Tailoring T-Duality Beyond the First Loop

In this article we review a recent calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. Using the effective action approach, and focusing on backgrounds with a single Abelian isometry, we give the $O(\alpha')$ modifications of the lowest-order duality transformations. The torsion plays an important role in the theory to $O(\alpha')$, because of the Chern-Simons couplings to the gauge fields that arise via dimensional reduction.Comment: 9 pages, Latex, no figures. Based on the talks given by N. Kaloper at the conferences Black Holes: Theory and Mathematical Aspects at Banff, AB, Canada and the $7^{th}~C^2GR^2A$ in Calgary, AB, Canada, May 31 - June 7, 199

Decaying Cosmological Constant of the Inflating Branes in the Randall-Sundrum -Oda Model

We examine the issue of the cosmological constant in the $many$ $inflating$ branes scenario, extending on two recent models by I.Oda and Randall-Sundrum. The exact solution in a closed form is found in the slow roll approximation of the radion. Defining an effective expansion rate, which depends on the location of each brane in the fifth dimension and demanding stability for this case we show that each positive tension brane has a localized, decaying cosmological constant (the opposite process applies to the negative energy branes [4]) . The reason is that the square of the effective expansion rate enters as a source term in the Einstein equations for the branes.Thus the brane has two scale factors depending on time and the fifth dimnesion respectively .The brane will roll along the fifth dimension in order to readjust its effective expansion rate in such a way that it compensates for its internal energy changes due to inflation and possible phase transitions.Comment: 9 pages, comments and ref.added, solution replaced with the exact one, submitted to PR

Brane Induced Gravity: Codimension-2

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tensions branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, but the crossover from 5D to 6D is not. This shows how the vacuum energy problem manifests in BIG: instead of tuning vacuum energy to adjust the 4D curvature, generically one must tune it to get the desired crossover scales and the hierarchy between the scales governing the 4D \to 5D \to 6D transitions. In the near-critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar-tensor theory.Comment: 16 pages latex, 2 .eps figs, based on the talks given at the "Sowers Workshop", Virginia Tech, May 14-18, 2007, "Cosmology and Strings" workshop at ICTP, Trieste, Italy, July 9-13, 2007, "Dark Energy In the Universe", Hakone, Japan, Sep 1-4, 2007 and "Zagreb Workshop 2007", Zagreb, Croatia, Nov 9-11, 2007; v2: added reference

Rotating Black Holes on Codimension-2 Branes

It has recently been demonstrated that certain types of non-tensional stress-energy can live on tensional codimension-2 branes, including gravitational shockwaves and small Schwarzschild black holes. In this note we generalize the earlier Schwarzschild results, and construct the exact gravitational fields of small rotating black holes on a codimension-2 brane. We focus on the phenomenologically interesting case of a three-brane embedded in a spacetime with two compactified extra dimensions. For a nonzero tension on the brane, we verify that these solutions also show the ``lightning rod'' effect found in the Schwarzschild solutions, the net effect of which is to rescale the fundamental Planck mass. This allows for larger black hole parameters, such as the event horizon, angular momentum, and lifetime than would be naively expected for a tensionless brane. It is also found that a black hole with angular momentum pointing purely along the brane directions has a smaller horizon angular velocity than the corresponding tensionless case, while a hole with bulk components of angular momentum has a larger angular velocity.Comment: 7 pages, uses revte

Infinitely Large New Dimensions

We construct intersecting brane configurations in Anti-de-Sitter space localizing gravity to the intersection region, with any number $n$ of extra dimensions. This allows us to construct two kinds of theories with infinitely large new dimensions, TeV scale quantum gravity and sub-millimeter deviations from Newton's Law. The effective 4D Planck scale $M_{Pl}$ is determined in terms of the fundamental Planck scale $M_*$ and the $AdS$ radius of curvature $L$ via the familiar relation $M_{Pl}^2 \sim M_{*}^{2+n} L^n$; $L$ acts as an effective radius of compactification for gravity on the intersection. Taking $M_* \sim$ TeV and $L \sim$ sub-mm reproduces the phenomenology of theories with large extra dimensions. Alternately, taking $M_* \sim L^{-1} \sim M_{Pl}$, and placing our 3-brane a distance $\sim 100 M_{Pl}^{-1}$ away from the intersection gives us a theory with an exponential determination of the Weak/Planck hierarchy.Comment: 4 pages, revtex, no figure

Backreaction in Axion Monodromy, 4-forms and the Swampland

Axion monodromy models can always be described in terms of an axion coupled to 3-form gauge fields with non-canonical kinetic terms. The presence of the saxions parametrising the kinetic metrics of the 3-form fields leads to backreaction effects in the inflationary dynamics. We review the case in which saxions backreact on the K\"ahler metric of the inflaton leading to a logarithmic scaling of the proper field distance at large field. This behaviour is universal in Type II string flux compactifications and consistent with a refinement of the Swampland Conjecture. The critical point at which this behaviour appears depends on the mass hierarchy between the inflaton and the saxions. However, in tractable compactifications, such a hierarchy cannot be realised without leaving the regime of validity of the effective theory, disfavouring transplanckian excursions in string theory.Comment: Proceedings prepared for the "Workshop on Geometry and Physics", November 2016, Ringberg Castl

Strongly Coupled Quintessence

We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from cosmological constant. These theories have discrete gauge symmetries which can protect them from quantum field theory and quantum gravity corrections, both perturbative and nonperturbative. The strong coupling effects, at scales \ga {\rm mm}^{-1}, flatten the potential and activate operators with higher powers of derivatives. The predicted equation of state is close to, but not exactly equal to $-1$, thus being within reach of the (near!) future programs to explore the nature of dark energy.Comment: 10 pages LaTe