6,691 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
Characters of graded parafermion conformal field theory
The graded parafermion conformal field theory at level k is a close cousin of
the much-studied Z_k parafermion model. Three character formulas for the graded
parafermion theory are presented, one bosonic, one fermionic (both previously
known) and one of spinon type (which is new). The main result of this paper is
a proof of the equivalence of these three forms using q-series methods combined
with the combinatorics of lattice paths. The pivotal step in our approach is
the observation that the graded parafermion theory -- which is equivalent to
the coset osp(1,2)_k/ u(1) -- can be factored as (osp(1,2)_k/ su(2)_k) x
(su(2)_k/ u(1)), with the two cosets on the right equivalent to the minimal
model M(k+2,2k+3) and the Z_k parafermion model, respectively. This
factorisation allows for a new combinatorial description of the graded
parafermion characters in terms of the one-dimensional configuration sums of
the (k+1)-state Andrews--Baxter--Forrester model.Comment: 36 page
Evolution of quantum observables: from non-commutativity to commutativity
A fundamental aspect of the quantum-to-classical limit is the transition from a non-
commutative algebra of observables to commutative one.However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.MINECO Grant MTM2014- 57129-C2-1-P. Junta de Castilla y Leon Grants BU229P18, VA137G18
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
Alien Registration- Fortin, Evelyn F. (Madison, Somerset County)
https://digitalmaine.com/alien_docs/6573/thumbnail.jp
Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques
We propose a method to study the second-order critical lines of classical
spin- Ising models on two-dimensional lattices in a crystal or splitting
field, using an exact expression for the bare mass of the underlying field
theory. Introducing a set of anticommuting variables to represent the partition
function, we derive an exact and compact expression for the bare mass of the
model including all local multi-fermions interactions. By extension of the
Ising and Blume-Capel models, we extract the free energy singularities in the
low momentum limit corresponding to a vanishing bare mass. The loci of these
singularities define the critical lines depending on the spin S, in good
agreement with previous numerical estimations. This scheme appears to be
general enough to be applied in a variety of classical Hamiltonians
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
- …