252 research outputs found
Gauge Consistent Wilson Renormalization Group II: Non-Abelian Case
We give a wilsonian formulation of non-abelian gauge theories explicitly
consistent with axial gauge Ward identitities. The issues of unitarity and
dependence on the quantization direction are carefully investigated. A
wilsonian computation of the one-loop QCD beta function is performed.Comment: 34 pages, 1 eps figure, latex2e. Minor changes, version to appear in
Int. J. Mod. Phy
Ultraviolet Complete Quantum Gravity
An ultraviolet complete quantum gravity theory is formulated in which vertex
functions in Feynman graphs are entire functions and the propagating graviton
is described by a local, causal propagator. The cosmological constant problem
is investigated in the context of the ultraviolet complete quantum gravity.Comment: 11 pages, no figures. Changes to text. Results remain the same.
References added. To be published in European Physics Journal Plu
The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
We discuss various basic conceptual issues related to coarse graining flows
in quantum gravity. In particular the requirement of background independence is
shown to lead to renormalization group (RG) flows which are significantly
different from their analogs on a rigid background spacetime. The importance of
these findings for the asymptotic safety approach to Quantum Einstein Gravity
(QEG) is demonstrated in a simplified setting where only the conformal factor
is quantized. We identify background independence as a (the ?) key prerequisite
for the existence of a non-Gaussian RG fixed point and the renormalizability of
QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum
Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to
appear in General Relativity and Gravitatio
Running Gauge Coupling in Asymptotically Safe Quantum Gravity
We investigate the non-perturbative renormalization group behavior of the
gauge coupling constant using a truncated form of the functional flow equation
for the effective average action of the Yang-Mills-gravity system. We find a
non-zero quantum gravity correction to the standard Yang-Mills beta function
which has the same sign as the gauge boson contribution. Our results fit into
the picture according to which Quantum Einstein Gravity (QEG) is asymptotically
safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page
Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
We find the exact non-perturbative expression for a simple Wilson loop of
arbitrary shape for U(N) and SU(N) Euclidean or Minkowskian two-dimensional
Yang-Mills theory regulated by the Wu-Mandelstam-Leibbrandt gauge prescription.
The result differs from the standard pure exponential area-law of YM_2, but
still exhibits confinement as well as invariance under area-preserving
diffeomorphisms and generalized axial gauge transformations. We show that the
large N limit is NOT a good approximation to the model at finite N and conclude
that Wu's N=infinity Bethe-Salpeter equation for QCD_2 should have no bound
state solutions. The main significance of our results derives from the
importance of the Wu-Mandelstam-Leibbrandt prescription in higher-dimensional
perturbative gauge theory.Comment: 7 pages, LaTeX, REVTE
Cosmological Dark Energy: Prospects for a Dynamical Theory
We present an approach to the problem of vacuum energy in cosmology, based on
dynamical screening of Lambda on the horizon scale. We review first the
physical basis of vacuum energy as a phenomenon connected with macroscopic
boundary conditions, and the origin of the idea of its screening by particle
creation and vacuum polarization effects. We discuss next the relevance of the
quantum trace anomaly to this issue. The trace anomaly implies additional terms
in the low energy effective theory of gravity, which amounts to a non-trivial
modification of the classical Einstein theory, fully consistent with the
Equivalence Principle. We show that the new dynamical degrees of freedom the
anomaly contains provide a natural mechanism for relaxing Lambda to zero on
cosmological scales. We consider possible signatures of the restoration of
conformal invariance predicted by the fluctuations of these new scalar degrees
of freedom on the spectrum and statistics of the CMB, in light of the latest
bounds from WMAP. Finally we assess the prospects for a new cosmological model
in which the dark energy adjusts itself dynamically to the cosmological horizon
boundary, and therefore remains naturally of order H^2 at all times without
fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue
on Dark Energ
Notes on Operator Equations of Supercurrent Multiplets and the Anomaly Puzzle in Supersymmetric Field Theories
Recently, Komargodski and Seiberg have proposed a new type of supercurrent
multiplet which contains the energy-momentum tensor and the supersymmetry
current consistently. In this paper we study quantum properties of the
supercurrent in renormalizable field theories. We point out that the new
supercurrent gives a quite simple resolution to the classic problem, called the
anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current
is inconsistent with all order corrections to functions. We propose an
operator equation for the supercurrent in all orders of perturbation theory,
and then perform several consistency checks of the equation. The operator
equation we propose is consisitent with the one proposed by Shifman and
Vainshtein, if we take some care in interpreting the meaning of non-conserved
currents.Comment: 28 pages; v2:clarifications and references added, some minor change
Consistency conditions and trace anomalies in six dimensions
Conformally invariant quantum field theories develop trace anomalies when
defined on curved backgrounds. We study again the problem of identifying all
possible trace anomalies in d=6 by studying the consistency conditions to
derive their 10 independent solutions. It is known that only 4 of these
solutions represent true anomalies, classified as one type A anomaly, given by
the topological Euler density, and three type B anomalies, made up by three
independent Weyl invariants. However, we also present the explicit expressions
of the remaining 6 trivial anomalies, namely those that can be obtained by the
Weyl variation of local functionals. The knowledge of the latter is in general
necessary to disentangle the universal coefficients of the type A and B
anomalies from calculations performed on concrete models.Comment: 16 pages, LaTe
See-Saw Modification of Gravity
We discuss a model in which the fundamental scale of gravity is restricted to
10^{-3} eV. An observable modification of gravity occurs simultaneously at the
Hubble distance and at around 0.1 mm. These predictions can be tested both by
the table-top experiments and by cosmological measurements. The model is
formulated as a brane-world theory embedded in a space with two or more
infinite-volume extra dimensions. Gravity on the brane reproduces the
four-dimensional laws at observable distances but turns to the high-dimensional
behavior at larger scales. To determine the crossover distance we smooth out
the singularities in the Green's functions by taking into account softening of
the graviton propagator due to the high-dimensional operators that are
suppressed by the fundamental scale. We find that irrespective of the precise
nature of microscopic gravity the ultraviolet and infrared scales of
gravity-modification are rigidly correlated. This fixes the fundamental scale
of gravity at 10^{-3} eV. The result persists for nonzero thickness branes.Comment: 24 LaTex pages; v2: comments added, typos correcte
Factorization Properties of Soft Graviton Amplitudes
We apply recently developed path integral resummation methods to perturbative
quantum gravity. In particular, we provide supporting evidence that eikonal
graviton amplitudes factorize into hard and soft parts, and confirm a recent
hypothesis that soft gravitons are modelled by vacuum expectation values of
products of certain Wilson line operators, which differ for massless and
massive particles. We also investigate terms which break this factorization,
and find that they are subleading with respect to the eikonal amplitude. The
results may help in understanding the connections between gravity and gauge
theories in more detail, as well as in studying gravitational radiation beyond
the eikonal approximation.Comment: 35 pages, 5 figure
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