The asymptotic form of the Hagedorn temperature in planar super Yang-Mills

We study the matrix quantum mechanics of two free hermitian N × N matrices subject to a singlet constraint in the microcanonical ensemble. This is the simplest example of a theory that at large N has a confinement/deconfinement transition. In the microcanonical ensemble, it also exhibits partial deconfinement with a Hagedorn density of states. We argue that the entropy of these configurations, based on a combinatorial counting of Young diagrams, are dominated by Young diagrams that have the VKLS shape. When the shape gets to the maximal depth allowed for a Young diagram of SU(N), namely N, we argue that the system stops exhibiting the Hagedorn behavior. The number of boxes (energy) at the transition is N2/4, independent of the charge of the state.

Section: Introductionmentioning

confidence: 99%

The endpoint of partial deconfinement

Berenstein,

Yan

2023

Fast QSC solver: tool for systematic study of $$ \mathcal{N} $$ = 4 Super-Yang-Mills spectrum

Gromov,

Hegedűs,

Julius

et al. 2024

Integrability methods give us access to a number of observables in the planar $$ \mathcal{N} $$ N = 4 SYM. Among them, the Quantum Spectral Curve (QSC) governs the spectrum of anomalous dimensions. Low lying states were successfully studied in the past using the QSC. However, with the increased demand for a systematic study of a large number of states for various applications, there is a clear need for a fast QSC solver which can easily access a large number of excited states. Here, we fill this gap by developing a new algorithm and applied it to study all 219 states with the bare dimension ∆0 ≤ 6 in a wide range of couplings.The new algorithm has an improved performance at weak coupling and allows to glue numerics smoothly the available perturbative data, resolving the previous obstruction. Further ∼ 8-fold efficiency gain comes from C++ implementation over the best available Mathematica implementation. We have made the code and the data to be available via a GitHub repository.The method is generalisable for non-local observables as well as for other theories such as deformations of $$ \mathcal{N} $$ N = 4 SYM and ABJM. It may find applications in the separation of variables and bootstrability approaches to the correlation functions. Some applications to correlators at strong coupling are also presented.

Hagedorn temperature from the thermal scalar in AdS and pp-wave backgrounds

Harmark

2024

We propose a thermal scalar equation of motion (EOM) that takes into account curvature corrections for backgrounds supported by Ramond-Ramond fluxes. This can be used to obtain the Hagedorn temperature for type II string theory on AdS and pp-wave backgrounds. For Ramond-Ramond flux supported pp-waves we show that the proposed thermal scalar EOM reproduces the leading curvature correction in the Hagedorn temperature equation obtained from the type II string theory spectrum. Furthermore, we use the thermal scalar EOM to obtain curvature corrections to the Hagedorn temperature for the AdS5 × S5 and AdS4 × ℂP3 backgrounds. These corrections match with strong coupling results of the integrable dual field theories, recently obtained by the Quantum Spectral Curve technique.