Week 14.10.2017 – 22.10.2017

Tuesday

Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach

 at: 15:00 City U.room ELG11 abstract: A total set of states for which we have no resolution of the identity (a 'pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a 'generalized basis', which is practically useful. The dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses Moebius transforms. There is non-independence and redundancy in these generalized bases, which is quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases, are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coefficients. Also in a physical system with ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system.

Wednesday

On the exact interpolating function in ABJ theory

Regular Seminar Andrea Cavaglia (KCL)

 at: 13:15 KCLroom K4.31 abstract: I will discuss integrability in the context of planar AdS4/CFT3, where the CFT is the so-called ABJ model depending on two t'Hooft couplings. When the two couplings are equal, this reduces to the ABJM theory, whose integrable structure is well understood but depends on an unspecified interpolating function of the coupling. I will motivate a proposal that the most general ABJ case is also integrable, and that the two coupling constants l1 and l2 recombine into a single interpolating function h( l1 , l2 ) , so that the spectrum is a function of h only. Extending and idea by N. Gromov and G. Sizov on the ABJM case, an explicit conjecture for the form of h(l1, l2) wil be made, based on the comparison between integrability and localization results. The talk is based on the paper hep-th/1605.04888 with N. Gromov and F. Levkovich-Maslyuk.