✎ past_projects [Jesse Thaler]

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====== Beyond the Standard Model Reading Group ======

{{ research:decon.gif|Deconstructing Dimensions}}

//Summer 2003//

I participated in a reading group led by [[http://www.physics.harvard.edu/fac_staff/arkani_hamed.html|Nima Arkani-Hamed]] exploring three topics in [[http://v1.jthaler.net/btsm/|Beyond the Standard Model Physics]]:  Cosmology, Extra Dimensions, and Supersymmetry.

The Standard Model of particle physics is an incredible triumph for theoretical physics.  Within a mathematically consistent framework, it explains all known subatomic interactions up to the energy scales of current particle accelerators.  It provides excellent predictions about the composition of the universe immediately after the big bang.  It even "predicted" the existence of the top quark in 1995.

But at best, the Standard Model is incomplete.  Many of the parameters of the theory cannot be known a priori and must be extracted from experiment.  There is no explanation for the particle content of the universe.  The Higgs mechanism, which is invoked to explain the masses and interactions of the particles we see at low energy, is both the glue that holds the Standard Model together and a theoretical sore point.

Therefore, we strive to find extensions to the Standard Model that enrich the structure of the universe without contradicting the famously accurate correspondence between theory and experiment.  We look for novel models and interesting symmetries not so much because we believe that we can pluck the correct theory out of thin air, but because we know that whatever happens at the next generation of particle accelerators has to be different than what we already have seen.  We feel obligated to search the space of "all possible worlds" to find hints of what might explain this, our world.

In June, I presented an introduction to the supermultiplet formalism of Supersymmetry.  Supersymmetry is an extended space-time symmetry that links bosons and fermions.  Though we haven't yet observed the so-called superpartners of ordinary matter, we have not yet ruled out the possibility that at very high energies, these "sparticles" might emerge.  Supermultiplets are merely a convienent way to group these fermion/boson pairs, and if we put every Standard Model particle into their own multiplets, we generate the Minimal Supersymmetric Standard Model.

In July, I explored dimensional deconstruction.  In deconstruction, a theory that is well-behaved and four dimensional at high energies becomes a model of a compact fifth dimension at low energies.  This is to be contrasted with the usual view of extra dimensions where a theory which looks four dimensional at low energies "opens up" to extra dimensions at high energies.  Deconstruction is based on the simple model building tool of Mooses, and in my talk I elaborated on the simple connection between so-called linear Mooses and deconstruction.

An extension of dimensional deconstruction is gravitational deconstruction, where different gravitational spaces are linked together.  In order to understand gravitational deconstruction, I wanted to first understand gravity as a field theory, so at the end of July, I gave a talk on the structure of gravitational theories.  In particular, we saw that Einstein's theory of gravitation is (almost) the unique consistent theory of a spin-2 particle.  Also, we saw that something very strange happens when you try to make gravity massive.

In August, I worked with Can Kilic to understand gravitational deconstruction and the structure of theories of massive gravity.  The key paper we analyzed was by N. Arkani-Hamed, H. Georgi, and M. Schwartz. "Effective Field Theory for Massive Gravitons and Gravity in Theory Space." [[http://www.arXiv.org/abs/hep-th/0210184|hep-th/0210184]].

For information about this reading course, including a list of scheduled talks, [[http://v1.jthaler.net/btsm/|click here]].

====== Black Hole Formation ======

{{ research:blackhole.gif|Forming a BTZ Black Hole}}

//Spring 2002//

The dynamics of black hole formation is one of the unsolved problems of modern physics.  This owes to both the unsolvability of two-body problems in Einstein's theory of General Relativity and the quantum nature of certain black hole processes.  With [[http://www.physics.brown.edu/Users/faculty/jevicki/jevicki.htm|Antal Jevicki]], I examined an exactly solvable model of black hole formation in 2 + 1 dimensions in order to predict qualitative features of black hole formation in higher dimensional spaces.

In particular, we found no exponential supression or enhancement of the process.  This is different from the result predicted by models that assume a test particle falling in an effective black hole background.  We believe the reason for the difference is that the total energy of the system is the mass of the created black hole, so models that assume a small mass test particle ignore the fact that the test mass kinetic energy must contribute to the mass of the black hole.  This changes the diverege of the momentum near the effective horizon from a linear to a logarithmic diverges, so the classical action is finite as opposed to infinite, therefore the semi-classical transition amplitude does not have an exponential suppression.

I was an [[http://www.aps.org/praw/apker/index.html|APS Apker Award]] finalist for this research.

  * **Dynamics of black hole formation in an exactly solvable model**.\\ Antal Jevicki and Jesse Thaler.\\  [[http://link.aps.org/abstract/PRD/v66/e024041|Phys. Rev. D66 024041]], [[http://www.arXiv.org/abs/hep-th/0203172|hep-th/0203172]].

====== Matrix Models & Group Theory ======

{{ research:twentyfive.gif|25 Element Group?}}

//Summer 2001//

During the summer of 2001, I worked with [[http://www.physics.brown.edu/Users/faculty/jevicki/jevicki.htm|Prof. Antal Jevicki]] on Matrix Models.  In particular, Group Theory and Lie Algebra is necessary to develop the language of Symmetry that seems to be essential for a description of the fundamental microscopic structure of the universe.

For most of the summer, I learned about the fundamentals of Group Theory and Lie Alegbra.  I gave three presentations as part of my study: the first covered classical and quantum mechanics on the //SU(2)// symmetry group; the second covered the characters and representations of //SU(N)// with a followup presentation on the equivalence between the characters of a group and the eigenstates of the group Hamiltonian; and the third covered the relationship between Matrix Models and Integrable Systems (i.e. systems with a conserved quantity for each degree of freedom).  

Then, I studied the relationship between Matrix Models and Supersymmetry.  Roughly speaking, supersymmetric systems are systems that are invariant under an exchange of bosons (force carriers) and fermions (matter particles).  The structure of supersymmetric systems is closely connected to a study of Clifford Algebras, and these algebras impose limits on the kinds of systems that can exhibit supersymmetry. 

This work was sponsored by an [[http://www.brown.edu/Administration/Dean_of_the_College/utra/|Undergraduate Teaching and Research Assistantship]] (UTRA) at Brown University.