On coincidence of Alday-Maldacena-regularized $\sigma$-model and Nambu-Goto areas of minimal surfaces

TL;DR

This paper demonstrates that the Alday-Maldacena-regularized actions for both the $\sigma$-model and Nambu-Goto minimal surfaces are proportional when evaluated on solutions with constant non-regularized Lagrangian, revealing a fundamental connection.

Contribution

It shows the coincidence of regularized actions for $\sigma$-model and Nambu-Goto surfaces under specific conditions, highlighting a new relation between these models.

Findings

Regularized actions coincide up to a boundary-condition-independent factor.

The results apply to solutions with constant non-regularized Lagrangian.

The study uncovers a fundamental link between $\sigma$-model and Nambu-Goto minimal surfaces.

Abstract

For the $\sigma$-model and Nambu-Goto actions, values of the Alday-Maldacena-regularized actions are calculated on solutions of the equations of motion with constant non-regularized Lagrangian. It turns out that these values coincide up to a factor, independent of boundary conditions.