879 research outputs found
Mixing Patterns from the Groups Sigma (n phi)
We survey the mixing patterns which can be derived from the discrete groups
Sigma (36 x 3), Sigma (72 x 3), Sigma (216 x 3) and Sigma (360 x 3), if these
are broken to abelian subgroups Ge and Gnu in the charged lepton and neutrino
sector, respectively. Since only Sigma (360 x 3) possesses Klein subgroups,
only this group allows neutrinos to be Majorana particles. We find a few
patterns that can agree well with the experimental data on lepton mixing in
scenarios with small corrections and that predict the reactor mixing angle
theta_{13} to be 0.1 <= theta_{13} <= 0.2. All these patterns lead to a trivial
Dirac phase. Patterns which instead reveal CP violation tend to accommodate the
data not well. We also comment on the outer automorphisms of the discussed
groups, since they can be useful for relating inequivalent representations of
these groups.Comment: 1+28 pages, 6 tables, no figures; v2: matches version published in J.
Phys. A: Math. Theo
NLO Renormalization in the Hamiltonian Truncation
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical
technique for solving strongly coupled QFTs, in which the full Hilbert space is
truncated to a finite-dimensional low-energy subspace. The accuracy of the
method is limited only by the available computational resources. The
renormalization program improves the accuracy by carefully integrating out the
high-energy states, instead of truncating them away. In this paper we develop
the most accurate ever variant of Hamiltonian Truncation, which implements
renormalization at the cubic order in the interaction strength. The novel idea
is to interpret the renormalization procedure as a result of integrating out
exactly a certain class of high-energy "tail states". We demonstrate the power
of the method with high-accuracy computations in the strongly coupled
two-dimensional quartic scalar theory, and benchmark it against other existing
approaches. Our work will also be useful for the future goal of extending
Hamiltonian Truncation to higher spacetime dimensions.Comment: 28pp + appendices, detailed version of arXiv:1706.0612
High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient
numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions.
Further theoretical developments are needed to increase its accuracy and the
range of applicability. With this goal in mind, here we present a new variant
of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff
than other existing implementations, and yields more accurate spectra. The key
idea for achieving this consists in integrating out exactly a certain class of
high energy states, which corresponds to performing renormalization at the
cubic order in the interaction strength. We test the new method on the strongly
coupled two-dimensional quartic scalar theory. Our work will also be useful for
the future goal of extending Hamiltonian Truncation to higher dimensions d >=
3.Comment: 8 pages, 4 figures; v2: published versio
The local Callan-Symanzik equation: structure and applications
The local Callan-Symanzik equation describes the response of a quantum field
theory to local scale transformations in the presence of background sources.
The consistency conditions associated with this anomalous equation imply
non-trivial relations among the -function, the anomalous dimensions of
composite operators and the short distance singularities of correlators. In
this paper we discuss various aspects of the local Callan-Symanzik equation and
present new results regarding the structure of its anomaly. We then use the
equation to systematically write the n-point correlators involving the trace of
the energy-momentum tensor. We use the latter result to give a fully detailed
proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also
correspond to CFTs. We also clarify the relation between the matrix entering
the gradient flow formula for the -function and a manifestly positive
metric in coupling space associated with matrix elements of the trace of the
energy momentum tensor.Comment: v2: Modified discussion of the amplitude; v3: typos fixe
Conformal Truncation of Chern-Simons Theory at Large
We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons
field coupled to fermions in the limit of large using conformal
truncation, i.e. with a truncated space of states corresponding to primary
operators with dimension below a maximum cutoff . In both the
Chern-Simons theory, and in the model at infinite , we compute the
current spectral functions analytically as a function of and
reproduce previous results in the limit that the truncation
is taken to . Along the way, we determine how to preserve gauge
invariance and how to choose an optimal discrete basis for the momenta of
states in the truncation space.Comment: 32+25 pages, 8 figures. v2: updated ref
A naturally light dilaton
Goldstone's theorem does not apply straightforwardly to the case of
spontaneously broken scale invariance. We elucidate under what conditions a
light scalar degree of freedom, identifiable with the dilaton, can naturally
arise. Our construction can be considered an explicit dynamical solution to the
cosmological constant problem in the scalar version of gravity.Comment: v2: published versio
Deterrence in Competition Law
This paper provides a comprehensive discussion of the deterrence properties of a competition policy regime. On the basis of the economic theory of law enforcement we identify several factors that are likely to affect its degree of deterrence: 1) sanctions and damages; 2) financial and human resources; 3) powers during the investigation; 4) quality of the law; 5) independence; and 6) separation of power. We then discuss how to measure deterrence. We review the literature that use surveys to solicit direct information on changes in the behavior of firms due to the threats posed by the enforcement of antitrust rules, and the literature based on the analysis of hard data. We finally argue that the most challenging task, both theoretically and empirically, is how to distinguish between âgoodâ deterrence and âbadâ deterrence
Measuring the deterrence properties of competition policy: the Competition Policy Indexes
The aim of this paper is to describe in detail a set of newly developed indicators of the quality of competition policy, Competition Policy Indexes, or CPIs. The CPIs measure the deterrence properties of a competition policy in a jurisdiction, where for competition policy we mean the antitrust legislation, including the merger control provisions, and its enforcement. The CPIs incorporate data on how the key features of a competition policy regime score against a benchmark of generally-agreed best practices and summarise them so as to allow cross-country and cross-time comparisons. The CPIs have been calculated for a sample of 13 OECD jurisdictions over the period 1995-2005
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