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SUMMARY:Resurgence for Superconductors
DTSTART;VALUE=DATE-TIME:20190611T144500Z
DTEND;VALUE=DATE-TIME:20190611T154500Z
DTSTAMP;VALUE=DATE-TIME:20190820T140041Z
UID:indico-contribution-3760@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marcos Mariño (University of Geneva)\nOne of the mo
st important non-perturbative effects in Nature is the energy gap of super
conductors\, which is exponentially small in the coupling constant. A natu
ral question is whether this effect can be incorporated in the theory of r
esurgence. In this talk I will argue that this is the case. More precisely
\, I conjecture that the perturbative series for the ground state energy o
f a superconductor is factorially divergent\, and its leading Borel singul
arity corresponds to the superconducting gap. In the case of the attractiv
e Gaudin-Yang model (a superconductor in one dimension)\, I develop techni
ques that make it possible to calculate the exact perturbative series of t
he ground state energy up to very high order\, providing a non-trivial tes
t of this conjecture. For superconductors in three dimensions\, evidence f
or this conjecture can be given by using diagrammatic methods. We also arg
ue that the leading Borel singularity is of the renormalon type\, associat
ed to factorially divergent subdiagrams.\n\nhttps://indico.math.cnrs.fr/ev
ent/4521/contributions/3760/
LOCATION:Le Bois-Marie Centre de Conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/4521/contributions/3760/
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