Stability of an oscillon un the SU (2) gauged Higgs model

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.Includes bibliographical references (leaf 35).Oscillons are localized solutions of nonlinear field theories that oscillate without dissipation. We have numerically found a family of very long-lived oscillons the spherical ansatz of the SU(2) gauged Higgs model -the standard model of the weak interactions without electromagnetism and fermions. In this thesis, we study the stability of these objects. We do this by adding a massless mode to the model and coupling it to the oscillating fields contained in the Higgs doublet. Such a mode is expected to provide a decaying mechanism for the oscillons. However, numerical investigation shows that our oscillons do not decay if the massless mode is sufficiently weakly coupled and suggests that our oscillons are stable long-lived solutions that could substantially influence the dynamics of this theory.by Ruza Markov.S.B

Static Charges in the Low-Energy Theory of the S-Duality Twist

We continue the study of the low-energy limit of N=4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N=6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and anti-quark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on a torus. Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.Comment: 73 pages, two paragraphs added, one to the introduction and one to the discussio

Dualities and Topological Field Theories from Twisted Geometries

I will present three studies of string theory on twisted geometries.In the first calculation included in this dissertation we use gauge/gravity dualityto study the Coulomb branch of an unusual type of nonlocal field theory, called PuffField Theory. On the gravity side, this theory is given in terms of D3-branes intype IIB string theory with a geometric twist. While the field theory description,available in the IR limit, is a deformation of Yang-Mills gauge theory by an orderseven operator which we here compute.In the rest of this disertation we explore N = 4 super Yang-Mills (SYM) theorycompactied on a circle with S-duality and R-symmetry twists that preserve N = 6supersymmetry in 2 + 1D. It was shown that abelian theory on a flat manifold givesChern-Simons theory in the low-energy limit and here we are interested in the non-abelian counterpart. To that end, we introduce external static supersymmetric quarkand anti-quark sources into the theory and calculate the Witten Index of the resultingHilbert space of ground states on a two-torus. Using these results we compute the ac-tion of simple Wilson loops on the Hilbert space of ground states without sources. Insome cases we find disagreement between our results for the Wilson loop eigenvaluesand previous conjectures about a connection with Chern-Simons theory.The last result discussed in this dissertation demonstrates a connection betweengravitational Chern-Simons theory and N = 4 four-dimensional SYM theory com-pactified on a circle twisted by S-duality where the remaining three-manifold is notflat starting with the explicit geometric realization of S-duality in terms of (2, 0)theory