Maximum temperature for an ideal gas of Û(1) Kac-Moody fermions.

A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody fermions. The canonical partition function for the Û(1) case is shown to have a maximum temperature kTM = |λ|/π, where λ is the coupling of the super charge operator G0 to the fermions. This result is similar to the case of strings but unlike strings the result is obtained from a well-defined lagrangian. To appear in Physical Review,Dec 15, 1995. E-mail address: [email protected] Introduction The existence of a maximum temperature is widely supposed to hold in string theory. In this paper we discuss another case where the same phenomenon occurs, and the result is shown to hold for a model with an exact lagrangian. Gauge fields coupled to fermions having an arbitrary Kac-Moody group for its gauge symmetry has been derived in Ref 1, and has a number of new features. The pure gauge sector is nonlinear even for Û(1) case. The fermion sector has a new masslike coupling to the super-charge operator G0 due to the necessity of attenuating the high mass states inside Feynman loop integrations (Ref 1). In this paper, we examine the pure fermion sector. The simplest case of Û(1) KacMoody fermions is studied and we derive the existence of a maximum temperature for the free energy. Consider a d-dimensional Euclidean space time Md. Let Qn and hn be the generators of Û(1) super Kac-Moody algebra with [Qn, Qm] = ikδn+m (1) [hn, hm] = kδn+m (2) We consider only the Ramond sector (integer modes hn). Hence we have the Virasoro generator Lo = 1 2k Q0 + 1 k ∞