Wednesday, August 26, 2015

Hawking on Black Hole Information Loss (Again)

At a conference in Stockholm, famed physicist Stephen Hawking explains how he thinks information is stored in black holes - it is stored as supertranslations of the black hole event horizons. (KTH Royal Institute of Technology) For more information see: arXiv:1401.7026 [hep-th]

Tuesday, June 30, 2015

Algebras at the very Foundations of Space and Time



















Excellent paper out today.  Revolutionary?  Maybe.

http://arxiv.org/abs/1506.08576
(Submitted on 29 Jun 2015)
While describing the results of our recent work on exceptional Lie and Jordan algebras, so tightly intertwined in their connection with elementary particles, we will try to stimulate a critical discussion on the nature of spacetime and indicate how these algebraic structures can inspire a new way of going beyond the current knowledge of fundamental physics.

Sunday, January 18, 2015

Shimura Varieties and Motives















Hermitian symmetric domains are complex manifolds isomorphic to bounded symmetric domains.  Every hermitian symmetric domain can be realized as a moduli space for Hodge structures plus tensors.  In general, hermitian symmetric domains are not algebraic varieties.  To obtain an algebraic variety one must pass to the quotient by an arithmetic group.  To obtain a moduli variety, one further assumes the arithmetic group is defined by congruence conditions.  The algebraic varities obtained this way are called connected Shimura varieties.

For all connected Shimura varieties except those of type E6, E7 and certain D types, the variety is a moduli variety for abelian motives with additional structure.  In the remaining cases, the connected Shimura variety is not a moduli variety for abelian motives and it is not know whether it is a moduli variety at all.

In supergravity applications, the hermitian symmetric domains of interest are E6/SO(10)xSO(2) and E7/E6xSO(2).  For real non-compact E6 and E7 quotients, such spaces are moduli for extremal black holes in D=5 and D=4 supergravity, with the real E6 and E7 groups acting as U-duality groups in compactified M-theory.  In the nonperturbative regime, due to charge quantization, it is quite natural to consider the quotients of the hermitian symmetric domains by an arithmetic group--which lives in a semisimple algebraic group over the rationals Q.

Further study of these exceptional Shimura varieties should lead to a deeper understanding of nonperturbative M-theory.

Saturday, January 03, 2015

Alain Connes: Geometry and the Quantum

 


The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. (17.12.2014)

Currently, Connes' approach is distinct from string theory; however, for some years the geometry of the worldvolume has been known to be described by C*-algebraic spectral triples.

See:

D-branes, Matrix Theory and K-homology
T. Asakawa, S. Sugimoto, S. Terashima

Hence, from an abstract perspective, Connes' approach is dual to the matrix model approach to M-theory.

Tuesday, December 23, 2014

Motivic Dreams


















To show that all L-functions associated to Shimura varieties - thus to any motive defined by a Shimura variety - can be expressed in terms of automorphic L-functions of is weaker, even very much weaker, than to show that all motivic L-functions are equal to such L-functions.  Moreover, although the stronger statement is expected to be valid, there is, so far as I know, no very compelling reason to expect that all motivic L-functions will be attached to Shimura varieties.  - R. Langlands