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

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. ∗ E-Mail address: [email protected] The purpose of this letter is two fold one is to study the free rigid string [1] to the first sub-leading quantum corrections and show that the beta function remains negative, thus implying that the extrinsic curvature becomes irrelevant at large distance scales in the disordered phase. This is of utmost importance for the decoupling of ghosts of the quantum theory [2]. Next the results here will serve as the foundations for solving a more complicated problem. This the problem of showing that the phase transition which we proved [3] to occur in the leading approximation of large N limit in the theory of rigid strings coupled to the long range Kalb-Ramond interactions, is stable when we include the sub-leading quantum loop corrections in Large N. This would be the topic of part II of this letter. The gauge fixed action of the free rigid string [1] is :