129 research outputs found
The -theorem and the Asymptotics of 4D Quantum Field Theory
We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary
quantum field theory. Our main tool is a generalization of the
Komargodski-Schwimmer proof for the -theorem. We use this to rule out a
large class of renormalization group flows that do not asymptote to conformal
field theories in the UV and IR. We show that if the IR (UV) asymptotics is
described by perturbation theory, all beta functions must vanish faster than
as (). This implies that the
only possible asymptotics within perturbation theory is conformal field theory.
In particular, it rules out perturbative theories with scale but not conformal
invariance, which are equivalent to theories with renormalization group
pseudocycles. Our arguments hold even for theories with gravitational
anomalies. We also give a non-perturbative argument that excludes theories with
scale but not conformal invariance. This argument holds for theories in which
the stress-energy tensor is sufficiently nontrivial in a technical sense that
we make precise.Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments
corrected, connection to previous work by Jack and Osborn described,
conclusions unaffecte
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
On the Trace Anomaly and the Anomaly Puzzle in N=1 Pure Yang-Mills
The trace anomaly of the energy-momentum tensor is usually quoted in the form
which is proportional to the beta function of the theory. However, there are in
general many definitions of gauge couplings depending on renormalization
schemes, and hence many beta functions. In particular, N=1 supersymmetric pure
Yang-Mills has the holomorphic gauge coupling whose beta function is one-loop
exact, and the canonical gauge coupling whose beta function is given by the
Novikov-Shifman-Vainshtein-Zakharov beta function. In this paper, we study
which beta function should appear in the trace anomaly in N=1 pure Yang-Mills.
We calculate the trace anomaly by employing the N=4 regularization of N=1 pure
Yang-Mills. It is shown that the trace anomaly is given by one-loop exact form
if the composite operator appearing in the trace anomaly is renormalized in a
preferred way. This result gives the simplest resolution to the anomaly puzzle
in N=1 pure Yang-Mills. The most important point is to examine in which scheme
the quantum action principle is valid, which is crucial in the derivation of
the trace anomaly.Comment: 25 pages, 1 figure; v2:slight correction in sec.5, minor addition in
appendi
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
Trace anomalies in chiral theories revisited
Motivated by the search for possible CP violating terms in the trace of the
energy-momentum tensor in theories coupled to gravity we revisit the problem of trace
anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of
the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin
density appears with an imaginary coefficient. We argue that this may break unitarity, in
which case the trace anomaly has to be used as a selective criterion for theories, analogous
to the chiral anomalies in gauge theories. We analyze some remarkable consequences of
this fact, that seem to have been overlooked in the literature
Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
We present a class of exact analytic and static, spherically symmetric black
hole solutions in the semi-classical Einstein equations with Weyl anomaly. The
solutions have two branches, one is asymptotically flat and the other
asymptotically de Sitter. We study thermodynamic properties of the black hole
solutions and find that there exists a logarithmic correction to the well-known
Bekenstein-Hawking area entropy. The logarithmic term might come from non-local
terms in the effective action of gravity theories. The appearance of the
logarithmic term in the gravity side is quite important in the sense that with
this term one is able to compare black hole entropy up to the subleading order,
in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE
Quantum gravitational corrections for spinning particles
We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian potential induced by massless conformal matter for spinless particles are well-known, and the same corrections due to massless minimally coupled scalars [Class. Quant. Grav. 27 (2010) 245008], massless non-conformal scalars [Phys. Rev. D 87 (2013) 104027] and massive scalars, fermions and vector bosons [Phys. Rev. D 91 (2015) 064047] have been recently derived, spinning particles receive additional corrections which are the subject of the present work. We give both fully analytic results valid for all distances from the particle, and present numerical results as well as asymptotic expansions. At large distances from the particle, the corrections due to massive fields are exponentially suppressed in comparison to the corrections from massless fields, as one would expect. However, a surprising result of our analysis is that close to the particle itself, on distances comparable to the Compton wavelength of the massive fields running in the loops, these corrections can be enhanced with respect to the massless case
Eikonal methods applied to gravitational scattering amplitudes
We apply factorization and eikonal methods from gauge theories to scattering
amplitudes in gravity. We hypothesize that these amplitudes factor into an
IR-divergent soft function and an IR-finite hard function, with the former
given by the expectation value of a product of gravitational Wilson line
operators. Using this approach, we show that the IR-divergent part of the
n-graviton scattering amplitude is given by the exponential of the one-loop IR
divergence, as originally discovered by Weinberg, with no additional subleading
IR-divergent contributions in dimensional regularization.Comment: 16 pages, 3 figures; v2: title change and minor rewording (published
version); v3: typos corrected in eqs.(3.2),(4.1
Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories
Through the AdS/CFT correspondence, we study a uniformly accelerated quark in
the vacuum of strongly-coupled conformal field theories in various dimensions,
and determine the resulting stochastic fluctuations of the quark trajectory.
From the perspective of an inertial observer, these are quantum fluctuations
induced by the gluonic radiation emitted by the accelerated quark. From the
point of view of the quark itself, they originate from the thermal medium
predicted by the Unruh effect. We scrutinize the relation between these two
descriptions in the gravity side of the correspondence, and show in particular
that upon transforming the conformal field theory from Rindler space to the
open Einstein universe, the acceleration horizon disappears from the boundary
theory but is preserved in the bulk. This transformation allows us to directly
connect our calculation of radiation-induced fluctuations in vacuum with the
analysis by de Boer et al. of the Brownian motion of a quark that is on average
static within a thermal medium. Combining this same bulk transformation with
previous results of Emparan, we are also able to compute the stress-energy
tensor of the Unruh thermal medium.Comment: 1+31 pages; v2: reference adde
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