFT.

I will explain how to use integrability to calculate the quark-antiquark potential in planar N=4 SYM, i.e., the infinite rectangular Wilson loop operator. It turns out that to formulate and solve the problem it is natural to consider much more general observables: cusped Wilson loops and Wilson loops with operator insertions. A rather laborious calculation which I will outline leads to a set of integral equations which can be solved iteratively (and presumably also numerically) to give the planar potential and its generalizations to arbitrary precision.