18381362
NAMBU STRING VERSUS DIRAC STRING IN EXTENDED QCD
Motivated by a recent observation that the monopoles in grand unified theories tend to force QCD to become nontrivial, we analyze the global topology of the extended QCD as a nontrivial non-Abelian gauge theory. In the electric gauge not only the *quarks but also the valence part of the potential develop the Nambu string, but the dual part of the potential remains free of any string singularity. In contrast, in the magnetic gauge the dual potential develops the Dirac string while the valence potential as well as the quarks become regular. Submitted to Physical Review Letters *Work supported in part by the Department of Energy, contract DEAC03-76SF00515, and in part by the Ministry of Education and Korean Science and Engineering Foundation. tPermanent address: Dept. of Physics, Seoul National University, Seoul 151, Korea. Recently the old problem of defining the color in QCD in the presence of the colored monopoles has been readdressed by some authors1p2 within the context of grand unified theories. The observation is that selecting the color direction of the monopoles in grand unified theories3 amounts to a topological obstruction to the color gauge symmetry in such a way that a choice of a global color SU(3) basis is not always possible. This observation raises two questions; first how to define the color,:! but perhaps more importantly how to interprete QCD itself,l in the presence of such a topological obstruction. As for the definition of the color there is, of course, a much more deeply rooted problem which exists even without the topological obstruction: a theorem due to Schlieder4 tells that the conserved color charge in classical non-Abelian gauge theories has such a severe gauge dependence that one can always choose a I 3 gauge in which the total charge vanishes completely, even when there is no topological obstruction. The impact of the topological obstruction to QCD itself, however, is indeed devastating because in the absence of a global SU(3) basis there can be no globally-defined gauge potentials, and consequently no perturbative &CD. Obviously the conventional QCD is not suited to this kind of circumstance. Fortunately there exists in the literature an unconventional version of QCD called the extended QCD5@ which can accommodate this difficulty. The purpose of this letter is to clarify the global topology of the extended QCD and discuss how it works under the above circumstance. Before we proceed, it is useful to clarify the problem that we face and put it in mathematical terms. Geometrically speaking the so-called topological obstruction1y2 originates from the fact that6j7 when one reduces a principal fibre bundle P(M, G) (with the base manifold M and the structure group G) to a reduced bundle P*(M, H*) where H* is a closed subgroup of G, P*( M, H*) could become nontrivial even when one starts from a trivial P(M, G). Thus P*(M, H*) does not always admit a global section
12642120
Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity
We study anti\char21{}de Sitter black holes in the Einstein-Gauss-Bonnet and the generic ${R}^{2}$ gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page\char21{}type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature $(k=1).$ But, with the Gauss-Bonnet and/or the $(\mathrm{Riemann}{)}^{2}$ interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature $(k=\ensuremath{-}1).$ We examine the finite coupling effects, and find that $Ng5$ could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on the first law and Noether charge. With a $(\mathrm{Riemann}{)}^{2}$ term, however, we can do this only approximately, and the two results agree when ${r}_{H}\ensuremath{\gg}L,$ the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy $({\mathcal{S}}_{H})$ and Bekenstein-Hawking entropy $({\mathcal{S}}_{\mathrm{BH}})$ with a $(\mathrm{Riemann}{)}^{2}$ term, which, for $k=0$ and $k=\ensuremath{-}1,$ implies ${\mathcal{S}}_{\mathrm{BH}}l~{\mathcal{S}}_{H}.$
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.
16229635
Dilatonic dark matter and unified cosmology: a new paradigm
We study the possibility that the dilaton - the fundamental scalar field which exists in all existing unified field theories - plays the role of the dark matter of the universe. We find that the condition for the dilaton to be the dark matter strongly restricts its mass to be around 0.5 keV or 270 MeV. For the other mass ranges, the dilaton either undercloses or overcloses the universe. The 0.5 keV dilaton has a free-streaming distance of about 1.4 Mpc and becomes an excellent candidate for warm dark matter, while the 270 MeV one has a free-streaming distance of about 7.4 pc and becomes cold dark matter. We discuss the possible ways to detect the dilaton experimentally.
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.
119190991
Confinement From The Gauge Invariant Abelian Decomposition
A common approach while considering confinement is to study the dominance of an Abelian subgroup of the SU(3) gauge Links. A good way to find the Abelian component of the field is through the Cho-Guan-De gauge invariant Abelian Decomposition, which uses a carefully chosen direction vector $n$ to split the gauge field into an Abelian restricted field and a remnant coloured field. The restricted field can be further subdivided into topological and non-topological terms. We show that there is a choice of $n$ which allows us to exactly represent the Wilson Loop of full QCD as a function of only the restricted Abelian field without requiring any path ordering or additional path integrals. We present numerical evidence showing that the topological part of the restricted field dominates the string tension. We also show that $n$ contains certain topological objects, which, if they exist, will be at least partially responsible for confinement. These leave distinctive patterns in the restricted field strength, and we search for these structures in quenched lattice QCD.