189 research outputs found
Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
The lattice superalgebra of the link approach is shown to satisfy a Hopf
algebraic supersymmetry where the difference operator is introduced as a
momentum operator. The breakdown of the Leibniz rule for the lattice difference
operator is accommodated as a coproduct operation of (quasi)triangular Hopf
algebra and the associated field theory is consistently defined as a braided
quantum field theory. Algebraic formulation of path integral is perturbatively
defined and Ward-Takahashi identity can be derived on the lattice. The claimed
inconsistency of the link approach leading to the ordering ambiguity for a
product of fields is solved by introducing an almost trivial braiding structure
corresponding to the triangular structure of the Hopf algebraic superalgebra.
This could be seen as a generalization of spin and statistics relation on the
lattice. From the consistency of this braiding structure of fields a grading
nature for the momentum operator is required.Comment: 45 page
Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional N=2
model with interactions has exact Lie algebraic supersymmetry on the lattice
for all super charges. In coordinate representation the finite difference
operator is made to satisfy Leibnitz rule by introducing a non local product,
the ``star'' product, and the exact lattice supersymmetry is realized. The
standard momentum conservation is replaced on the lattice by the conservation
of the sine of the momentum, which plays a crucial role in the formulation.
Half lattice spacing structure is essential for the one dimensional model and
the lattice supersymmetry transformation can be identified as a half lattice
spacing translation combined with alternating sign structure. Invariance under
finite translations and locality in the continuum limit are explicitly
investigated and shown to be recovered. Supersymmetric Ward identities are
shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry
algebra of this model suggests a close connection with Hopf algebraic exactness
of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure
Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills
model. We start from the CKKU model for this system, which is valid only for
U(N) gauge group. We give a reduction of U(1) part keeping a part of
supersymmetry. In order to suppress artifact vacua, we use an admissibility
condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to
appear in JHE
Gauge symmetry enhancement in Hamiltonian formalism
We study the Hamiltonian structure of the gauge symmetry enhancement in the
enlarged CP(N) model coupled with U(2) Chern-Simons term, which contains a free
parameter governing explicit symmetry breaking and symmetry enhancement. After
giving a general discussion of the geometry of constrained phase space suitable
for the symmetry enhancement, we explicitly perform the Dirac analysis of our
model and compute the Dirac brackets for the symmetry enhanced and broken
cases. We also discuss some related issues.Comment: 8 pages, typos correcte
Theta dependence of CP^9 model
We apply to the model two recently proposed numerical techniques for
simulation of systems with a theta term. The algorithms, successfully tested in
the strong coupling limit, are applied to the weak coupling region. The results
agree and errors have been evaluated and are at % level. The results scale well
with the renormalization group equation and show that, for in presence
of a theta term, CP symmetry is spontaneously broken at in the
continuum limit.Comment: 4 pages, 4 figure
Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
We study the information metric on instanton moduli spaces in two-dimensional
nonlinear sigma models. In the CP^1 model, the information metric on the moduli
space of one instanton with the topological charge Q=k which is any positive
integer is a three-dimensional hyperbolic metric, which corresponds to
Euclidean anti--de Sitter space-time metric in three dimensions, and the
overall scale factor of the information metric is (4k^2)/3; this means that the
sectional curvature is -3/(4k^2). We also calculate the information metric in
the CP^2 model.Comment: 9 pages, LaTeX; added references for section 1; typos adde
On the BPS Spectrum at the Root of the Higgs Branch
We study the BPS spectrum and walls of marginal stability of the
supersymmetric theory in four dimensions with gauge group SU(n)
and fundamental flavours at the root of the Higgs branch. The
strong-coupling spectrum of this theory was conjectured in hep-th/9902134 to
coincide with that of the two-dimensional supersymmetric
sigma model. Using the Kontsevich--Soibelman
wall-crossing formula, we start with the conjectured strong-coupling spectrum
and extrapolate it to all other regions of the moduli space. In the
weak-coupling regime, our results precisely agree with the semiclassical
analysis of hep-th/9902134: in addition to the usual dyons, quarks, and
bosons, if the complex masses obey a particular inequality, the resulting
weak-coupling spectrum includes a tower of bound states consisting of a dyon
and one or more quarks. In the special case of -symmetric
masses, there are bound states with one quark for odd and no bound states
for even .Comment: 11 pages, 4 figure
Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories
Using instanton calculus we check, in the weak coupling region, the
nonperturbative relation =i\pi\left(\cf-{a\over 2}
{\partial\cf\over\partial a}\right) obtained for a N=2 globally
supersymmetric gauge theory. Our computations are performed for instantons of
winding number k, up to k=2 and turn out to agree with previous nonperturbative
results.Comment: 18 pages, latex file, no figure
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
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
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