Renormalizability and Quantum Stability of the Phase Transition in Rigid String Coupled to Kalb-Ramond Fields I

TL;DR

This paper investigates the quantum properties of rigid strings coupled to Kalb-Ramond fields, demonstrating that a phase transition persists under quantum fluctuations and establishing the theory's asymptotic freedom.

Contribution

It provides the first analysis of quantum corrections and renormalization group behavior in rigid strings with Kalb-Ramond interactions, confirming the stability of the phase transition.

Findings

The theory is asymptotically free at large distances.

Quantum corrections do not eliminate the phase transition.

The renormalized mass gap and critical line are derived.

Abstract

Recently we have shown that a phase transition occurs in the leading approximation of the large N limit in rigid strings coupled to long range Kalb-Ramond interactions. The disordered phase is essentially the Nambu-Goto-Polyakov string theory while The ordered phase is a new theory. In this part I letter we study the first sub-leading quantum corrections of the free rigid string and derive the renormalization group equation. We show that the theory is asymptotically free, thus the extrinsic curvature of the string drops out at large distance scales in the disordered phase. In part II we generalize the results of this letter to the interacting theory of rigid strings with the long range Kalb-Ramond interactions. We derive the renormalized mass gap equation and obtain the renormalized critical line. Our main and final result is that the phase transition does indeed survive quantum fluctuations.