119190881
The static quark potential from the gauge invariant Abelian decomposition
Abstract We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement.
11333859
No ghost state of Gauss–Bonnet interaction in warped backgrounds
Abstract A general solution to the Einstein field equations with the Gauss–Bonnet (GB) term in an AdS 5 bulk background implies that the GB coupling α can take either sign (+ or −), though a positive α will be more meaningful. By considering linearized gravity with the GB term in the Randall–Sundrum (RS) a singular 3-brane model, we study the gravitational interactions between matter sources localized on the brane. With correctly defined boundary conditions on the brane, we find a smooth behavior of graviton propagators and hence the zero-mode solution as a 4d massless graviton localized on the brane with correct momentum and tensor structures. The coupling α modifies the graviton propagators both on the brane and in the bulk. The issue on ghost state of the GB term is resolved, and we find that there is no real ghost (negative norm) state of the GB term in the RS single brane picture. The latter condition leads to a consistency in the coupling between the brane matter and the bulk gravity. We also elucidate about the possibilities for behavior of a test particle on the brane and in the bulk.
119290148
Vacuum tunneling in gravity
Topologically non-trivial vacuum structures in gravity models with Cartan variables (vielbein and contortion) are considered. We study the possibility of vacuum spacetime tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology, the tunneling between non-trivial topological vacuums can be realized by means of Eguchi?Hanson gravitational instanton. In the Riemann?Cartan geometric approach to quantum gravity, the vacuum tunneling can be provided by means of contortion quantum fluctuations. We define a double self-duality condition for the contortion and give explicit self-dual configurations which can contribute to vacuum tunneling amplitude.
121597932
Gravitating 't Hooft Monopoles
The 't Hooft magnetic monopole solution of the SO(3) Higgs model generates, when coupled to gravity, a geometry which for large distances is of the Reissner--Nordstroem form corresponding to a (magnetic) charge 1/e. The Higgs fields can contribute a cosmological term. In the absence of scalar fields the corresponding Wu--Yang solution of the SO(3) gauge theory still generates the Reissner--Nordstroem geometry. (AIP)
118204832
Gauge Invariance and Stability of SNO vacuum in QCD
We point out a critical defect in the calculation of the functional determinant of the gluon loop in the Savvidy-Nielsen-Olesen (SNO) effective action. We prove that the gauge invariance naturally exclude the unstable tachyonic modes from the gluon loop integral. This guarantees the stability of the magnetic condensation in QCD.
12520342
DIRAC QUANTIZATION OF RESTRICTED QCD
We discuss the quantization of the restricted gauge theory of SU(2) QCD regarding it as a second-class constraint system, and construct the BRST symmetry of the constrained system in the framework of the improved Dirac quantization scheme. Our analysis tells that one could efficiently quantize the restricted QCD under the BRST symmetry as if it is a first-class constraint system.
121443233
MONOPOLE CONDENSATION AND MASS GAP IN SU(3) QCD
We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.