Spacetime Fluctuations in AdS/CFT

We compute fluctuations in the modular energy of the vacuum associated with a Rindler-wedge in AdS spacetime in the context of AdS/CFT. We discuss the possible effect of these energy fluctuations on the spacetime geometry, and on the traversal time of a light beam propagating from the boundary to the bulk and back.Comment: 25 pages, 1 figur

Observational Signatures of Quantum Gravity in Interferometers

We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal that could be observed in a gravitational wave interferometer. We connect the positional uncertainty principle arising from our calculations to the 't Hooft gravitational S-matrix.Comment: 6 pages, 1 figur

On the partition sum of the NS five-brane

We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a double-scaled decoupling limit. We calculate the euclidean partition function in the presence of a flat RR 3-form field. The classical contribution is given by a sum over fluxes of the self-dual tensor field which reduces to a theta-function. The quantum contributions are computed using a T-dual IIB background where the five-branes are replaced by an ALE singularity. Using the supergravity effective action we find that the loop corrections to the free energy are given by B-model topological string amplitudes. This seems to provide a direct link between the double-scaled little strings on the five-brane worldvolume and topological strings. Both the classical and quantum contributions to the partition function satisfy (conjugate) holomorphic anomaly equations, which explains an observation of Witten relating topological string theory to the quantization of three-form fields.Comment: 35 page

New perspective on space and time from Lorentz violation

I present a brief review on space and time in different periods of physics, and then talk on the nature of space and time from physical arguments. I discuss the ways to test such a new perspective on space and time through searching for Lorentz violation in some physical processes. I also make an introduce to a newly proposed theory of Lorentz violation from basic considerations.Comment: 10 latex pages. Plenary talk at First LeCosPA Symposium: Towards Ultimate Understanding of the Universe (LeCosPA2012), National Taiwan University, Taipei, Taiwan, February 6-9, 201

On RG-flow and the Cosmological Constant

The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d gravity. Using an analogy with the relativistic point particle, I construct a low energy effective action that includes the Einstein action and obeys a Callan-Symanzik-type RG-flow equation. It follows from the flow equation that under quite general conditions the Einstein equations admit a flat space-time solution, but other solutions with non-zero cosmological constant are also allowed. I discuss the geometric interpretation of this result in the context of warped compactifications.Comment: 11 pages, 1 figure, contribution to the proceedings of Strings '99, misprint correcte

Entropic gravity, minimum temperature, and modified Newtonian dynamics

Verlinde's heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de-Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.Comment: 12 pages, v6: published versio

Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence

We discuss the relation between the Matrix theory definitions of a class of decoupled theories and their AdS/CFT description in terms of the corresponding near-horizon geometry. The near horizon geometry, naively part of the Coulomb branch, is embedded in the Higgs branch via a natural change of variables. The principles of the map apply to all DLCQ descriptions in terms of hyper-Kähler quotients, such as the ADHM quantum mechanics for the D1-D5 system. We then focus the (2,0) field theory, and obtain an explicit mapping from all states in the $N_0=1$ momentum sector of $N_4$ M5-branes to states in (a DLCQ version of) $AdS_7\times S^4$. We show that, even for a single D0-brane, the space-time coordinates become non-commuting variables, suggesting an inherent non-commutativity of space-time in the presence of field strengths even for theories with gravity

Modular Fluctuations from Shockwave Geometries

Modular fluctuations have previously been shown to obey an area law $\langle \Delta K^2 \rangle = \langle K \rangle = {A}/{4 G_N}$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d-$dimensionsal Minkowski space, can be reproduced from shockwaves arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in light-ray operators, of the same form postulated by 't Hooft in the context of black hole horizons.Comment: 22 pages, 4 figure