Topology change in commuting saddles of thermal N=4 SYM theory

We demonstrate that weakly coupled, large N, d-dimensional SU(N) gauge theories on a class of compact spatial manifolds (including S^{d-1} \times time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N^2. These p...

Recently lattice simulation in pure Yang-Mills theory exposes significant quadratic corrections for both the thermodynamic quantities and the renormalized Polyakov loop in the deconfined phase. These terms are previously found to appear naturally for ${\mathcal N}=4$ Super Yang-Mills~(SYM) on a sphere at strong coupling, through the gauge/gravity duality. Here we extend the investigation to the weak coupling regime, and for general large-$N$ gauge theories. Employing the matr...

Gauge theories with confining phases at low temperatures tend to deconfine at high temperatures. In some cases, for example in supersymmetric theories, confinement can persist for all temperatures provided the partition function includes a grading by $(-1)^F$. When it is possible to define partition functions which smoothly interpolate between no grading and $(-1)^F$ grading, it is natural to ask if there are other choices of grading that have the same effect as $(-1)^F$ on c...

We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with gauge group SU(N). These decoupling limits lead to decoupled theories that are much simpler than the full N=4 SYM but still contain many of its interesting features. The decoupling limits correspond to being in a near-critical region, near a point with zero temperature and critical chemical potentials. The new decoupling limits are found by generalizing the limits of hep-th/0605234 to include not only...

We present initial results from ongoing lattice investigations into the thermal phase structure of the Berenstein--Maldacena--Nastase deformation of maximally supersymmetric Yang--Mills quantum mechanics. The phase diagram of the theory depends on both the temperature $T$ and the deformation parameter $\mu$, through the dimensionless ratios $T / \mu$ and $g \equiv \lambda / \mu^3$ with $\lambda$ the 't Hooft coupling. Considering couplings $g$ that span three orders of magnit...

We study the thermodynamics of maximally supersymmetric U(N) Yang-Mills theory on $\mathds{R}\times S^2$ at large $N$. The model arises as a consistent truncation of ${\cal N}=4$ super Yang-Mills on $\mathds{R}\times S^3$ and as the continuum limit of the plane-wave matrix model expanded around the $N$ spherical membrane vacuum. The theory has an infinite number of classical BPS vacua, labeled by a set of monopole numbers, described by dual supergravity solutions. We first de...

We study the thermodynamics of large N pure 2+1 dimensional Yang-Mills theory on a small spatial sphere. By studying the effective action for the Polyakov loop order parameter, we show analytically that the theory has a second order deconfinement transition to a phase where the eigenvalue distribution of the Polyakov loop is non-uniform but still spread over the whole unit circle. At a higher temperature, the eigenvalue distribution develops a gap, via an additional third-ord...

We investigate the large-N behavior of the topological susceptibility in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N=4,6. The results indicate that the topological susceptibility has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological properties rema...

We review the thermodynamics of the confined and unconfined phases of superconformal Yang-Mills at large N on a three-sphere, focussing especially on the confinement-deconfinement transition. We determine an N-dependent phase boundary and point out some directions for future work.

The thermodynamics of supersymmetric Yang-Mills theories is studied by computing the two-loop correction to the canonical free energy and to the equation of state for theories with 16, 8 and 4 supercharges in any dimension $4\leq d\leq 10$, and in two dimensions at finite volume. In the four-dimensional case we also evaluate the first non-analytic contribution in the 't Hooft coupling to the free energy, arising from the resummation of ring diagrams. To conclude, we discuss s...