478,896 research outputs found
The O(1)-Kepler Problems
Let be an integer. To each irreducible representation of
, an -Kepler problem in dimension is
constructed and analyzed. This system is super integrable and when it is
equivalent to a generalized MICZ-Kepler problem in dimension two. The dynamical
symmetry group of this system is
with the Hilbert space of bound states being the unitary
highest weight representation of
with highest weight
which occurs at the right-most nontrivial reduction point in the
Enright-Howe-Wallach classification diagram for the unitary highest weight
modules. (Here or 1 depending on whether is trivial or
not.) Furthermore, it is shown that the correspondence is the theta-correspondence for dual pair .Comment: Final published for
The Lipatov Kernels
Leading plus next-to leading log results for the Regge limit of massless
Yang-Mills theories are reproduced by reggeon diagrams in which the Regge slope
and reggeon amplitudes satisfy Ward identity constraints at
zero transverse momentum. Using reggeon unitarity together with multiple
discontinuity theory a complete set of such diagrams can be constructed. The
resulting two-two, one-three and two-four kernels which generalise the Lipatov
equation at are determined uniquely.Comment: 12 pages, ANL-HEP-PR-94-2
Bootstrapping the O(N) Vector Models
We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We
obtain rigorous upper bounds on the scaling dimensions of the first O(N)
singlet and symmetric tensor operators appearing in the
OPE, where is a fundamental of O(N). Comparing these bounds to
previous determinations of critical exponents in the O(N) vector models, we
find strong numerical evidence that the O(N) vector models saturate the
bootstrap constraints at all values of N. We also compute general lower bounds
on the central charge, giving numerical predictions for the values realized in
the O(N) vector models. We compare our predictions to previous computations in
the 1/N expansion, finding precise agreement at large values of N.Comment: 26 pages, 5 figures; V2: typos correcte
Robustness of the O() universality class
We calculate the critical exponents for Lorentz-violating O()
scalar field theories by using two independent methods. In
the first situation we renormalize a massless theory by utilizing normalization
conditions. An identical task is fulfilled in the second case in a massive
version of the same theory, previously renormalized in the BPHZ method in four
dimensions. We show that although the renormalization constants, the
and anomalous dimensions acquire Lorentz-violating quantum corrections, the
outcome for the critical exponents in both methods are identical and
furthermore they are equal to their Lorentz-invariant counterparts. Finally we
generalize the last two results for all loop levels and we provide symmetry
arguments for justifying the latter
Shear Viscosity in the O(N) Model
We compute the shear viscosity in the O(N) model at first nontrivial order in
the large N expansion. The calculation is organized using the 1/N expansion of
the 2PI effective action (2PI-1/N expansion) to next-to-leading order, which
leads to an integral equation summing ladder and bubble diagrams. We also
consider the weakly coupled theory for arbitrary N, using the three-loop
expansion of the 2PI effective action. In the limit of weak coupling and
vanishing mass, we find an approximate analytical solution of the integral
equation. For general coupling and mass, the integral equation is solved
numerically using a variational approach. The shear viscosity turns out to be
close to the result obtained in the weak-coupling analysis.Comment: 37 pages, few typos corrected; to appear in JHE
Fractal Behaviour in the O(3) Model
We study domain formation in the two-dimensional O(3) model near criticality.
The fractal dimension of these domains is determined with good statistical
accuracy.Comment: 6 pages + 3 figures (concatenated PS files, uuencoded gz-compressed
The O(n) model on the annulus
We use Coulomb gas methods to propose an explicit form for the scaling limit
of the partition function of the critical O(n) model on an annulus, with free
boundary conditions, as a function of its modulus. This correctly takes into
account the magnetic charge asymmetry and the decoupling of the null states. It
agrees with an earlier conjecture based on Bethe ansatz and quantum group
symmetry, and with all known results for special values of n. It gives new
formulae for percolation (the probability that a cluster connects the two
opposite boundaries) and for self-avoiding loops (the partition function for a
single loop wrapping non-trivially around the annulus.) The limit n->0 also
gives explicit examples of partition functions in logarithmic conformal field
theory.Comment: 20 pp. v.2: important references added to earlier work, minor typos
correcte
Heating the O(N) nonlinear sigma model
The thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions is
studied. We calculate the finite temperature effective potential in leading
order in the 1/N expansion and show that at this order the effective potential
can be made finite by temperature independent renormalization. We will show
that this is not longer possible at next-to-leading order in 1/N. In that case
one can only renormalize the minimum of the effective potential in a
temperature independent way, which gives us finite physical quantities like the
pressure.Comment: 8 pages, 2 figures, Seminar talk given at the 43st Cracow School of
Theoretical Physics, 30 May - 8 June 2003, Zakopane, Polan
The O(dd) Story of Massive Supergravity
The low energy effective action describing the standard Kaluza-Klein
reduction of heterotic string theory on a d-torus possesses a manifest
O(d,d+16) symmetry. We consider generalized Scherk-Schwarz reductions of the
heterotic string to construct massive gauged supergravities. We show that the
resulting action can still be written in a manifestly O(d,d+16) invariant form,
however, the U-duality transformations also act on the mass parameters. The
latter play the dual role of defining the scalar potential and the nonabelian
structure constants. We conjecture that just as for the standard reduction, a
subgroup of this symmetry corresponds to an exact duality symmetry of the
heterotic string theory.Comment: 55 pages, latex, no figures, added a few references, published in
JHEP05(1999)01
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