Thermofield Dynamics of the Heterotic String — Global Phase Structure —

Physical aspects of the thermofield dynamics of the D = 10 heterotic thermal string theory are exemplified through the infrared behaviour of the one-loop dual symmetric cosmological constant in association with the global phase structure of the thermal string ensemble. ∗e-mail: [email protected] ∗∗e-mail: [email protected] Elaboration of thermal string theories based upon the thermofield dynamics (TFD) [1] has gradually turned out to be a good practical subject of high energy physics [2] [9]. In a previous paper of ourselves [8], we have succeeded in shedding some light upon the global phase structure of the thermal string excitation in proper reference to the thermal duality relation [10], [11] for the D = 26 closed bosonic thermal string theory within the TFD framework. In the present communication, physical aspects of the D = 10 heterotic thermal string theory based upon the TFD algorithm are exemplified through the infrared behaviour of the one-loop cosmological constant in respect of the thermal duality symmetry. The global phase structure of the TFD thermal string amplitude is then examined à la O’Brien and Tan [10] on the basis of the thermal stability of modular invariance. Let us start with describing the one-loop cosmological constant Λ(β) at any finite temperature β = kT as Λ(β) = α 2 lim μ→0 Tr [ ∫ μ ∞ dm ( ∆βB(p, P ;m ) + ∆βF (p, P ;m ) ) ] (1) for the D = 10 heterotic thermal string theory in the TFD framework, where the string tension σ is expressed in terms of the slope parameter α as σ = 1/2πα, p reads loop momentum and P I lie on the even self-dual root lattice L = Γ8 × Γ8 for the exceptional group G = E8×E8 [12], respectively. Here the thermal propagator ∆βB[F ](p, P ;m) of the free closed bosonic [fermionic] string is expressed at D = 10 as ∆βB[F ](p, P ;m ) = ∫ π −π dφ 4π e( ∑ 16 I=1 (P )) × ( 