UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory

TL;DR

This paper demonstrates that the Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory is UV finite at the quantum level, supporting its consistency and potential equivalence to the original superstring model.

Contribution

The authors explicitly verify the one-loop finiteness and scheme dependence of two-loop divergences, providing evidence for all-order UV finiteness of the reduced theory.

Findings

The reduced theory is power counting renormalizable.

One-loop divergences are explicitly canceled.

Two-loop divergences depend on the renormalization scheme and vanish in dimensional reduction.

Abstract

We consider the Pohlmeyer-type reduced theory found by explicitly solving the Virasoro constraints in the formulation of AdS_5xS^5 superstring in terms of supercoset currents. The resulting set of classically equivalent, integrable Lagrangian equations of motion has the advantage of involving only a physical number of degrees of freedom and yet being 2d Lorentz invariant. The corresponding reduced theory action may be written as a gauged WZW model coupled to fermions with further bosonic and fermionic potential terms. Since the AdS_5xS^5 superstring sigma model is conformally invariant, its classical relation to the reduced theory may extend to the quantum level only if the latter is, in fact, UV finite. This theory is power counting renormalizable with the only possible divergences being of potential type. We explicitly verify its 1-loop finiteness and show that the 2-loop divergences are, in general, scheme dependent and vanish in dimensional reduction scheme. We expect that the reduced theory is finite to all orders in the loop expansion.