3,034 research outputs found
Schwarzschild Spacetime without Coordinates
We discuss how to construct the full Schwarzschild (Kruskal-Szekeres)
spacetime in one swoop by using the bundle of orthonormal Lorentz frames and
the Einstein equation without the use of coordinates. We never have to write
down the Kruskal-Szekeres or an equivalent form of the metric.Comment: 36 pages, 4 figures; some typos corrected, a few paragraphs added for
clarificatio
Target Space Duality II: Applications
We apply the framework developed in Target Space Duality I: General Theory.
We show that both nonabelian duality and Poisson-Lie duality are examples of
the general theory. We propose how the formalism leads to a systematic study of
duality by studying few scenarios that lead to open questions in the theory of
Lie algebras. We present evidence that there are probably new examples of
irreducible target space duality.Comment: LaTeX, 28 pages. Companion to Target Space Duality I: General Theory.
Added a couple of references and corrected a couple of typos. An FAQ that
discusses some subtle points is at
http://www.physics.miami.edu/~alvarez/papers/duality
Black Holes Without Coordinates
These lectures describe how to study the geometry of some black holes without
the use of coordinates.Comment: 10 pages, 2 figures. Lectures presented at the Cargese Summer School,
"Theory and Particle Physics: the LHC perspective and beyond" (June 16 to
June 28, 2008). This paper is a sequel to gr-qc/070111
Some Exact Solutions for Maximally Symmetric Topological Defects in Anti de Sitter Space
We obtain exact analytical solutions for a class of SO() Higgs field
theories in a non-dynamic background -dimensional anti de Sitter space.
These finite transverse energy solutions are maximally symmetric
-dimensional topological defects where . The radius of curvature
of anti de Sitter space provides an extra length scale that allows us to study
the equations of motion in a limit where the masses of the Higgs field and the
massive vector bosons are both vanishing. We call this the double BPS limit. In
anti de Sitter space, the equations of motion depend on both and . The
exact analytical solutions are expressed in terms of standard special
functions. The known exact analytical solutions are for kink-like defects
(), vortex-like defects (), and the
'tHooft-Polyakov monopole (). A bonus is that the double BPS limit
automatically gives a maximally symmetric classical glueball type solution. In
certain cases where we did not find an analytic solution, we present numerical
solutions to the equations of motion. The asymptotically exponentially
increasing volume with distance of anti de Sitter space imposes different
constraints than those found in the study of defects in Minkowski space.Comment: 45 pages, 19 figures. In version 2: added two paragraphs about how
our double BPS limit automatically gives a solution to the Yang-Mills
equation, and related it to Yang-Mills solutions in AdS_4 that appeared on
the same day in eprint 1708.0636
Perturbations to Generalized Kink-like Topological Defects in
We explore perturbations to a kink-like (codimension 1) topological defect
whose world brane is embedded into . Previously, we found
solutions in the limit the mass of the scalar field vanishes. In this article
we extend a calculation previously done in to higher-dimensional
embedding spaces and find that all perturbations to the mass of the field are
stable to first order as expected in a theory with topological defects. We find
that the equation of motion to the correction strongly resembles a problem
well-known in quantum mechanics.Comment: 23 pages, 6 figure
Target Space Pseudoduality Between Dual Symmetric Spaces
A set of on shell duality equations is proposed that leads to a map between
strings moving on symmetric spaces with opposite curvatures. The transformation
maps "waves" on a riemannian symmetric space to "waves" on its dual riemannian
symmetric space. This transformation preserves the energy momentum tensor
though it is not a canonical transformation. The preservation of the energy
momentum tensor has a natural geometrical interpretation. The transformation
maps "particle-like solutions" into static "soliton-like solutions". The
results presented here generalize earlier results of E. Ivanov.Comment: LaTeX, 20 pages. Added an important reference and a section
discussing some earlier work by E.A. Ivano
Compensating strong coupling with large charge
We study some (conformal) field theories with global symmetries in the sector
where the value of the global charge is large. We find (as expected) that
the low energy excitations of this sector are described by the general form of
Goldstone's theorem in the non-relativistic regime. We also derive the
unexpected result, first presented in [Hellerman et al. 2015], that the
effective field theory describing such sector of fixed contains effective
couplings , where is the
original coupling. Hence, large charge leads to weak coupling. In the last
section of the paper we present an outline of how to compute anomalous
dimensions of the model in this limit.Comment: 20 pages, 2 figures. Version accepted by JHE
Beyond the String Genus
In an earlier work we used a path integral analysis to propose a higher genus
generalization of the elliptic genus. We found a cobordism invariant
parametrized by Teichmuller space. Here we simplify the formula and study the
behavior of our invariant under the action of the mapping class group of the
Riemann surface. We find that our invariant is a modular function with
multiplier just as in genus one.Comment: 40 pages, 1 figur
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