429 research outputs found

### Isospin susceptibility in the O($n$) sigma-model in the delta-regime

We compute the isospin susceptibility in an effective O($n$) scalar field
theory (in $d=4$ dimensions), to third order in chiral perturbation theory
($\chi$PT) in the delta--regime using the quantum mechanical rotator picture.
This is done in the presence of an additional coupling, involving a parameter
$\eta$, describing the effect of a small explicit symmetry breaking term (quark
mass). For the chiral limit $\eta=0$ we demonstrate consistency with our
previous $\chi$PT computations of the finite-volume mass gap and isospin
susceptibility. For the massive case by computing the leading mass effect in
the susceptibility using $\chi$PT with dimensional regularization, we determine
the $\chi$PT expansion for $\eta$ to third order. The behavior of the shape
coefficients for long tube geometry obtained here might be of broader interest.
The susceptibility calculated from the rotator approximation differs from the
$\chi$PT result in terms vanishing like $1/\ell$ for $\ell=L_t/L_s\to\infty$.
We show that this deviation can be described by a correction to the rotator
spectrum proportional to the square of the quadratic Casimir invariant.Comment: 34 page

### Locality and exponential error reduction in numerical lattice gauge theory

In non-abelian gauge theories without matter fields, expectation values of
large Wilson loops and loop correlation functions are difficult to compute
through numerical simulation, because the signal-to-noise ratio is very rapidly
decaying for increasing loop sizes. Using a multilevel scheme that exploits the
locality of the theory, we show that the statistical errors in such
calculations can be exponentially reduced. We explicitly demonstrate this in
the SU(3) theory, for the case of the Polyakov loop correlation function, where
the efficiency of the simulation is improved by many orders of magnitude when
the area bounded by the loops exceeds 1 fm^2.Comment: Plain TeX source, 18 pages, figures include

### Bethe--Salpeter wave functions in integrable models

We investigate some properties of Bethe--Salpeter wave functions in
integrable models. In particular we illustrate the application of the operator
product expansion in determining the short distance behavior. The energy
dependence of the potentials obtained from such wave functions is studied, and
further we discuss the (limited) phenomenological significance of zero--energy
potentials.Comment: LaTeX, 38 pages, 9 figure

### O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has
been introduced in refs. [1,2]. We here apply Symanzik's improvement programme
to this theory and list the counterterms which arise at first order in the
lattice spacing a. Based on the generalised transfer matrix, we define the
tmQCD Schrodinger functional and use it to derive renormalized on-shell
correlation functions. By studying their continuum approach in perturbation
theory we then determine the new O(a) counterterms of the action and of a few
quark bilinear operators to one-loop order.Comment: 31 pages latex, no figure

### Walking in the 3-dimensional large $N$ scalar model

The solvability of the three-dimensional O($N$) scalar field theory in the
large $N$ limit makes it an ideal toy model exhibiting "walking" behavior,
expected in some SU($N$) gauge theories with a large number of fermion flavors.
We study the model using lattice regularization and show that when the ratio of
the particle mass to an effective 4-point coupling (with dimension mass) is
small, the beta function associated to the running 4-point coupling is
"walking". We also study lattice artifacts and finite size effects, and find
that while the former can be sizable at realistic correlation length, the
latter are under control already at lattice sizes a few ($\sim$3) correlation
lengths. We show the robustness of the walking phenomenon by showing that it
can also be observed by studying physical observables such as the scattering
phase shifts and the mass gap in finite volume.Comment: 27 pages, 5 figures, typos in the published version are correcte

### Flow equation for the scalar model in the large $N$ expansion and its applications

We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions
at the next-to-leading order (NLO) in the $1/N$ expansion. Using the
Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields.
As the first application of the NLO calculations, we study the running coupling
defined from the connected 4-pt function of flowed fields in the $d+1$
dimensional theory. We show in particular that this running coupling has not
only the UV fixed point but also an IR fixed point (Wilson-Fisher fixed point)
in the 3 dimensional massless scalar theory. As the second application, we
calculate the NLO correction to the induced metric in $d+1$ dimensions with
$d=3$ in the massless limit. While the induced metric describes a 4-dimensional
Euclidean Anti-de-Sitter (AdS) space at the leading order as shown in the
previous paper, the NLO corrections make the space asymptotically AdS only in
UV and IR limits. Remarkably, while the AdS radius does not receive a NLO
correction in the UV limit, the AdS radius decreases at the NLO in the IR
limit, which corresponds to the Wilson-Fisher fixed point in the original
scalar model in 3 dimensions.Comment: 39 page

### Chiral symmetry and O(a) improvement in lattice QCD

The dominant cutoff effects in lattice QCD with Wilson quarks are
proportional to the lattice spacing a. In particular, the isovector axial
current satisfies the PCAC relation only up to such effects. Following a
suggestion of Symanzik, they can be cancelled by adding local O(a) correction
terms to the action and the axial current. We here address a number of
theoretical issues in connection with the O(a) improvement of lattice QCD and
then show that chiral symmetry can be used to fix the coefficients multiplying
the correction terms.Comment: 43 pages, uuencoded gzipped postscript fil

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