Caricatures of Big Bang from Matrices full report
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Caricatures of Big Bang from Matrices.ppt (Size: 1.12 MB / Downloads: 102) Caricatures of Big Bang from Matrices Presented By: Sumit R. Das University of Kentucky, Lexington Spacetime from Matrices A common slogan in string theory is that space and time are not fundamental, but derived concepts which emerge out of more fundamental structures. In a few cases we have some hint of what this structure could be â€œ these are situations where the spacetime physics has a holographic description â€œ usually in terms of a field theory of matrices. These are in fact description of closed string dynamics in terms of open strings Examples Closed String Theory Open String Theory 2 dimensional strings Matrix Quantum Mechanics M theory/ critical string SUSY Matrix Quantum in light cone gauge Mechanics/ 1+1 YM Strings in 3+1 dimensional N=4 YangMills These holographic descriptions have played a crucial role in our understanding of puzzling aspects of quantum gravitational physics, e.g. Black Holes Can we use these to address some puzzling questions in timedependent spacetimes â€œ in particular cosmologies where time appears to begin or end â€œ e.g. Big Bangs or Big crunches ? Can we ask what do we even mean when we say that time begins or ends ? In this talk I will discuss some recent attempts in this direction. 2d Closed String from Double scaled Matrix Quantum Mechanics  hermitian matrix. This is the degree of freedom of open strings joining D0 branes Gauging â€œ states are singlet under SU(N) Eigenvalues are fermions. Single particle hamiltonian Density of fermions To leading order in 1/N, the dynamics of the scalar field is given by the action This collective field theory would be in fact the field theory of closed strings in two dimensions â€œ the space dimension has emerged out of the matrix The fundamental quantum description is in terms of fermions Collective field theory used to find the emergent spacetime as seen by closed strings Ground State and fluctuations Filled fermi sea Collective field Fluctuations Two scalar fields for the two sides. The quadratic action for fluctuations Metric determined up to conformal factor There are actually two fields for the two branches of the fermi surface Space time structure is transparent in Minkowskian coordinates is independent of time Any other conformal frame will destroy this property A Timedependent solution S.R.D. and J. Karczmarek, PRD D71 (2005) 086006 An infinite symmetry of the theory generates time dependent solutions. One example The spacetime generated has a space like boundary Similarly a timereversed solution This is a geodesically incomplete spacetime. The spacelike boundary has regions of strong coupling Normally one would simply extend the spacetime to complete it However in this case there is a fundamental definition of time provided by the matrix model â€œ t The spacetime perceived by closed strings is an emergent description Lesson The open string time can go over the full range The closed string time can be terminated The underlying theory of open strings is still that of free fermions â€œ but there is no clear spacetime interpretation. Spacetime in Matrix String Theory for Type IIA By a standard chain of dualities, Type IIA string theory with a compact light cone direction with radius R and with momentum is equivalent to 1+1 dimensional SU(J) YangMills theory with on a spatial circle of radius Time dependent couplings Craps, Sethi and E.Verlinde : Matrix String Theory in a background with flat string frame metric, but a dilaton An alternative view Equivalently the YM theory can be thought to have a constant coupling, but living on the future wedge of the Milne universe PP Wave Big Bangs S.R.D. and J. MichelsonPhys.Rev.D72(2005)086005, S.R.D, J. Michelson,Â¦Â¦Â¦ to appear Motivation : to find a situation where there is some control of the precise nature of nonabelian excitations Possible for ppwave solutions with null linear dilatons For example in IIB theory IIB closed string on a 2torus with some momentum along one direction This is dual to a 2+1 dimensional YM theory on a 2torus Matrix membrane for usual ppwaves For timeindependent ppwaves (Q=0) and for weak IIB coupling (i) only diagonal Xâ„¢s survive (ii) The gauge field gets dualized into a scalar field â€œ so we have 8 scalars now (iii) The size of the direction is small â€œ effectively becomes a 1+1 dimensional theory (iv) This 1+1 dimensional theory becomes the worldsheet theory of the original IIB string moving in this background Fuzzy ellipsoids : semiclassical limit in which classical solutions important In this case the classical solutions are fuzzy ellipsoids formed by Myersâ„¢ effect with timedependent sizes Time evolution For generic initial conditions at the big bang the size of the fuzzy ellipsoids vanish at late times Similarly, very small fuzzy ellipsoids at late times grow large at early times The time dependence of is responsible for releasing nonabelian degrees of freedom near the big bang The time dependence in front of means that the masses of the Kaluza Klein modes in the direction is time dependent In terms of the original IIB theory these KK modes are D1 branes wrapped around Particle depletion This results in production or depletion of these KK modes with time For scalars, the is defined in terms of the modes The vacuum is defined in terms of the modes Correspondingly there are creation operators and which are not equivalent The nontrivial Bogoliubov relations imply that If the state at late time does not contain any of these modes, the state at early time contains lots of pairs of these particles in a squeezed state Big Bangs in AdS/CFT The time independent IIB ppwave has another holographic dual â€œ this is the large R charge sector of a 3+1 dimensional N=4 YM theory Can we extend this duality to our null dilaton ppwave ? This requires a deformation of geometry whose Penrose limit is this ppwave. We haveâ„¢nt found this yet If we succeed, we can pose interesting cosmological questions in this gauge theory. Conclusions In the toy models considered in this talk, what appears to be initial or final singularities from the point of view of closed string theory (and hence usual gravity) are not really singular in the holographic theory Rather in these regions the reduction of degrees of freedom which leads to an interpretation of the space of matrices as spacetime is not valid â€œ in some cases the full noncommutative nature of the theory becomes significant Mapping these problems into problems in gauge theory is likely to yield significant insight Use Search at http://topicideas.net/search.php wisely To Get Information About Project Topic and Seminar ideas with report/source code along pdf and ppt presenaion



