Modeling pion physics in the ϵ\epsilon-regime of two-flavor QCD using strong coupling lattice QED

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1) symmetry and thus incorporate the physics of the QCD anomaly. We can also tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles. However, unlike lattice QCD, a major advantage of our model is that we can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $\epsilon$-regime.Comment: 24 pages, 7 figure

Absence of vortex condensation in a two dimensional fermionic XY model

Motivated by a puzzle in the study of two dimensional lattice Quantum Electrodynamics with staggered fermions, we construct a two dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a non-compact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a KT transition.Comment: 5 pages, 5 figure

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-\eta}$ at large volumes with $0\leq\eta\leq 0.25$ for $0\leq T\leq T_c$.Comment: Revtex format; 4 pages, 2 figure

Four-dimensional lattice chiral gauge theories with anomalous fermion content

In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the St\"uckelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.Comment: 18 pages, the final version to appear in JHE

Role of the σ\sigma-resonance in determining the convergence of chiral perturbation theory

The dimensionless parameter $\xi = M_\pi^2/(16 \pi^2 F_\pi^2)$, where $F_\pi$ is the pion decay constant and $M_\pi$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $\sigma$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $\xi$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $\epsilon$-regime as expected. However, $\xi \lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $\xi > 0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $\sigma$-resonance in our model. Our findings may be useful for lattice QCD studies.Comment: 5 pages, 6 figures, revtex forma

Indigenous trawl operations during fishing ban period in Chennai

North Chennai is a major centre for mechanised fishing with approximately 1200 fishing units. Generally during the fishing ban period, the fishermen from these units either sit idle or enroll as labourers for fishing in permitted traditional fishing units. But during the mechanised fishing ban period in 2017, some of the fishers in North Chennai started mini trawl operations to tide over their lean period. The size of the trawl net was 15 m in length and cod end mesh size of 24 mm

Restriction Properties of Annulus SLE

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\kappa)$. Using this property, we construct $n\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\kappa)$ trace.Comment: 37 page

The continuing saga of patents and non-invasive prenatal testing

This is the final version. Available on open access from Wiley via the DOI in this recordObjective: This paper examines the IP landscape for NIPT in three key regions: USA; Europe, with particular focus on the UK, and Australia. Method: We explore the patent law issues against the commercial and healthcare environment in these regions, and consider the implications for development and implementation of NIPT. Results: There are many patents held by many parties internationally, with litigation over these patents ongoing in many countries. Importantly, there are significant international differences in patent law, with patents invalidated in the USA that remain valid in Europe. Despite the many patents and ongoing litigation, there are multiple providers of testing internationally, and patents do not appear to be preventing patient access to testing for those who can pay out of pocket. Conclusion: The patent situation in NIPT remains in a state of flux, with uncertainty about how patent rights will be conferred in different jurisdictions, and how patents might affect clinical access. However, patents are unlikely to result in a monopoly for a single provider, with several providers and testing technologies, including both public and private sector entities, likely to remain engaged in delivery of NIPT. However, the effects on access in public healthcare systems are more complex and need to be monitored.Economic and Social Research Council (ESRC)Australian Research CouncilNational Institute for Health Research (NIHR