On emergent particles and stable neutral plasma balls in SU(2) Yang-Mills thermodynamics
Thierry Grandou, Ralf Hofmann
备注：
11 pages, 1 Figure.The previous Introduction has been drastically streamlined, from 6 to 2 pages; @ extra references added, and small changes brought to the presentation of Section 2.3. arXiv admin note: text overlap with arXiv:1809.08234
For a pure SU(2) Yang-Mills theory in 4D we revisit the spatial (3D), ball-like region of radius $r_0$, in its bulk subject to the pressureless, deconfining phase at $T_0=1.32\,T_c$ where $T_c$ denotes the critical temperature for the onset of the deconfining-preconfining phase transition. Such a region possesses of a finite energy density and represents the self-intersection of a figure-eight shaped center-vortex loop if a BPS monopole of core radius $\sim \frac{r_0}{52.4}$, isolated from its antimonopole by repulsion externally invoked through a transient shift of (anti)caloron holonomy (pair creation), is trapped therein. The entire soliton (vortex line plus region of self-intersection of mass $m_0$ containing the monopole) can be considered an excitation of the pressureless and energyless ground state of the confining phase. Correcting an earlier estimate of $r_0$, we show that the vortex-loop self-intersection region associates with the {\sl central part} of a(n) (anti)caloron and that this region carries one unit of electric U(1) charge via the (electric-magnetic dually interpreted) charge of the monopole. The monopole core quantum vibrates at a thermodynamically determined frequency $ω_0$ and is unresolved. For a deconfining-phase plasma oscillation about the zero-pressure background at $T=T_0$ we compute the lowest frequency $Ω_0$ within a {\sl neutral} and homogeneous spatial ball (no trapped monopole) in dependence of its radius $R_0$. For $R_0=r_0$ a comparison of $Ω_0$ with $ω_0$ reveals that the neutral plasma oscillates much slower than the same plasma driven by the oscillation of a monopole core.
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We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the cohomological approach and the Monte Carlo method. In the bosonic models we show the existence of an exotic first/second order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first order due to the discontinuity in th…
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We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field whic…
We re-address the self-intersection region in a figure-eight shaped center-vortex loop containing a frequently perturbed {\sl BPS monopole} subject to a core-oscillation frequency $ω_0$, rectifying a numerical error in estimating the system's radius $r_0$ in comparison to the spatial coarse-graining scale of infinite-volume thermodynamics. Implications are discussed. We also compute the lowest frequency $Ω_0$ of a spherically symmetric plasma oscillation within a {\sl neutral} and spatially homogeneous ball-like region of deconfining phase in dependence of its radius $R_0$. For $r_0=R_0$ we co…
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A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative $U(1)$ gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres ${\bf S}^2_N$ and ${\bf S}^2_N\times{\bf S}^2_N$ respectively. The three and six matrix models are in the same universality class with some differences. For example, in t…
