In theoretical physics, S-duality (also a strong-weak duality) is an equivalence of two quantum field theories, string theories, or M-theory. An S-duality transformation maps the states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1 / g in the dual theory. This has permitted the use of perturbation theory, normally useful only for “weakly coupled” theories with g less than 1, to also describe the “strongly coupled” (g greater than 1) regimes of string theory, by mapping them onto dual, weakly coupled regimes.

— Wikipedia on S-duality

2010.07.01 Thursday ACHK

It wasn’t clear how relevant this is to the physics of our particular universe, but at the end of the talk Dijkgraaf urged us not to worry about that too much: after all, the math is so pretty in its own right. Insofar as I’m a physicist this makes me unhappy – but in my other persona, as a mathematician, it makes sense.

— John Baez

2010.06.29 Tuesday ACHK

String theory and cosmic strings

There is no direct connection between string theory and the theory of cosmic strings (the names were chosen independently by analogy with ordinary string).

However, work in string theory revived interest in cosmic strings in the early 2000s. In 2002 Henry Tye and collaborators observed the production of cosmic strings during the last stages of brane inflation. It was also pointed out by string theorist Joseph Polchinski that the expanding Universe could have stretched a “fundamental” string (the sort which superstring theory considers) until it was of intergalactic size. Such a stretched string would exhibit many of the properties of the old “cosmic” string variety, making the older calculations useful again. Furthermore, modern superstring theories offer other objects which could feasibly resemble cosmic strings, such as highly elongated one-dimensional D-branes (known as “D-strings”). As theorist Tom Kibble remarks, “string theory cosmologists have discovered cosmic strings lurking everywhere in the undergrowth”. Older proposals for detecting cosmic strings could now be used to investigate superstring theory.

— Wikipedia on Cosmic string

2010.06.28 Monday ACHK

Some of the differences between the familiar Newtonian equation of gravity and the predictions of general relativity flow from the fact that gravity in general relativity bends both time and space, not just space. In normal circumstances, gravity bends time so slightly that the difference between Newtonian gravity and general relativity that results is so slight that it is impossible to detect without scientific instruments.

— Wikipedia on Anti de Sitter space

2010.06.26 Saturday ACHK

In physics, Gravitation is a very important reference book on Einstein’s theory of gravity by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. Often considered the “Bible” of General Relativity by researchers for its prominence, it is frequently called MTW after its authors’ initials, or “the Phone Book” due to its immense size. It was published by W.H. Freeman and Company in 1973. The book, a massive tome of over 1200 pages, covers many aspects of the General Theory of Relativity and also considers some extensions and experimental confirmation. The book is divided into two “tracks”, the second of which covers more advanced topics for more capable or determined students. MTW uses the -+++ metric convention. The book is famous/infamous for its use of boxes to add supplementary substance to the already thorough main text.

* Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973-09-15 1973), Gravitation, San Francisco: W. H. Freeman, ISBN 978-0-7167-0344-0

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— Wikipedia on Gravitation (book)

2010.06.25 Friday ACHK