Week 07.12.2014 – 13.12.2014

TBA

I will review the calculation of the partition function of 3d supersymmetric field theories on S^3 using the fermi-gas approach to solve the matrix integral. The resulting expression is an Airy function and is valid perturbatively to all orders in 1/N for a wide class of theories (including ABJM). This suggests that a similar formula can be derived by studying quantum gravity on AdS_4. I will explain several of the steps needed to implement this idea and some intriguing results.

Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24.

By studying the cosmological dynamics of the moduli and axion fields we develop a set of "generic predictions" of solutions to string/M theory which have low energy supersymmetry breaking and grand unification. The nature of dark matter plays an important role in much of the discussion.

The Bekenstein-Hawking formula for the entropy of a black hole suggests that entropy in strong gravity situations should be proportional to bounding area rather than enclosed volume. But we argue that the S and T dualities of string theory suggest an entropy formula that is extensive in the volume, with the area formula appearing as a special case. In particular we find a set of states in string theory that violate the covariant entropy bound, which seeks to extend the area entropy formula to situations like the early Universe.