285 research outputs found
Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a
homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a
cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7
implies a Chern-Simons flow on K/H which runs between instantons on the coset.
For K-equivariant connections, the torsionful Yang-Mills equation reduces to a
particular quartic dynamics for a Newtonian particle on C. When the torsion
corresponds to one of the G_2-structures, this dynamics follows from a gradient
or hamiltonian flow equation, respectively. We present the analytic (kink-type)
solutions and plot numerical non-BPS solutions for general torsion values
interpolating between the instantonic ones.Comment: 1+8 pages, 14 figures; talk presented at SQS-11 during 18-23 July,
2011, at JINR, Dubna, Russia; v2: missing * in eq.(1) adde
The Solution of the d-Dimensional Twisted Group Lattices
The general d-dimensional twisted group lattice is solved. The irreducible
representations of the corresponding group are constructed by an explicit
procedure. It is proven that they are complete. All matrix representation
solutions to the quantum hyperplane equations are obtained.Comment: 21 pages in Latex, replaced version is journal versio
A note on fermionic flows of the N=(1|1) supersymmetric Toda lattice hierarchy
We extend the Sato equations of the N=(1|1) supersymmetric Toda lattice
hierarchy by two new infinite series of fermionic flows and demonstrate that
the algebra of the flows of the extended hierarchy is the Borel subalgebra of
the N=(2|2) loop superalgebra.Comment: 4 pages LaTe
Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
Interactions of noncommutative waves and solitons in 2+1 dimensions can be
analyzed exactly for a supersymmetric and integrable U(n) chiral model
extending the Ward model. Using the Moyal-deformed dressing method in an
antichiral superspace, we construct explicit time-dependent solutions of its
noncommutative field equations by iteratively solving linear equations. The
approach is illustrated by presenting scattering configurations for two
noncommutative U(2) plane waves and for two noncommutative U(2) solitons as
well as by producing a noncommutative U(1) two-soliton bound state.Comment: 1+13 pages; v2: reference added, version published in JHE
Phase transitions and gaps in quantum random energy models
By using a previously established exact characterization of the ground state
of random potential systems in the thermodynamic limit, we determine the ground
and first excited energy levels of quantum random energy models, discrete and
continuous. We rigorously establish the existence of a universal first order
quantum phase transition, obeyed by both the ground and the first excited
states. The presence of an exponentially vanishing minimal gap at the
transition is general but, quite interestingly, the gap averaged over the
realizations of the random potential is finite. This fact leaves still open the
chance for some effective quantum annealing algorithm, not necessarily based on
a quantum adiabatic scheme.Comment: 8 pages, 4 figure
N=4 Supersymmetry and the BPST Instanton
In this paper we construct the Lagrangian and Hamiltonian formulations of N=4
supersymmetric systems describing the motion of an isospin particle on a
conformally flat four-manifold with SO(4) isometry carrying the non-Abelian
field of a BPST instanton. The conformal factor can be specified to yield
various particular systems, such as superconformally invariant mechanics as
well as a particle on the four-sphere, the pseudosphere or on R x S^3. The
isospin degrees of freedom arise as bosonic components of an additional
fermionic N=4 supermultiplet, whose other components are rendered auxiliary by
a nonlocal redefinition. Our on-shell component action coincides with the one
recently proposed in arXiv:0912.3289.Comment: 1+8 pages; v2: two references added, published versio
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