6,030 research outputs found
Limit Cycles and Conformal Invariance
There is a widely held belief that conformal field theories (CFTs) require
zero beta functions. Nevertheless, the work of Jack and Osborn implies that the
beta functions are not actually the quantites that decide conformality, but
until recently no such behavior had been exhibited. Our recent work has led to
the discovery of CFTs with nonzero beta functions, more precisely CFTs that
live on recurrent trajectories, e.g., limit cycles, of the beta-function vector
field. To demonstrate this we study the S function of Jack and Osborn. We use
Weyl consistency conditions to show that it vanishes at fixed points and agrees
with the generator Q of limit cycles on them. Moreover, we compute S to third
order in perturbation theory, and explicitly verify that it agrees with our
previous determinations of Q. A byproduct of our analysis is that, in
perturbation theory, unitarity and scale invariance imply conformal invariance
in four-dimensional quantum field theories. Finally, we study some properties
of these new, "cyclic" CFTs, and point out that the a-theorem still governs the
asymptotic behavior of renormalization-group flows.Comment: 31 pages, 4 figures. Expanded introduction to make clear that cycles
discussed in this work are not associated with unitary theories that are
scale but not conformally invarian
Limit Cycles in Four Dimensions
We present an example of a limit cycle, i.e., a recurrent flow-line of the
beta-function vector field, in a unitary four-dimensional gauge theory. We thus
prove that beta functions of four-dimensional gauge theories do not produce
gradient flows. The limit cycle is established in perturbation theory with a
three-loop calculation which we describe in detail.Comment: 12 pages, 1 figure. Significant revision of the interpretation of our
result. Improved description of three-loop calculatio
SM(2,4k) fermionic characters and restricted jagged partitions
A derivation of the basis of states for the superconformal minimal
models is presented. It relies on a general hypothesis concerning the role of
the null field of dimension . The basis is expressed solely in terms of
modes and it takes the form of simple exclusion conditions (being thus a
quasi-particle-type basis). Its elements are in correspondence with
-restricted jagged partitions. The generating functions of the latter
provide novel fermionic forms for the characters of the irreducible
representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page
Properties of Non-Abelian Fractional Quantum Hall States at Filling
We compute the physical properties of non-Abelian Fractional Quantum Hall
(FQH) states described by Jack polynomials at general filling
. For , these states are identical to the
Read-Rezayi parafermions, whereas for they represent new FQH states. The
states, multiplied by a Vandermonde determinant, are a non-Abelian
alternative construction of states at fermionic filling . We
obtain the thermal Hall coefficient, the quantum dimensions, the electron
scaling exponent, and show that the non-Abelian quasihole has a well-defined
propagator falling off with the distance. The clustering properties of the Jack
polynomials, provide a strong indication that the states with can be
obtained as correlators of fields of \emph{non-unitary} conformal field
theories, but the CFT-FQH connection fails when invoked to compute physical
properties such as thermal Hall coefficient or, more importantly, the quasihole
propagator. The quasihole wavefuntion, when written as a coherent state
representation of Jack polynomials, has an identical structure for \emph{all}
non-Abelian states at filling .Comment: 2 figure
Scale without Conformal Invariance at Three Loops
We carry out a three-loop computation that establishes the existence of scale
without conformal invariance in dimensional regularization with the MS scheme
in d=4-epsilon spacetime dimensions. We also comment on the effects of scheme
changes in theories with many couplings, as well as in theories that live on
non-conformal scale-invariant renormalization group trajectories. Stability
properties of such trajectories are analyzed, revealing both attractive and
repulsive directions in a specific example. We explain how our results are in
accord with those of Jack & Osborn on a c-theorem in d=4 (and d=4-epsilon)
dimensions. Finally, we point out that limit cycles with turning points are
unlike limit cycles with continuous scale invariance.Comment: 21 pages, 3 figures, Erratum adde
Neutron star radii and crusts: uncertainties and unified equations of state
The uncertainties in neutron star (NS) radii and crust properties due to our
limited knowledge of the equation of state (EOS) are quantitatively analysed.
We first demonstrate the importance of a unified microscopic description for
the different baryonic densities of the star. If the pressure functional is
obtained matching a crust and a core EOS based on models with different
properties at nuclear matter saturation, the uncertainties can be as large as
for the crust thickness and for the radius. Necessary
conditions for causal and thermodynamically consistent matchings between the
core and the crust are formulated and their consequences examined. A large set
of unified EOS for purely nucleonic matter is obtained based on 24 Skyrme
interactions and 9 relativistic mean-field nuclear parametrizations. In
addition, for relativistic models 17 EOS including a transition to hyperonic
matter at high density are presented. All these EOS have in common the property
of describing a star and of being causal within stable NS. A span
of km and km is obtained for the radius of, respectively,
and star. Applying a set of nine further
constraints from experiment and ab-initio calculations the uncertainty is
reduced to km and km, respectively. These residual uncertainties
reflect lack of constraints at large densities and insufficient information on
the density dependence of the EOS near the nuclear matter saturation point. The
most important parameter to be constrained is shown to be the symmetry energy
slope which exhibits a linear correlation with the stellar radius,
particularly for masses . Potential constraints on , the
NS radius and the EOS from observations of thermal states of NS are also
discussed. [Abriged]Comment: Submitted to Phys. Rev. C. Supplemental material not include
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
New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions
We present a new path description for the states of the non-unitary
M(k+1,2k+3) models. This description differs from the one induced by the
Forrester-Baxter solution, in terms of configuration sums, of their
restricted-solid-on-solid model. The proposed path representation is actually
very similar to the one underlying the unitary minimal models M(k+1,k+2), with
an analogous Fermi-gas interpretation. This interpretation leads to fermionic
expressions for the finitized M(k+1,2k+3) characters, whose infinite-length
limit represent new fermionic characters for the irreducible modules. The
M(k+1,2k+3) models are also shown to be related to the Z_k graded parafermions
via a (q to 1/q) duality transformation.Comment: 43 pages (minor typo corrected and minor rewording in the
introduction
Interaction of a high-mass X-ray binary with the interstellar medium through stellar wind. The case of GX 301-2
GX 301-2 is a high-mass X-ray binary (HMXB) with strong stellar outflows. The
evolution of these binaries can be closely related with the interstellar
environment due to strong wind interactions. We try to constrain the energy
injected in the interstellar medium by GX 301-2 through stellar wind using
HAWK-I and Herschel data. We analysed HAWK-I images in four different filters
(Br, H, J, and Ks) and tried to retrieve signatures of the impact
of GX 301-2 on its environment. We used Herschel data to outline the
interstellar medium and the Gaia DR3 catalogue to infer the proper motion of GX
301-2. Finally, we estimated the energy injected in the interstellar medium
since the first supernova event of the HMXB. Using both HAWK-I and Herschel
images, we deduce an approximation of the total mass injected from GX~301-2 in
the interstellar medium of .Comment: 7 pages, 3 figure
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