216 research outputs found
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
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
Quantum Vortex Strings: A Review
The quantum worldsheet dynamics of vortex strings contains information about
the 4d non-Abelian gauge theory in which the string lives. Here I tell this
story. The string worldsheet theory is typically some variant of the CP^{N-1}
sigma-model, describing the orientation of the string in a U(N) gauge group.
Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories
have been known since the 1970s. The vortex string provides a quantitative link
between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum
of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning
parameters, the CP^{N-1} sigma-model can be coaxed to flow to an interacting
conformal fixed point which is related to the 4d Argyres-Douglas fixed point.
For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical
supersymmetry breaking and, more interestingly, supersymmetry restoration, in a
way which captures the physics of Seiberg's quantum deformed moduli space.Comment: Adams Prize Essay. 40 pages with 4 colourful picture
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
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.
Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques
Two-dimensional CP**(N-1) models are used to compare the behavior of
different cooling techniques on the lattice. Cooling is one of the most
frequently used tools to study on the lattice the topological properties of the
vacuum of a field theory. We show that different cooling methods behave in an
equivalent way. To see this we apply the cooling methods on classical
instantonic configurations and on configurations of the thermal equilibrium
ensemble. We also calculate the topological susceptibility by using the cooling
technique.Comment: 24 pages, 10 figures (from 16 eps files
On the dynamical generation of the Maxwell term and scale invariance
Gauge theories with no Maxwell term are investigated in various setups. The
dynamical generation of the Maxwell term is correlated to the scale invariance
properties of the system. This is discussed mainly in the cases where the gauge
coupling carries dimensions. The term is generated when the theory contains a
scale explicitly, when it is asymptotically free and in particular also when
the scale invariance is spontaneously broken. The terms are not generated when
the scale invariance is maintained. Examples studied include the large
limit of the model in dimensions, a 3D gauged
vector model and its supersymmetric extension. In the latter case the
generation of the Maxwell term at a fixed point is explored. The phase
structure of the case is investigated in the presence of a Chern-Simons
term as well. In the supersymmetric model the emergence of the Maxwell
term is accompanied by the dynamical generation of the Chern-Simons term and
its multiplet and dynamical breaking of the parity symmetry. In some of the
phases long range forces emerge which may result in logarithmic confinement.
These include a dilaton exchange which plays a role also in the case when the
theory has no gauge symmetry. Gauged Lagrangian realizations of the 2D coset
models do not lead to emergent Maxwell terms. We discuss a case where the gauge
symmetry is anomalous.Comment: 38 pages, 4 figures; v2 slightly improved, typos fixed, references
added, published versio
Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have
sign problem in the continuum limit, that is, under the phase-quenched
simulation phase of the determinant localizes to 1 and hence the phase-quench
approximation becomes exact. Among several formulations, we study models by
Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem
is absent in both models and that they converge to the identical continuum
limit without fine tuning. We provide a simple explanation why previous works
by other authors, which claim an existence of the sign problem, do not capture
the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures
on U(1) mass independence and references added, to appear in JHE
The coupling of fermions to the three-dimensional noncommutative model: minimal and supersymmetric extensions
We consider the coupling of fermions to the three-dimensional noncommutative
model. In the case of minimal coupling, although the infrared
behavior of the gauge sector is improved, there are dangerous (quadratic)
infrared divergences in the corrections to the two point vertex function of the
scalar field. However, using superfield techniques we prove that the
supersymmetric version of this model with ``antisymmetrized'' coupling of the
Lagrange multiplier field is renormalizable up to the first order in
. The auxiliary spinor gauge field acquires a nontrivial
(nonlocal) dynamics with a generation of Maxwell and Chern-Simons
noncommutative terms in the effective action. Up to the 1/N order all
divergences are only logarithimic so that the model is free from nonintegrable
infrared singularities.Comment: Minor corrections in the text and modifications in the list of
reference
Interlayer Exchange Interactions, SU(4) Soft Waves and Skyrmions in Bilayer Quantum Hall Ferromagnets
The Coulomb exchange interaction is the driving force for quantum coherence
in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for
the exchange interaction in bilayer quantum Hall ferromagnets, which is
characterized by the SU(4) isospin structure. By taking a continuous limit, the
Hamiltonian gives rise to the SU(4) nonlinear sigma model in the
von-Neumann-lattice formulation. The ground-state energy is evaluated at
filling factors . It is shown at that there are 3
independent soft waves, where only one soft wave is responsible for the
coherent tunneling of electrons between the two layers. It is also shown at
that there are 3 independent skyrmion states apart from the
translational degree of freedom. They are CP skyrmions enjoying the
spin-charge entanglement confined within the \LLL.Comment: 12 pages, 2 figure
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