34,611 research outputs found
SU(2) higher-order effective quark interactions from polarization
Higher order quark effective interactions are found for SU(2) flavor by
departing from a non local quark-quark interaction. By integrating out a
component of the quark field, the determinant is expanded in chirally symmetric
and symmetry breaking effective interactions up to the fifh order in the quark
bilinears. The resulting coupling constants are resolved in the leading order
of the longwavelength limit and exact numerical ratios between several of these
coupling constants are obtained in the large quark mass limit. In this level,
chiral invariant interactions only show up in even powers of the quark
bilinears, i.e. (), whereas
(explicit) chiral symmetry breaking terms emerge as being always proportional to some power of the Lagrangian quark
mass.Comment: 11 pages, revised version, submitted to publicatio
Low energy constituent quark and pion effective couplings in a weak external magnetic field
An effective model with pions and constituent quarks in the presence of a
weak external background electromagnetic field is derived by starting from a
dressed one gluon exchange quark-quark interaction.By applying the auxiliary
field and background field methods, the structureless pion limit is considered
to extract effective pion and constituent quark couplings in the presence of a
weak magnetic field. The leading terms of a large quark and gluon masses
expansion are obtained by resolving effective coupling constants which turn out
to depend on a weak magnetic field. Two pion field definitions are considered
for that. Several relations between the effective coupling constants and
parameters can be derived exactly or in the limit of very large quark mass at
zero and weak constant magnetic field. Among these ratios, the Gell Mann Oakes
Renner and the quark level Goldberger Treiman relations are obtained. In
addition to that, in the pion sector, the leading terms of Chiral Perturbation
Theory coupled to the electromagnetic field is recovered. Some numerical
estimates are provided for the effective coupling constants and parameters.Comment: 26 pages, revised and improved version with numerical estimates. To
be published in Eur.Phys. Journ. A (2018
Wilson Loop Invariants from Conformal Blocks
Knot and link polynomials are topological invariants calculated from the
expectation value of loop operators in topological field theories. In 3D
Chern-Simons theory, these invariants can be found from crossing and braiding
matrices of four-point conformal blocks of the boundary 2D CFT. We calculate
crossing and braiding matrices for conformal blocks with one component in
the fundamental representation and another in a rectangular representation of
, which can be used to obtain HOMFLY knot and link invariants for these
cases. We also discuss how our approach can be generalized to invariants in
higher-representations of algebra.Comment: 20 pages, 2 figure
Decomposing 8-regular graphs into paths of length 4
A -decomposition of a graph is a set of edge-disjoint copies of in
that cover the edge set of . Graham and H\"aggkvist (1989) conjectured
that any -regular graph admits a -decomposition if is a tree
with edges. Kouider and Lonc (1999) conjectured that, in the special
case where is the path with edges, admits a -decomposition
where every vertex of is the end-vertex of exactly two paths
of , and proved that this statement holds when has girth at
least . In this paper we verify Kouider and Lonc's Conjecture for
paths of length
- …