2,122 research outputs found
On the cohomology of stable map spaces
We describe an approach to calculating the cohomology rings of stable map
spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action
and a vector field which is equivariant with respect to this C^*-action. We
give an explicit description of the big Bialynicky-Birula cell of the
C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to
calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and
d=3. Of particular interest is the case as n approaches infinity.Comment: 63 page
Higher Spin Alternating Sign Matrices
We define a higher spin alternating sign matrix to be an integer-entry square
matrix in which, for a nonnegative integer r, all complete row and column sums
are r, and all partial row and column sums extending from each end of the row
or column are nonnegative. Such matrices correspond to configurations of spin
r/2 statistical mechanical vertex models with domain-wall boundary conditions.
The case r=1 gives standard alternating sign matrices, while the case in which
all matrix entries are nonnegative gives semimagic squares. We show that the
higher spin alternating sign matrices of size n are the integer points of the
r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices
are the standard alternating sign matrices of size n. It then follows that, for
fixed n, these matrices are enumerated by an Ehrhart polynomial in r.Comment: 41 pages; v2: minor change
Solutions of the boundary Yang-Baxter equation for ADE models
We present the general diagonal and, in some cases, non-diagonal solutions of
the boundary Yang-Baxter equation for a number of related
interaction-round-a-face models, including the standard and dilute A_L, D_L and
E_{6,7,8} models.Comment: 32 pages. Sections 7.2 and 9.2 revise
Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules
The minimal theories are labelled by a Lie algebra pair where
is of -- type. For these theories on a cylinder we conjecture a
complete set of conformal boundary conditions labelled by the nodes of the
tensor product graph . The cylinder partition functions are given
by fusion rules arising from the graph fusion algebra of . We
further conjecture that, for each conformal boundary condition, an integrable
boundary condition exists as a solution of the boundary Yang-Baxter equation
for the associated lattice model. The theory is illustrated using the
or 3-state Potts model.Comment: 4 pages, REVTe
Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
We use boundary weights and reflection equations to obtain families of
commuting double-row transfer matrices for interaction-round-a-face models with
fixed boundary conditions. In particular, we consider the fusion hierarchy of
the Andrews-Baxter-Forrester models, for which we find that the double-row
transfer matrices satisfy functional equations with an su(2) structure.Comment: 48 pages, LaTeX, requires about 79000 words of TeX memory. Submitted
to J. Stat. Phy
Exceptional boundary states at c=1
We consider the CFT of a free boson compactified on a circle, such that the
compactification radius is an irrational multiple of . Apart
from the standard Dirichlet and Neumann boundary states, Friedan suggested [1]
that an additional 1-parameter family of boundary states exists. These states
break U(1) symmetry of the theory, but still preserve conformal invariance. In
this paper we give an explicit construction of these states, show that they are
uniquely determined by the Cardy-Lewellen sewing constraints, and we study the
spectrum in the `open string channel', which is given here by a continous
integral with a nonnegative measure on the space of conformal weights.Comment: 18 pages; v2 corrected assumptions (now weaker), results unchange
Lattice Approach to Excited TBA Boundary Flows: Tricritical Ising Model
We show how a lattice approach can be used to derive Thermodynamic Bethe
Ansatz (TBA) equations describing all excitations for boundary flows. The
method is illustrated for a prototypical flow of the tricritical Ising model by
considering the continuum scaling limit of the A4 lattice model with integrable
boundaries. Fixing the bulk weights to their critical values, the integrable
boundary weights admit two boundary fields and which play the role
of the perturbing boundary fields and inducing the
renormalization group flow between boundary fixed points. The excitations are
completely classified in terms of (m,n) systems and quantum numbers but the
string content changes by certain mechanisms along the flow. For our
prototypical example, we identify these mechanisms and the induced map between
the relevant finitized Virasoro characters. We also solve the boundary TBA
equations numerically to determine the flows for the leading excitations.Comment: 11 pages, 3 figures, LaTeX; v2: some useful notations and one
reference added; to appear in PL
Gauges and Cosmological Backreaction
We present a formalism for spatial averaging in cosmology applicable to
general spacetimes and coordinates, and allowing the easy incorporation of a
wide variety of matter sources. We apply this formalism to a
Friedmann-LeMaitre-Robertson-Walker universe perturbed to second-order and
present the corrections to the background in an unfixed gauge. We then present
the corrections that arise in uniform curvature and conformal Newtonian gauges.Comment: 13 pages. Updated: reference added, typos corrected, exposition
clarified. Version 3: Replaced with version published by JCA
Pion transition form factor at the two-loop level vis-\`a-vis experimental data
We use light-cone QCD sum rules to calculate the pion-photon transition form
factor, taking into account radiative corrections up to the
next-to-next-to-leading order of perturbation theory. We compare the obtained
predictions with all available experimental data from the CELLO, CLEO, and the
BaBar Collaborations. We point out that the BaBar data are incompatible with
the convolution scheme of QCD, on which our predictions are based, and can
possibly be explained only with a violation of the factorization theorem. We
pull together recent theoretical results and comment on their significance.Comment: 10 pages, 4 figures, 3 tables. Presented by the first author at
Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25
July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th
Birthday. v2 wrong reference tag removed. v3 Fig. 4 and Ref. [27] correcte
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