PI: David Schaich
DiRAC Project dp162/APP50526, “Lattice studies of maximally supersymmetric Yang–Mills in three dimensions”, is exploring conjectured holographic dualities that relate supersymmetric quantum field theories to quantum gravity in a higher number of space-time dimensions. Such holographic dualities are widely employed in theoretical physics, and are beginning to benefit from first-principles lattice field theory studies. While holography is best understood in the limit of a large number of colours (N) with strong coupling, lattice field theory provides a powerful non-perturbative tool to explore the validity and applications of holography for smaller N.
The specific focus of this project is on maximally supersymmetric Yang–Mills theory in three space-time dimensions, with N=8 colours. Building on our prior work that confirmed consistency between the low-temperature, large-volume behaviour of this field theory and the ‘D2’ phase of a homogeneous euclidean D2-brane black hole in the dual IIA supergravity, we are carrying out numerical lattice field theory computations to study the expected first-order phase transition between this homogeneous D2 phase and a localized D0 phase as the volume decreases. On the field-theory side, this corresponds to a ‘spatial deconfinement’ transition signalled by the Wilson lines that wrap around the spatial cycles of the lattice.
In the framework of lattice field theory, phase transitions can be identified from a peak in the susceptibility of the order parameter, in this case the spatial Wilson lines. The accompanying figure presents preliminary results for this susceptibility, obtained from our ongoing computations employing DiRAC resources at Cambridge. These particular results come from L^2xNt lattice volumes with L=16, 20, 24 and fixed aspect ratio alpha=L/Nt=2. The three temporal extents Nt=8, 10, 12 enable extrapolations to the continuum limit of vanishing lattice spacing.
The clear peak in the susceptibility confirms the presence of a phase transition, with a critical temperature T_c~1.5. We are also analysing larger lattice volumes with aspect ratios alpha=5/2 and 3, which cause the spatial deconfinement transition to occur at higher temperatures further from the regime in which holography is most reliable. Preliminary results presented in the recent conference proceedings arXiv:2510.18140 find this shift in the critical temperature to be in good agreement with holographic expectations. Future work can consider larger numbers of colours N>8 in order to analyse critical scaling at the transition and determine whether it is first order or continuous.
