Appendix: Complete List of Abstracts |
835 |
2.0.14 Gauge Fields, Strings and Integrable Systems
Konstantin Zarembo
Uppsala University
Konstantin.Zarembo@teorfys.uu.se
The discovery of the holographic duality made it clear that there is a tight relationship between gauge fields and strings. Quite unexpectedly, this relationship involves close ties to quantum spin chains and integrable systems. I will review various aspects of the gauge/string duality, and will explain how integrability arises in gauge and string theories.
3XV International Congress on Mathematical Physics Specialized Sessions
3.1 Condensed Matter Physics
Organizer J.P. Solovej (Copenhagen)
3.1.1 Rigorous Construction of Luttinger Liquids Through Ward Identities
Giuseppe Benfatto
Università di Roma “Tor Vergata” benfatto@mat.uniroma2.it
There are up to now two different ways to prove the key property on which our Luttinger liquid rigorous construction rests, the vanishing of the leading part of the Beta function.
The first one was developed in the last years and is based in an essential way on the exact Mattis-Lieb solution of the Luttinger model.
More recently, we found a new proof, based on the Ward identities obtained by a chiral local gauge transformation, applied to a Luttinger model with ultraviolet and infrared cutoffs. This is an old approach in the physical literature, but its implementation in an RG scheme is not trivial at all, because the ultraviolet and infrared cutoffs destroy local Gauge invariance and produce “correction terms” with respect to the formal Ward identities. We discover however a new set of identities, called “Correction Identities”, relating the corrections to the Schwinger functions. By combining Ward and Correction identities with a Dyson equation, the vanishing of the Beta function follows, so that the infrared cutoff can be removed.
As a byproduct, even the ultraviolet cutoff can be removed, after a suitable ultraviolet renormalization, so that a Quantum Field Theory corresponding to the Thirring model is constructed, showing the phenomenon of Chiral anomaly.