188 research outputs found
Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
We reexamine the issue of the soliton mass in two-dimensional models with N
=1 supersymmetry. The superalgebra has a central extension, and at the
classical level the soliton solution preserves 1/2 of supersymmetry which is
equivalent to BPS saturation. We prove that the property of BPS saturation,
i.e. the equality of the soliton mass to the central charge, remains intact at
the quantum level in all orders of the weak coupling expansion. Our key finding
is an anomaly in the expression for the central charge. The classical central
charge, equal to the jump of the superpotential, is amended by an anomalous
term proportional to the second derivative of the superpotential. The anomaly
is established by various methods in explicit one-loop calculations. We argue
that this one-loop result is not affected by higher orders. We discuss in
detail how the impact of the boundary conditions can be untangled from the
soliton mass calculation. In particular, the soliton profile and the energy
distribution are found at one loop. A "supersymmetry" in the soliton mass
calculations in the non-supersymmetric models is observed.Comment: 50 pages, LaTex, 2 figures. The version exactly matching that
published in Phys.Rev. D. The most essential addition is a footnote,
clarifying multiplet shortenin
Novel Branches of (0,2) Theories
We show that recently proposed linear sigma models with torsion can be
obtained from unconventional branches of conventional gauge theories. This
observation puts models with log interactions on firm footing. If non-anomalous
multiplets are integrated out, the resulting low-energy theory involves log
interactions of neutral fields. For these cases, we find a sigma model geometry
which is both non-toric and includes brane sources. These are heterotic sigma
models with branes. Surprisingly, there are massive models with compact complex
non-Kahler target spaces, which include brane/anti-brane sources. The simplest
conformal models describe wrapped heterotic NS5-branes. We present examples of
both types.Comment: 36 pages, LaTeX, 2 figures; typo in Appendix fixed; references added
and additional minor change
The self-dual gauge fields and the domain wall fermion zero modes
A new type of gauge fixing of the Coulomb gauge domain wall fermion system
that reduces the fluctuation of the effective running coupling and the
effective mass of arbitrary momentum direction including the region outside the
cylinder cut region is proposed and tested in the
gauge configurations of RBC/UKQCD collaboration.
The running coupling at the lowest momentum point does not show infrared
suppression and compatible with the experimental data extracted from the JLab
collaboration. The source of the fluctuation of the effective mass near
momentum 0.6GeV region is expected to be due to the domain wall fermion
zero modes.Comment: 12 pages 2 figures, extended arguments and references adde
Exact vortex solutions in a CP^N Skyrme-Faddeev type model
We consider a four dimensional field theory with target space being CP^N
which constitutes a generalization of the usual Skyrme-Faddeev model defined on
CP^1. We show that it possesses an integrable sector presenting an infinite
number of local conservation laws, which are associated to the hidden
symmetries of the zero curvature representation of the theory in loop space. We
construct an infinite class of exact solutions for that integrable submodel
where the fields are meromorphic functions of the combinations (x^1+i x^2) and
(x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski
space-time. Among those solutions we have static vortices and also vortices
with waves traveling along them with the speed of light. The energy per unity
of length of the vortices show an interesting and intricate interaction among
the vortices and waves.Comment: 21 pages, plain latex, no figure
Nonperturbative SUSY Correlators at Finite Temperature
We calculate finite temperature effects on a correlation function in the two
dimensional supersymmetric nonlinear O(3) sigma model. The correlation function
violates chiral symmetry and at zero temperature it has been shown to be a
constant, which gives rise to a double-valued condensate. Within the bilinear
approximation we find an exact result in a one-instanton background at finite
temperature. In contrast to the result at zero temperature we find that the
correlation function decays exponentially at large distances.Comment: Latex, 27 pages, 1 Postscript figur
Gauge Symmetry Enhancement and Radiatively Induced Mass in the Large N Nonlinear Sigma Model
We consider a hybrid of nonlinear sigma models in which two complex
projective spaces are coupled with each other under a duality. We study the
large N effective action in 1+1 dimensions. We find that some of the
dynamically generated gauge bosons acquire radiatively induced masses which,
however, vanish along the self-dual points where the two couplings
characterizing each complex projective space coincide. These points correspond
to the target space of the Grassmann manifold along which the gauge symmetry is
enhanced, and the theory favors the non-Abelian ultraviolet fixed point.Comment: 11 pages, REVTEX, typos are corrected, version to appear in Phys.
Rev.
Topological Lattice Actions
We consider lattice field theories with topological actions, which are
invariant against small deformations of the fields. Some of these actions have
infinite barriers separating different topological sectors. Topological actions
do not have the correct classical continuum limit and they cannot be treated
using perturbation theory, but they still yield the correct quantum continuum
limit. To show this, we present analytic studies of the 1-d O(2) and O(3)
model, as well as Monte Carlo simulations of the 2-d O(3) model using
topological lattice actions. Some topological actions obey and others violate a
lattice Schwarz inequality between the action and the topological charge Q.
Irrespective of this, in the 2-d O(3) model the topological susceptibility
\chi_t = \l/V is logarithmically divergent in the continuum limit.
Still, at non-zero distance the correlator of the topological charge density
has a finite continuum limit which is consistent with analytic predictions. Our
study shows explicitly that some classically important features of an action
are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure
Yang-Mills Theory as a Deformation of Topological Field Theory, Dimensional Reduction and Quark Confinement
We propose a reformulation of Yang-Mills theory as a perturbative deformation
of a novel topological (quantum) field theory. We prove that this reformulation
of the four-dimensional QCD leads to quark confinement in the sense of area law
of the Wilson loop. First, Yang-Mills theory with a non-Abelian gauge group G
is reformulated as a deformation of a novel topological field theory. Next, a
special class of topological field theories is defined by both BRST and
anti-BRST exact action corresponding to the maximal Abelian gauge leaving the
maximal torus group H of G invariant. Then we find the topological field theory
() has a hidden supersymmetry for a choice of maximal Abelian gauge. As a
result, the D-dimensional topological field theory is equivalent to the
(D-2)-dimensional coset G/H non-linear sigma model in the sense of Parisi and
Sourlas dimensional reduction. After maximal Abelian gauge fixing, the
topological property of magnetic monopole and anti-monopole of four-dimensional
Yang-Mills theory is translated into that of instanton and anti-instanton in
two-dimensional equivalent model. It is shown that the linear static potential
in four-dimensions follows from the instanton--anti-instanton gas in the
equivalent two-dimensional non-linear sigma model obtained from the
four-dimensional topological field theory by dimensional reduction, while the
remaining Coulomb potential comes from the perturbative part in
four-dimensional Yang-Mills theory. The dimensional reduction opens a path for
applying various exact methods developed in two-dimensional quantum field
theory to study the non-perturbative problem in low-energy physics of
four-dimensional quantum field theories.Comment: 58 pages, Latex, no figures, version accepted for publication in
Phys. Rev. D (additions of Discussion, references and minor changes
On the sign problem in 2D lattice super Yang--Mills
In recent years a new class of supersymmetric lattice theories have been
proposed which retain one or more exact supersymmetries for non-zero lattice
spacing. Recently there has been some controversy in the literature concerning
whether these theories suffer from a sign problem. In this paper we address
this issue by conducting simulations of the N=(2, 2) and N=(8, 8)
supersymmetric Yang--Mills theories in two dimensions for the U(N) theories
with N=2,3,4, using the new twisted lattice formulations. Our results provide
evidence that these theories do not suffer from a sign problem in the continuum
limit. These results thus boost confidence that the new lattice formulations
can be used successfully to explore non-perturbative aspects of
four-dimensional N=4 supersymmetric Yang--Mills theory.Comment: 22 pages, 12 figure
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