Abstract
We perform lattice simulations of N D0-branes at finite temperature in the decoupling limit, namely 16 supercharge SU(N) Yang-Mills quantum mechanics in the ’t Hooft limit. At low temperature this theory is conjectured to be dual to certain supergravity black holes. We emphasize that the existence of a non-compact moduli space renders the partition function of the quantum mechanics theory divergent, and we perform one loop calculations that demonstrate this explicitly. In consequence we use a scalar mass term to regulate this divergence and argue that the dual black hole thermodynamics may be recovered in the appropriate large N limit as the regulator is removed. We report on simulations for N up to 5 including the Pfaffian phase, and N up to 12 in the phase quenched approximation. Interestingly, in the former case, where we may calculate this potentially difficult phase, we find that it appears to play little role dynamically over the temperature range tested, which is certainly encouraging for future simulations of this theory.
Highlights
In this paper we use 1-loop methods to examine the divergence in the continuum theory and claim that it exists at for any N and any temperature
We propose regulating the divergence with a mass for the scalar fields in the theory, and argue how to recover the relevant dual gravitational physics as the regulator is removed
Given that the quantum mechanics has an exact non-compact quantum moduli space and a corresponding continuum of states extending to zero energy, it follows that the thermal partition function for N D0-branes is likely ill-defined at low temperatures due to the infra-red divergence associated to the integral over this moduli space
Summary
Following Itzhaki et al [4], we consider the “decoupling” limit of N coincident D0-branes. The decoupling limit is defined by considering excitations of these D0-branes with fixed energy while sending the string length scale to zero so α → 0. U 3/λ ∼ N −4/7, outside the ’t Hooft scaling limit, the dilaton blows up and the string theory becomes strongly coupled. In conclusion the closed string description in vacuum reduces to the above supergravity solution above in the approximate range N −4/7 < U 3/λ < 1. For ultra low temperatures outside the ’t Hooft scaling limit, t
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