163 research outputs found
How to make the gravitational action on non-compact space finite
The recently proposed technique to regularize the divergences of the
gravitational action on non-compact space by adding boundary counterterms is
studied. We propose prescription for constructing the boundary counterterms
which are polynomial in the boundary curvature. This prescription is efficient
for both asymptotically Anti-de Sitter and asymptotically flat spaces. Being
mostly interested in the asymptotically flat case we demonstrate how our
procedure works for known examples of non-compact spaces: Eguchi-Hanson metric,
Kerr-Newman metric, Taub-NUT and Taub-bolt metrics and others. Analyzing the
regularization procedure when boundary is not round sphere we observe that our
counterterm helps to cancel large divergence of the action in the zero and
first orders in small deviations of the geometry of the boundary from that of
the round sphere. In order to cancel the divergence in the second order in
deviations a new quadratic in boundary curvature counterterm is introduced. We
argue that cancelation of the divergence for finite deviations possibly
requires infinite series of (higher order in the boundary curvature) boundary
counterterms.Comment: 27 pages, latex, no figure
Conformal description of horizon's states
The existence of black hole horizon is considered as a boundary condition to
be imposed on the fluctuating metrics. The coordinate invariant form of the
condition for class of spherically symmetric metrics is formulated. The
diffeomorphisms preserving this condition act in (arbitrary small) vicinity of
the horizon and form the group of conformal transformations of two-dimensional
space ( sector of the total space-time). The corresponding algebra
recovered at the horizon is one copy of the Virasoro algebra. For general
relativity in dimensions we find an effective two-dimensional theory
governing the conformal dynamics at the horizon universally for any .
The corresponding Virasoro algebra has central charge proportional to the
Bekenstein-Hawking entropy. Identifying the zero-mode configuration we
calculate . The counting of states of this horizon's conformal field
theory by means of Cardy's formula is in complete agreement with the
Bekenstein-Hawking expression for the entropy of black hole in dimensions.Comment: 13 pages, latex, no figures; the final version to appear in Phys.
Lett.
Single State Supermultiplet in 1+1 Dimensions
We consider multiplet shortening for BPS solitons in N=1 two-dimensional
models. Examples of the single-state multiplets were established previously in
N=1 Landau-Ginzburg models. The shortening comes at a price of loosing the
fermion parity due to boundary effects. This implies the disappearance
of the boson-fermion classification resulting in abnormal statistics. We
discuss an appropriate index that counts such short multiplets.
A broad class of hybrid models which extend the Landau-Ginzburg models to
include a nonflat metric on the target space is considered. Our index turns out
to be related to the index of the Dirac operator on the soliton reduced moduli
space (the moduli space is reduced by factoring out the translational modulus).
The index vanishes in most cases implying the absence of shortening. In
particular, it vanishes when there are only two critical points on the compact
target space and the reduced moduli space has nonvanishing dimension.
We also generalize the anomaly in the central charge to take into account the
target space metric.Comment: LaTex, 42 pages, no figures. Contribution to the Michael Marinov
Memorial Volume, ``Multiple facets of quantization and supersymmetry'' (eds.
M.Olshanetsky and A. Vainshtein, to be publish by World Scientific). The
paper is drastically revised compared to the first version. We add sections
treating the following issues: (i) a new index counting one-state
supermultiplets; (ii) analysis of hybrid models of general type; (iii)
generalization of the anomaly in the central charge accounting for the target
space metri
Scattering Amplitudes and Toric Geometry
In this paper we provide a first attempt towards a toric geometric
interpretation of scattering amplitudes. In recent investigations it has indeed
been proposed that the all-loop integrand of planar N=4 SYM can be represented
in terms of well defined finite objects called on-shell diagrams drawn on
disks. Furthermore it has been shown that the physical information of on-shell
diagrams is encoded in the geometry of auxiliary algebraic varieties called the
totally non negative Grassmannians. In this new formulation the infinite
dimensional symmetry of the theory is manifest and many results, that are quite
tricky to obtain in terms of the standard Lagrangian formulation of the theory,
are instead manifest. In this paper, elaborating on previous results, we
provide another picture of the scattering amplitudes in terms of toric
geometry. In particular we describe in detail the toric varieties associated to
an on-shell diagram, how the singularities of the amplitudes are encoded in
some subspaces of the toric variety, and how this picture maps onto the
Grassmannian description. Eventually we discuss the action of cluster
transformations on the toric varieties. The hope is to provide an alternative
description of the scattering amplitudes that could contribute in the
developing of this very interesting field of research.Comment: 58 pages, 25 figures, typos corrected, a reference added, to be
published in JHE
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