A Note on Multi-trace Deformations and AdS/CFT

We derive the general formula, at a finite cutoff, for the change in the boundary condition of a scalar field in AdS under a Multiple-trace deformation of the dual CFT. Our analysis suggests that fluctuations around the classical solution in AdS should not be constrained by boundary conditions.Comment: 11 pages, 1 figure, harvmac. v2 typos corrected, version sent to JHEP. v3 references adde

Comparing Profitability for Game Developers: Xbox vs PlayStation vs PC

Ever since the beginning of the video game industry, consoles have come and gone such as the Atari 2600 and the Nintendo Gameboy. However, there are two main series of consoles that have continued to modern day: the Xbox’s and the PlayStation’s. These two series of consoles have been rivals for more than a decade, consistently releasing systems to compete with each other. Furthermore, similar to consoles coming and going, many companies have gone bankrupt due to significant gaming failures and losses. Because of this, there are only few major companies still producing games, along with some independent game developers struggling to succeed. However, more successful, independent companies and developers means a greater variety of games for consumers to play. Therefore, I determined which series of consoles appears to be the more profitable series for small companies and individual developers. Along with these series of consoles, the gaming industry for the PC has recently expanded rapidly and appears to be more friendly to low-budget games. Therefore, I analyzed PC game sales and concluded where should new video-game developers invest their time and money for producing games: for Xbox’s, PlayStation’s, or the PC

On the Phase Space of Block-Hiding Strategies in Bitcoin-like networks

We calculate the probability of success of block-hiding mining strategies in Bitcoin-like networks. These strategies involve building a secret branch of the block-tree and publishing it opportunistically, aiming to replace the top of the main branch and rip the reward associated with the secretly mined blocks. We identify two types of block-hiding strategies and chart the parameter space where those are more beneficial than the standard mining strategy described in Nakamoto's paper. Our analysis suggests a generalization of the notion of the relative hashing power as a measure for a miner's influence on the network. Block-hiding strategies are beneficial only when this measure of influence exceeds a certain threshold.Comment: 28 pages, 7 figure

The Mathematics of Chinese Checkers

Our goal for this project was to expand and improve upon the findings of George I. Bell and Nicholas Fonseca, who have both written papers on optimization in Chinese Checkers. While their work focuses mainly on cooperative games between one, two, and three players, we have considered games for six players. While doing this, we have redefined the playing board in a more intuitive manner, while developing and proving its associated distance formula. As well, we have found the shortest game for six players, and are working to generalize a formula for the number of moves required to finish a six player game as fast as possible. This could further incite research to generalize a lower bound for any number of players

Superstrings on AdS_3 and Symmetric Products

Some properties of N=2 superstrings on AdS_3 x N are studied. Their spectrum has the same pattern as 2-d CFTs in the moduli space of symmetric products M^p/S_p, where p is associated with the number of long fundamental strings required to construct the AdS_3 background, and M is the spacetime CFT corresponding to short string excitations of a single long string. Worldsheet operators associated with w long strings correspond to twisted sectors of M^p/S_p.Comment: 43 pages, harvma

Superstring Theory on AdS_3 x G/H and Boundary N=3 Superconformal Symmetry

Superstrings propagating on backgrounds of the form AdS_3 x G/H are studied using the coset CFT approach. We focus on seven dimensional cosets which have a semiclassical limit, and which give rise to N=3 superconformal symmetry in the dual CFT. This is realized for the two cases AdS_3 x SU(3)/U(1) and AdS_3 x SO(5)/SO(3), for which we present an explicit construction. We also provide sufficient conditions on a CFT background to enable a similar construction, and comment on the geometrical interpretation of our results.Comment: 22 pages, harvmac; added reference

Towards observable signatures of other bubble universes

We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's "sky," finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky. After a qualitative discussion of the physics involved in collisions between arbitrary bubbles, we evaluate the implications of our results, and outline possible detectable effects. In an optimistic sense, then, the present paper constitutes a first step in an assessment of the possible effects of other bubble universes on the cosmic microwave background and other observables.Comment: 17 PRD-style pages including 13 embedded figures. Minor corrections to figures 4 and 7 and added discussion in Sec. III.E.2 and

A note on Gauge Theories Coupled to Gravity

We analyze the bound on gauge couplings $e\geq m/m_p$, suggested by Arkani-Hamed et.al. We show this bound can be derived from simple semi-classical considerations and holds in spacetime dimensions greater than or equal to four. Non abelian gauge symmetries seem to satisfy the bound in a trivial manner. We comment on the case of discrete symmetries and close by performing some checks for the bound in higher dimensions in the context of string theory.Comment: 15 pages, 1 figure, Late

"Double-trace" Deformations, Boundary Conditions and Spacetime Singularities

Double-trace deformations of the AdS/CFT duality result in a new perturbation expansion for string theory, based on a non-local worldsheet. We discuss some aspects of the deformation in the low energy gravity approximation, where it appears as a change in the boundary condition of fields. We relate unique features of the boundary of AdS to the worldsheet becoming non-local, and conjecture that non-local worldsheet actions may be generic in other classes of backgrounds.Comment: 21 pages, 2 figures, harvmac. v2: minor changes, references added, version sent to JHEP. v3 minor correction