Talks

When a pair of particles is produced close to threshold, they may form a bound state if the potential between them is attractive. Can we use such bound states to obtain information about new colored particles at the LHC? I will discuss the relevant issues using examples from the MSSM and other beyond the standard model scenarios.

In the context of AdS/CFT correspondence the AdS_3/CFT_2 instance of the duality stands apart from other well studied cases, like AdS_5/CFT_4 or AdS_4/CFT_3. One of the reasons is that the CFT side of this duality is not a theory of matrices but rather a two dimensional orbifold based on the group of permutations. In this talk we will discuss some aspects of this theory. In particular a diagrammatic language, akin to Feynman diagrams used for gauge theories, will be developed. Moreover, we will compute a large set of protected quantities in a certain symmetric product orbifold CFT, and show that these are elegantly given in terms of Hurwitz numbers.

Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. Inspired by the success of the statistical study of classical constraint optimization problems, we study random ensembles of the QMA$_1$-complete quantum satisfiability (QSAT) problem introduced by Bravyi. QSAT appropriately generalizes the NP-complete classical satisfiability (SAT) problem. We show that, as the density of clauses/projectors is varied, the ensembles exhibit quantum phase transitions between phases that are product satisfiable, entangled satisfiable and unsatisfiable. Remarkably, almost all instances of QSAT for a fixed interaction graph exhibit the same dimension of the satisfying manifold. This establishes the generic QSAT decision problem as equivalent to a purely graph theoretic property and that the hardest typical instances are likely to be localized in a bounded range of clause density. Based on papers: C.R. Laumann, R. Moessner, A. Scardicchio, and S.L. Sondhi. Phase transitions and random quantum satisfiability. QIC 10 (1/2), (2009). arXiv:0903.1904 C.R. Laumann, A.M. Lauchli, R. Moessner, A. Scardicchio, and S.L. Sondhi. On product, generic and random generic quantum satisfiability. arXiv:0910.2058