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arxiv: 2606.23088 · v1 · pith:I2DB7HOHnew · submitted 2026-06-22 · ✦ hep-th · math-ph· math.MP

On background fields and a cutoff in sigma models

classification ✦ hep-th math-phmath.MP
keywords backgroundfieldactioncutofffunctionalsigmaapproximationcalculate
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In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the construction of the generating functional by introducing a background field. Furthermore, we perform a one-loop renormalization of the quantum action, calculate power-law singularities in the two-loop approximation, and consider transition to an extended classical action. Finally, we study the consistency of the cutoff with special functional relations within the framework of the background field method.

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