# Three roads to the energy gap

@article{Mario2020ThreeRT, title={Three roads to the energy gap}, author={Marcos Mari{\~n}o and Tom{\'a}s Reis}, journal={arXiv: High Energy Physics - Theory}, year={2020} }

We determine analytically the energy gap at weak coupling in the attractive multi-component Gaudin--Yang model, an integrable model which describes interacting fermions in one dimension with $\kappa$ components. We use three different methods. The first one is based on a direct analysis of the Bethe ansatz equations. The second method uses the theory of resurgence and the large order behavior of the perturbative series for the ground state energy. The third method is based on a renormalization…

## 5 Citations

Testing the Bethe ansatz with large N renormalons

- Medicine, PhysicsThe European physical journal. Special topics
- 2021

The ground-state energy of integrable asymptotically free theories can be conjecturally computed using the Bethe ansatz once the theory has been coupled to an external potential through a conserved…

Resurgence and renormalons in the one-dimensional Hubbard model

- Physics, Mathematics
- 2020

We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we…

Analytic resurgence in the O(4) model

- Physics, Mathematics
- 2021

We study the perturbative expansion of the ground state energy in the presence of an external field coupled to a conserved charge in the integrable two-dimensional O(4) nonlinear sigma model. By…

Resurgence and 1/N Expansion in Integrable Field Theories

- Physics, MathematicsJournal of High Energy Physics
- 2021

Abstract
In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for the…

Quantum phase transition and Resurgence: Lessons from 3d N = 4 SQED

- Physics, MathematicsProgress of Theoretical and Experimental Physics
- 2021

We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional N = 4…

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