Federico Ambrosino (DESY)
Exploring (Generalized) QCD_2 with Integrability abstract
Abstract:
The \'t Hooft model, 2d QCD in the large N limit, offers a unique playground for exploring the dynamics of confinement in gauge theories. In this talk, based onjoint works with S. Komatsu, I will illustrate that the Fredholm integral equation (\'t Hooft equation) determining the masses of mesons in the model is equivalent to finding solutions to a TQ-Baxter equation. This reformulation ofthe problem illustrates a rich analytical structure of the spectrum in the complex plane of the quark masses, and makes possible to extract systematicanalytical expansions for spectral determinants, energy levels, andwavefunctions. I will comment on possible connections between ourtechniques and TS/ST correspondence.Remarkably, this integrable structure is unique to the \'t Hooft model, but persists also in the broad class of theories called generalized QCD, obtainedby replacing the gluon kinetic term with a BF coupling plus a potential for the B-field. I will show that, also in this case, the associated \'t Hooft equation is recasted into a TQ-equation with a transfer matrix given in closed form for anygiven potential. Applying the techniques developed for the \'t Hooft model to these theories allows for a novel systematic study of the spectrum in the complex space of the couplings.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Ryan Unger (Princeton University)
Retiring the third law of black hole thermodynamics abstract
Abstract:
Extremal black holes are exceptional solutions of Einstein’s equations which have absolute zero temperature in the thermodynamic analogy of black hole mechanics. In this talk, I will present a disproof of the “third law of black hole thermodynamics” by showing that extremal black holes can form in the gravitational collapse of charged matter. This has opened the door to studying a new critical phenomenon on the black hole formation threshold that we call “extremal critical collapse.” This is joint work with Christoph Kehle (ETH Zürich).
14:15 • EPF Lausanne, MA B2 485
Alexander Bobenko (TU Berlin)
Dimers and M-curves abstract
Abstract:
We develop a general approach to dimer models analogous to Krichever’s scheme in the theory of integrable systems. This leads to dimer models on doubly periodic bipartite graphs with quasiperiodic positive weights. This generalization from Harnack curves to general M-curves leads totransparent algebro-geometric structures. In particular explicitformulas for the Ronkin function and surface tension as integrals ofmeromorphic differentials on M-curves are obtained. Based on Schottky uniformizations of Riemann surfaces we compute the weights and dimer configurations. The computational results are in complete agreement with the theoretical predictions. Also relation to discrete conformalmappings and to hyperbolic polyhedra is explained. This is a joint work with N. Bobenko and Yu. Suris.
14:30 • Université de Genève, Conseil Général 7-9, Room 1-05