32 research outputs found
Non-Perturbative Field Theory - From two dimensional conformal field theory to QCD in four dimensions
This note is based on the summary of our book entitled "Non-perturbative
field theoryfrom two dimensional conformal field theory to QCD in four
dimensions", published recently by Cambridge University Press. It includes 436
pages.
The book provides a detailed description of the tool box of non-perturbative
techniques, presents applications of them to simplified systems, mainly of
gauge dynamics in two dimensions, and examines the lessons one can learn from
those systems about four dimensional QCD and hadron physics.
In particular the book deals with conformal invariance, integrability,
bosonization, large N, solitons in two dimensions and monopoles and instantons
in four dimensions, confinement versus screening and finally the hadronic
spectrum and scattering.
We also attach the table of contents and the list of references of the book.
We would be grateful for any comments or suggestions related to the material
in the book. These may be incorporated in a possible future edition. They may
be sent via the e-mails below.Comment: 44 Pages; Summary note for Book published by Cambridge University
Press 201
Large N Chern-Simons with massive fundamental fermions - A model with no bound states
In a previous paper, we analyzed the theory of massive fermions in the
fundamental representation coupled to a U(N) Chern-Simons gauge theory in three
dimensions at level K. It was done in the large N, large K limits where
Lambda=N/K was kept fixed. Among other results, we showed there that there are
no high mass quark anti-quark bound states. Here we show that there are no
bound states at all.Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1306.6465. A reference and acknowledgement adde
On bound-states of the Gross Neveu model with massive fundamental fermions
In the search for QFT's that admit boundstates, we reinvestigate the two
dimensional Gross-Neveu model, but with massive fermions. By computing the
self-energy for the auxiliary boundstate field and the effective potential, we
show that there are no bound states around the lowest minimum, but there is a
meta-stable bound state around the other minimum, a local one. The latter
decays by tunneling. We determine the dependence of its lifetime on the fermion
mass and coupling constant.Comment: 10 pages, 2 figures Version to be published in JHE
Meson-Baryon Scattering in QCD_2 for any Coupling
Extending earlier work on strong-coupling meson-baryon scattering in QCD_2,
we derive the effective meson-baryon action for any value of the coupling
constant, in the large-N_c limit. Colour degrees of freedom play an important
role, and we show that meson-baryon scattering can be formulated as a
relativistic potential problem. We distinguish two cases that are non-trivial
for unequal quark masses, and present the resulting equations for meson-baryon
scattering amplitudes.Comment: 13 pages; acknowledgements adde
Quark solitons as constituents of hadrons
We exhibit static solutions of multi-flavour QCD in two dimensions that have
the quantum numbers of baryons and mesons, constructed out of quark and
anti-quark solitons. In isolation the latter solitons have infinite energy,
corresponding to the presence of a string carrying the non-singlet colour flux
off to spatial infinity. When solitons of this type are combined, a
static, finite-energy, colour singlet solution is formed, corresponding to a
baryon. Similarly, static meson solutions are formed out of a soliton and an
anti-soliton of different flavours. The stability of the mesons against
annihilation is ensured by flavour conservation. The static solutions exist
only when the fundamental fields of the bosonized Lagrangian belong to
rather than to . Discussion of
flavour symmetry breaking requires a careful treatment of the normal ordering
ambiguity. Our results can be viewed as a derivation of the constituent quark
model in QCD, allowing a detailed study of constituent mass generation and
of the heavy quark symmetry.Comment: 27 p. + 8 figures (not included). Figures are available via ftp, see
instructions in the pape
Scattering and Resonances in QCD_2
Extending previous works on the spectrum of QCD_2, we now investigate the 2D
analogue of meson-baryon scattering. We use semi-classical methods, perturbing
around classical soliton solutions. We start with the abelian case,
corresponding to one flavor,and find that in this case the effective potential
is reflectionless. We obtain an explicit expression for the forward phase
shift. In the non-abelian case of several flavors, the method yields a
potential which depends on the momentum of the incoming particle. In this case
there is both transmission and reflection. In both cases no resonances appear.
As a byproduct, we derive the general conditions for a 2D quantum field
theoretical action to yield a reflectionless effective potential when one
expands in small fluctuations about the classical solution.Comment: Figs. 2 and 3 and the accompanying text amended, following sign
correction in the first term in the potential V in eq. (58). Qualitative
conclusions unchange
Exotic Baryons in Two-Dimensional QCD
Two-dimensional QCD has often been used as a laboratory for studying the full
four-dimensional theory, providing, for example, an explicit realization of
baryons as solitons. We review aspects of conventional baryons in
two-dimensional QCD, including the classical and quantum contributions to their
masses. We then discuss the spectrum of exotic baryons in two-dimensional QCD,
commenting on the solitonic radius inferred from the excitation spectrum as
well as the two-dimensional version of the Goldberger-Treiman relation relating
meson couplings to current matrix elements. Two-dimensional QCD provides strong
overall support to the chiral-soliton picture for the structure of normal and
exotic baryons in four dimensions.Comment: 15 pages latex, no figure