30,421 research outputs found
Holography, Singularities on Orbifolds and 4D N=2 SQCD
Type II string theory compactified on a Calabi-Yau manifold, with a
singularity modeled by a hypersurface in an orbifold, is considered. In the
limit of vanishing string coupling, one expects a non gravitational theory
concentrated at the singularity. It is proposed that this theory is
holographicly dual to a family of ``non-critical'' superstring vacua,
generalizing a previous proposal for hypersurfaces in flat space. It is argued
that a class of such singularities is relevant for the study of non-trivial IR
fixed points that appear in the moduli space of four-dimensional N=2 SQCD:
SU(N_c) gauge theory with matter in the fundamental representation. This
includes the origin in the moduli space of the SU(N_c) gauge theory with
N_f=2N_c fundamentals. The 4D IR fixed points are studied using the
anti-holographic description and the results agree with information available
from gauge theory.Comment: 33 pages (Latex
Deformation of LeBrun's ALE metrics with negative mass
In this article we investigate deformations of a scalar-flat K\"ahler metric
on the total space of complex line bundles over CP^1 constructed by C. LeBrun.
In particular, we find that the metric is included in a one-dimensional family
of such metrics on the four-manifold, where the complex structure in the
deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the
proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family
of a Hirzebruch surface stated in the last paragraph in the proof of Theorem
1.2, and fixed a relevant error in the proof. Also added a reference [24]
about Kuranishi family of Hirzebruch surface
Three-dimensional Black Holes and Liouville Field Theory
A quantization of (2+1)-dimensional gravity with negative cosmological
constant is presented and quantum aspects of the (2+1)-dimensional black holes
are studied thereby. The quantization consists of two procedures. One is
related with quantization of the asymptotic Virasoro symmetry. A notion of the
Virasoro deformation of 3-geometry is introduced. For a given black hole, the
deformation of the exterior of the outer horizon is identified with a product
of appropriate coadjoint orbits of the Virasoro groups .
Its quantization provides unitary irreducible representations of the Virasoro
algebra, in which state of the black hole becomes primary. To make the
quantization complete, holonomies, the global degrees of freedom, are taken
into account. By an identification of these topological operators with zero
modes of the Liouville field, the aforementioned unitary representations
reveal, as far as , as the Hilbert space of this two-dimensional
conformal field theory. This conformal field theory, living on the cylinder at
infinity of the black hole and having continuous spectrums, can recognize the
outer horizon only as a it one-dimensional object in and
realize it as insertions of the corresponding vertex operator. Therefore it can
not be a conformal field theory on the horizon. Two possible descriptions of
the horizon conformal field theory are proposed.Comment: 39 pages, LaTeX, 8 figures are added. Section 4.3 is revised and
enlarged to include the case of conical singularities. Several typos are
corrected. References are adde
The M theory lift of two O6 planes and four D6 branes
We solve for the effective actions on the Coulomb branches of a class of N=2
supersymmetric theories by finding the complex structure of an M5 brane in an
appropriate background hyperkahler geometry corresponding to the lift of two
O6^- orientifolds and four D6 branes to M theory. The resulting Seiberg-Witten
curves are of finite genus, unlike other solutions proposed in the literature.
The simplest theories in this class are the scale invariant Sp(k) theory with
one antisymmetric and four fundamental hypermultiplets and the SU(k) theory
with two antisymmetric and four fundamental hypermultiplets. Infinite classes
of related theories are obtained by adding extra SU(k) factors with
bifundamental matter and by turning on masses to flow down to various
asymptotically free theories. The N=4 supersymmetric SU(k) theory can be
embedded in these asymptotically free theories, allowing a derivation of a
subgroup of its S duality group as an exact equivalence of quantum field
theories.Comment: 45 pages, 3 figures. Reference adde
Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance
A covariant approach towards a theory of deformations is developed to examine
both the first and second variation of the Helfrich-Canham Hamiltonian --
quadratic in the extrinsic curvature -- which describes fluid vesicles at
mesoscopic scales. Deformations are decomposed into tangential and normal
components; At first order, tangential deformations may always be identified
with a reparametrization; at second order, they differ. The relationship
between tangential deformations and reparametrizations, as well as the coupling
between tangential and normal deformations, is examined at this order for both
the metric and the extrinsic curvature tensors. Expressions for the expansion
to second order in deformations of geometrical invariants constructed with
these tensors are obtained; in particular, the expansion of the Hamiltonian to
this order about an equilibrium is considered. Our approach applies as well to
any geometrical model for membranes.Comment: 20 page
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