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Register a new userResurgence in the O(4) sigma model
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We analyze the free energy of the integrable two dimensional O(4) sigma model in a magnetic field. We use Volins method to extract high number (2000) of perturbative coefficients with very high precision. The factorial growth of these coefficients are regulated by switching to the Borel transform, where we perform several asymptotic analysis. High precision data allowed to identify Stokes constants and alien derivatives with exact expressions. These reveal a nice resurgence structure which enables to formulate the first few terms of the ambiguity free trans-series. We check these results against the direct numerical solution of the exact integral equation and find complete agreement.
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TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.
We study dual strong coupling description of integrability-preserving deformation of the $O(N)$ sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the $eta-$deformed $O(N)$ sigma-model after $T-$duality transformation.
A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of critical behavior in the O(4) universality class. For example, the finite-temperature phase transition in QCD with two flavors is expected to fall into this class. Critical exponents are calculated in local potential approximation. Parameterizations of the scaling functions for the order parameter and for the longitudinal susceptibility are given. Relations from universal scaling arguments between these scaling functions are investigated and confirmed. The expected asymptotic behavior of the scaling functions predicted by Griffiths is observed. Corrections to the scaling behavior at large values of the external field are studied qualitatively. These scaling corrections can become large, which might have implications for the scaling analysis of lattice QCD results.
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 $mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.
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