Talk delivered at the conference on 'Strong Interactions in the 21st Century', held at the Tata Institute of Fundamental Research, Mumbai, Feb. 10 - 12, 2010
The stable chromomagnetic vacuum for SU(2) Yang-Mills theory found earlier is shown to give a model for confinement in QCD, using Wilson loop, and a linear potential (in the leading order) for quark-antiquark interaction. The coefficient $k$ in this potential is found to be $\sim 0.25 GeV^2$, in satisfactory agreement with non-relativistic potential model calculations for charmonium. At finite temperature, the real effective energy density found earlier is used to obtain estimates of the deconfining temperature agreeing reasonably with lattice study for SU(2).
In this paper we study the effects associated to quantum vacuum fluctuations of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static and homogeneous chromomagnetic-like background field, at zero temperature. We use periodic and antiperiodic boundary conditions in order to calculate the Casimir energy by means of the frequency sum technique and of the regularization method based on zeta functions, analyzing its behavior in the weak and strong coupling regimes. We compare the obtained results with the similar ones found for scalar and spinor fields placed in an ordinary magn…
I reexamine the phenomena of the chromomagnetic gluon condensation in Yang-Mills theory. The extension of the Heisenberg-Euler Lagrangian to the Yang-Mills theory allows to calculate the effective action, the energy-momentum tensor and demonstrate that the energy density curve crosses the zero energy level of the perturbative vacuum state at nonzero angle and continuously enters to the negative energy density region. At the crossing point and further down the effective coupling constant is small and demonstrate that the true vacuum state of the Yang-Mills theory is below the perturbative vacuu…
I consider the chromomagnetic vacuum in SU(2). The effective Lagrangian in one loop approximation is known to have a minimum below zero which results in a spontaneously generated magnetic field. However, this minimum is not stable; the effective action has an imaginary part. Over the past decades, there were many attempts to handle this situation which all were at some point unsatisfactory. I propose an idea for a new solution by assuming that the tachyonic mode, at low temperature, acquires a condensate and, as a result, undergoes a phase transition like in the Higgs model. I consider the app…
I review the main features of our model of the 4-dimensional Yang-Mills theory vacuum as a liquid of fractional instantons. The model provides a possible microscopic mechanism for Confinement in four dimensional Yang-Mills theory at $T=0$. It also connects this property to other non-perturbative properties of the theory which can be explained by the same model. This paper is a, somewhat enlarged, written up version of my recent talks on the subject given at ICTS-Bangalore, KITP-Santa Barbara and IMSC-Chennai.
Dynamical Couplings, Dynamical Vacuum Energy and Confinement/Deconfinement from R^2-Gravity
我们在Palatini形式下研究了f（R）= R + αR^2的f（R）-引力与一个介子和一种特殊的非线性规范场系统的相互作用，该系统包含一个标准麦克斯韦项的平方根，已知它会在平坦时空中产生禁闭。在物理爱因斯坦框架中重新构建模型，我们发现标量场有效势具有平坦区域，在该区域中约束动力学消失，而在其他区域中它保持完整。有效的规范耦合以及诱导的宇宙学常数成为动态的。特别是，一个传统的麦克斯韦动力学项的规范场是动态产生的，即使在原来的理论缺席。我们发现了几类有趣的显式解：（i）具有附加真空电势的非标准型渐近（反）de Sitter黑洞，即使对于电中性黑洞也是如此;（ii）具有附加恒定真空电场的非标准Reissner-Nordstroem黑洞，具有非平坦时空的“刺猬”渐近性;（iii）广义Levi-Civitta-Bertotti-Robinson“管状”时空。
QCD Confinement and Theta Vacuum: Dynamical Spontaneous Symmetry Breaking
本文提出，作为SU（3）_C规范理论的量子色动力学（QCD）的长期问题，禁闭机制和Θ真空，可以通过单重态胶子凝聚的动力学自发对称性破缺（DSSB）和作为SU（2）_N x U（1）_Z规范理论的量子核动力学（QND）来解决。禁闭机制是大质量胶子的结果，汤川势提供了强子的形成。DSSB过程中离散对称性（C，P，T，CP）破缺的明显证据是：没有宇称伙伴的重子和介子，矢量流守恒和轴矢量流部分守恒，重子不对称性δ B \simeq 10^{-10}，中子电偶极矩Θ< 10^{-9}。强子质量产生机制是由Θ真空引起的DSSB。
Single quarks moving in the vacuum of confining gauge theories are stopped by a drag force. The holographic description relates the confining scale in the bulk geometry with a range of physical values for the drag force in the vacuum. The vacuum drag force acting on the isolated quark directly manifests quark confinement since it prevents the quark from walking freely in the vacuum. However, analytical expressions for the drag force as a function of the quark velocity were lacking. In the present work, we propose that the vacuum drag force is given by the regularized zero-temperature limit of …
The review of vacuum and matter restructuring in space-time with boundaries is presented. We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates. We also discuss mass scale shifts in such systems and their possible dynamical and geometrical nature.
We report on recent progress in understanding confinement of colour in $QCD$ as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order parameter. This order parameter is gauge-invariant from scratch, has no infrared divergences, is finite in the confined phase and vanishes in the deconfined phase. A natural explanation also emerges of why the electric field lines in the flux tubes keep no memory of the colour orientation of the condensing monopoles. A further by-product is that the order p…
In this paper we improve the existing order parameter for monopole condensation in gauge theory vacuum, making it gauge-invariant from scratch and free of the spurious infrared problems which plagued the old one. Computing the new parameter on the lattice will unambiguously detect weather dual superconductivity is the mechanism for color confinement. As a byproduct we relate confinement to the existence of a finite correlation length in the gauge-invariant correlator of chromo-electric field strengths.
