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($l$) Higgs field theories in a non-dynamic background $n$-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric $p$-dimensional topological defects where $n=(p+1)+l$. 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 $p$ and $l$. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ($p=0,1,2,\dotsc;\, l=1$), vortex-like defects ($p=1,2,3;\, l=2$), and the 'tHooft-Polyakov monopole ($p=0;\, l=3$). 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

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 $Q$ 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 $Q$ contains effective couplings $\lambda_{\text{eff}}\sim \lambda^b /Q^{a}$, where $\lambda$ 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 $O(n)$ 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